A 98-qubit trapped-ion quantum computer with all-to-all connectivity

Article

Open access

Published: 17 June 2026

Anthony Ransford

ORCID: orcid.org/0009-0007-9497-56671,

M. S. Allman1,

Jake Arkinstall2,

J. P. Campora III1,

Samuel F. Cooper1,

Robert D. Delaney1,

Joan M. Dreiling1,

Brian Estey1,

Caroline Figgatt1,

Alex Hall1,

Ali A. Husain3,

Akhil Isanaka1,

Colin J. Kennedy1,

Nikhil Kotibhaskar4,

Ivaylo S. Madjarov1,

Karl Mayer1,

Alistair R. Milne4,

Annie J. Park1,

Adam P. Reed1,

Riley Ancona1,

Molly P. Andersen5,

Pablo Andres-Martinez2,

Will Angenent2,

Liz Argueta1,

Benjamin Arkin1,

Leonardo Ascarrunz1,

William Baker1,

Corey Barnes1,

John Bartolotta1,

Jordan Berg1,

Ryan Besand1,

Bryce Bjork1,

Matt Blain5,

Paul Blanchard1,

Robin Blume-Kohout6,

Matt Bohn1,

Agustíin Borgna2,

Daniel Y. Botamanenko1,

Robert Boutelle1,

Natalie Brown1,

Grant T. Buckingham1,

Nathaniel Q. Burdick3,

William Cody Burton1,

Varis Carey1,

Christopher J. Carron5,

Joe Chambers1,

Jia Wen Chan1,

John Children2,

Victor E. Colussi1,

Steven Crepinsek1,

Andrew Cureton1,

Joe Davies5,

Daniel Davis1,

Matthew DeCross1,

David Deen3,

Conor Delaney1,

Davide DelVento1,

B. J. DeSalvo1,

Jason Dominy1,

Sydney Drotar1,

Ross Duncan7,

Vanya Eccles2,

Alec Edgington2,

Neal Erickson1,

Stephen Erickson1,

Christopher T. Ertsgaard5,

Jay Esposito5,

Bruce Evans1,

Tyler Evans1,

Maya I. Fabrikant1,

Andrew Fischer1,

Cameron Foltz1,

Michael Foss-Feig1,

David Francois1,

Brad Freyberg1,

Charles Gao1,

Robert Garay1,

Jane Garvin1,

David M. Gaudiosi1,

Christopher N. Gilbreth1,

Josh Giles1,

Erin Glynn1,

Jeff Graves1,

Azure Hansen1,

David Hayes1,

Lukas Heidemann2,

Bob Higashi5,

Tyler Hilbun1,

Jordan Hines6,

Ariana Hlavaty2,

Kyle Hoffman1,

Ian M. Hoffman1,

Craig Holliman7,

Isobel Hooper2,

Bob Horning5,

James Hostetter3,

Daniel Hothem8,

Jack Houlton1,

Jared Hout1,

Ross Hutson1,

Ryan T. Jacobs1,

Trent Jacobs1,

Melf Johannsen2,

Jacob Johansen1,

Loren Jones1,

Sydney Julian1,

Ryan Jung5,

Aidan Keay2,

Todd Klein5,

Mark Koch2,

Ryo Kondo1,

Chang Kong1,

Asa Kosto1,

Alan Lawrence2,

David Liefer1,

Michelle Lollie1,

Dominic Lucchetti1,

Nathan K. Lysne7,

Christian Lytle1,

Callum MacPherson2,

Andrew Malm1,

Spencer Mather1,

Brian Mathewson1,

Daniel Maxwell3,

Lauren McCaffrey1,

Hannah McDougall1,

Robin Mendoza1,

David B. Miller1,

Michael Mills1,

Richard Morrison2,

Louis Narmour1,

Nhung Nguyen1,

Lora Nugent1,

Scott Olson5,

Daniel Ouellette5,

Jeremy Parks1,

Zach Peters1,

Timothy A. Peterson3,

Jessie Petricka1,

Juan M. Pino1,

Frank Polito1,

Andrew C. Potter1,

Matthias Preidl5,

Gabriel Price1,

Timothy Proctor8,

McKinley Pugh1,

Noah Ratcliff1,

Daisy Raymondson1,

Peter Rhodes1,

Conrad Roman1,

Craig Roy2,

Ciaran Ryan-Anderson1,

Fernando Betanzo Sanchez2,

George Sangiolo2,

Tatiana Sawadski2,

Andrew Schaffer3,

Peter Schow1,

Jon Sedlacek3,

Henry Semenenko2,

Peter Shevchuk1,

Susan Shore5,

Peter Siegfried1,

Kartik Singhal1,

Seyon Sivarajah2,

Thomas Skripka1,

Lucas Sletten3,

Ben Spaun1,

R. Tucker Sprenkle1,

Paul Stoufer1,

Mariel Tader1,

Stephen F. Taylor3,

Travis H. Thompson2,

Raanan Tobey1,

Anh Tran1,

Tam Tran1,

Grahame Vittorini3,

Curtis Volin3,

Jim Walker1,

Sam White2,

Garrett R. Williams3,

Douglas Wilson2,

Quinn Wolf1,

Chester Wringe2,

Kevin Young8,

Jian Zheng1,

Kristen Zuraski1,

Charles H. Baldwin1,

Alex Chernoguzov1,

John P. Gaebler1,

Steven J. Sanders1,

Brian Neyenhuis1,

Russell Stutz1 &

…

Justin G. Bohnet

ORCID: orcid.org/0000-0002-2228-402X1

Nature

(2026) Cite this article

Abstract

Quantum computers require both high-fidelity operations and large qubit numbers to surpass classical capabilities1. Trapped-ion platforms have demonstrated the highest gate fidelities of any modality2,3,4,5,6 but scaling to larger qubit numbers while preserving performance has remained a central challenge. We report on Quantinuum Helios, a 98-qubit trapped-ion quantum processor based on the quantum charge-coupled device (QCCD) architecture7. Helios features 137Ba+ hyperfine qubits8,9, all-to-all connectivity enabled by a rotatable ion storage ring connecting two quantum operation regions by a junction10,11, speed improvements from parallelized operations12 and a new software stack with real-time compilation of dynamic programs13. Averaged over all operational zones in the system, we achieve average infidelities of 2.5(1) × 10−5 for single-qubit (1Q) gates, 7.9(2) × 10−4 for two-qubit (2Q) gates and 3.3(5) × 10−4 for state preparation and measurement (SPAM), none of which are fundamentally limited and probably able to be improved. These component infidelities are predictive of system-level performance in both random Clifford circuits and random circuit sampling (RCS), the latter demonstrating that Helios operates well beyond the reach of classical simulation and establishes a new frontier of fidelity and complexity for quantum computers14.

Main

As several quantum processing units (QPUs) demonstrate key milestones on the path to utility, including experimental evidence of quantum supremacy14,15,16 and the feasibility of fault tolerance17,18, the focus of progress is shifting to making use of the unique advantages of each architecture to scale to much larger sizes without affecting performance. Like all modalities, the trapped-ion QPU based on the QCCD architecture7,19,20,21,22,23 has its unique set of challenges and advantages in scaling. For example, trapped ions can require complex optical systems for implementing quantum operations. However, mobile qubit architectures, such as QCCD and optical tweezers24,25, can distribute resources more efficiently than stationary qubit architectures26,27,28, because qubits flow through the QPU like bits in a classical processor, with separated memory structures, data buses and logic units, each optimized for their purpose12. Here we present Quantinuum Helios, a 98-qubit trapped-ion QCCD quantum processor with three key advances from earlier Quantinuum QPUs21,22. First, Helios uses barium ions as the qubits8, achieving 99.92% two-qubit gate fidelity with a more scalable laser architecture. Second, Helios uses a four-way ‘X’ junction10,11,29,30,31,32,33,34,35 to connect memory regions to quantum logic regions without increasing electrical control or device fabrication complexity. Third, Helios is orchestrated by a new classical control implementation capable of executing truly arbitrary quantum programs with all-to-all connectivity and complex control flow logic. The cumulative impact of these advances enable us to scale the system size, from six qubits in the first QCCD quantum computer demonstrated five years ago21 to now 98 qubits, while setting a new state-of-the-art performance across all metrics, confirmed here by system benchmarks, including RCS, and seen in associated applications run on Helios in materials science and cryptography36,37,38.

Hardware and software architecture

QPU architecture and ion trap design

Helios is a transport-based quantum processor with spatially separated qubit memory regions and quantum logic regions. These elements are realized on a 2D surface electrode QCCD21,39, which confines ions with electric fields generated by a pattern of electrodes (Figs. 1 and 2), and the QPU uses individual ions for qubits. To apply gates to qubits or pairs of qubits, the ions are physically transported to isolated trapping zones to facilitate low-crosstalk addressing and maintain high fidelity.

Figure 2 illustrates how Helios operates. The quantum logic region processes batches of up to 16 qubits at a time, using eight high-fidelity operation zones, each with the capability to perform state preparation, measurement, ground-state laser cooling and quantum logic gates. Each operation is implemented by means of focused laser beams propagating about 65 μm above and parallel to the chip surface, as shown in Fig. 2e. High-fidelity quantum logic operations necessitate low noise, independent electrode voltages and several laser beams for each zone, consuming most of the control resources in the processor. By using shared lasers across several operation zones (Fig. 2e), the quantum logic region design scales these essential components more efficiently than previous systems.

Qubits outside the operation zones are stored in functionally distinct memory regions: ring storage, leg storage and cache (Fig. 2b). Memory regions require fewer control resources as the only operations available are sympathetic laser cooling40 and qubit transport. To minimize the number of transport control signals, segmented DC electrodes in the memory regions use voltages that are broadcast in a repeating triplet pattern similar to in ref. 22. The cache is a small memory region that holds the next batch of pre-sorted qubits before going to the quantum logic region. The leg storage operates as a first in last out memory, whereas the ring storage acts as a random access memory, connecting to the operational region by means of an X-junction.

The junction is a key structure enabling this architecture. As qubits move through the junction, they can be routed to remain in memory or be added to the cache in either the upper or the lower legs. Furthermore, by implementing qubit routing in a separate structure from the quantum logic region, qubit sorting can proceed in parallel with the ground-state cooling of ions in the logic region, increasing the effective clock speed of the QPU. Comparisons with the Quantinuum H1 (ref. 21) and Quantinuum H2 (ref. 22) QPUs summarize the cumulative impact of these design choices in the electrical control subsystems (Table 1).

Ion species: qubit and coolant

Helios is the first programmable quantum computer we are aware of to use 137Ba+. We define |F = 1, mf = 0⟩ and |F = 2, mf = 0⟩ hyperfine levels in the 137Ba+ electronic ground state as |0⟩ and |1⟩, respectively. The optical transitions used to implement quantum operations are in the visible part of the wavelength spectrum, allowing for laser and optical components that are more mature, reliable and cost-effective and enables fundamentally better performance. Using more available laser power with better phase performance, we can suppress several of the leading sources of errors in logic gates, including spontaneous emission errors and laser phase fluctuations.

QCCD operation

In this section, we describe how Helios executes quantum programs using the operations depicted in Fig. 2. An arbitrary quantum program is decomposed into ion transport and quantum operations. These operations are not pre-planned but instead executed with a new real-time and dynamic classical control software called ‘Helios runtime’, which is described in detail in Methods.

Ions move through the trap using transport operations from four categories: shift, split/combine, junction transport and rotate. Shift operations translate ions along linear sections in the cache, quantum logic and leg storage regions. These operations can move both two-ion Ba–Yb (BY) and four-ion Ba–Yb–Yb–Ba (BYYB) crystals. Split (combine) operations separate (merge) BYYB (BY and YB) crystals in the eight operation zones. Junction exit (enter) operations move crystals from (into) the junction into (from) the desired leg in the cache with the desired order, BY or YB. Rotate operations collectively move crystals in the ring clockwise or anticlockwise.

Programs use these transport operations to move qubits between the memory and processor regions of the trap. This cycle occurs during a single layer in a program, in which qubits are removed from ring storage, processed in batches within the quantum logic region and then returned to ring storage. Every program begins with qubits in a default configuration: eight BYYB crystals in the quantum logic region and 82 BY crystals in ring storage. Each layer contains up to seven batches, with a maximum of 16 qubits per batch.

Using appropriate ion-to-qubit assignments, quantum operations immediately begin on the qubits already in the eight operation zones, with individual addressing operations occurring first: state preparation (or reset), 1Q gates and measure operations. Next, if 2Q gates are required, the BY and YB pairs associated with each zone are combined into BYYB crystals and ground-state cooling begins. In parallel with cooling, qubits for the next batch of gating are moved from ring storage to the cache. This parallel sorting with ground-state cooling allows cooling and gating cycles to run nearly continuously, as the next batch of qubits is ready to shift in as the current batch finishes operations.

Unlike 1Q, reset and measure operations, 2Q operations are executed in only four of the eight quantum logic zones (second and fourth zones on the top and bottom legs as shown in green in Fig. 2b,e). To perform 2Q gates on all 8-qubit pairs, the qubits are first merged and cooled as eight four-ion crystals in all operation zones and then 2Q beams are applied in the four 2Q operation zones. Immediately after executing the 2Q gates, the four-ion shift operation moves all crystals over by one zone (the crystals in the right edge operational zones are split into BY and YB pairs and then shifted into the storage legs). We then apply a small (approximately 300 μs) extra amount of cooling to remove any energy gained from the shift operation and then gate the remaining four crystals. The 2Q gate operation itself requires approximately 70 μs to execute.

After executing quantum operations, a batch is complete: its qubits move to leg storage, whereas qubits in the cache shift to the quantum logic region. This process repeats until all qubits requiring operations have been processed. Last, all qubits move from leg storage to the ring and the cycle begins for the next layer.

Figure 3a shows timing estimates and a breakdown of operations per layer for a representative program on Helios. The program is constructed as a sequence of ten layers, in which qubits are randomly paired and receive 1Q and 2Q gates each layer. We define the ‘depth-1 time’ as the time required to perform the random pairing and 1Q and 2Q gates in a single layer and use this time as our characteristic figure of merit for processor speed. We estimate the average depth-1 time by measuring the duration of the depth-10 program and dividing it by the number of layers to average any fortunate sort cases, resulting in an average of 55 ms per layer. To illustrate how program details such as 2Q gate density and qubit connectivity affect depth-1 time, we present timing results in Fig. 3b for three example programs as a function of the number of active qubits (Supplementary Information).

Real-time compilation of sorting and gates

To realize the full capability of the Helios QPU, the system must be capable of executing arbitrary quantum programs efficiently, including dynamic quantum programs. Optimal decision-making for dynamic quantum programs requires a new classical control hardware unit and software compilation stack. This new stack both allows for real-time qubit routing decisions and increases the level of abstraction of quantum programs—mirroring the way classical computers advanced from writing assembly code to writing high-level programs.

In particular, Helios is the first trapped-ion QPU to translate operations on a program’s ‘virtual qubits’ (user program qubit variables whose physical qubit assignment depends on the structure of the program)41 into operations on corresponding physical qubits on the device in real time—that is, while the program is executing and quantum state is live. This is enabled by the Helios runtime, whose responsibility is to efficiently map virtual qubits to physical qubits on the device and turn declarative gates on virtual qubits into operations on physical qubits. This runtime enables state-of-the-art user programming constructs for use on a quantum computer (functions that can allocate and de-allocate qubits depending on the control flow of the program), early termination of programs based on mid-circuit measurement or arbitrary classical logic and classical control flow such as if-then-else statements, for loops and while loops. This is by strong contrast to the way most gate-level quantum programs, commonly referred to as ‘dynamic circuits’42, are written right now—as a flat series of gates with certain gates conditioned on measurements.

The core responsibilities of the Helios runtime are as follows: (1) receive qubit allocation requests on virtual qubits and resolve them to physical qubits; (2) receive gating requests on allocated virtual qubits; (3) transform requested gates on sets of virtual qubits into parallel operations on as many physical qubits as can fit in the quantum operation zones; and (4) transport batches of physical qubits from the ring into these zones, referred to as a ‘sort’. For details on how the Helios runtime performs these responsibilities, see Methods.

Benchmarking

To see how Helios performs in practice, we characterize individual operations with component-level benchmarks and measure full-device operations with system-level benchmarks22. Individual operations include SPAM, 1Q and 2Q gates and mid-circuit measurements and resets (MCMRs). We perform two separate system-level benchmarking experiments43,44,45,46,47,48, both of which are examples of volumetric benchmarks44. The first involves random Clifford circuits with MCMR, which can be simulated classically and are similar in structure to the quantum instrument randomized benchmarking (RB) circuits in ref. 49. We include MCMRs because they are necessary for quantum error correction. The second involves mirror benchmarking of random quantum circuits, which assesses the ability of Helios to perform RCS. This benchmark quantifies the fidelity with which Helios can run circuits of a fixed (and well understood) classical simulation complexity.

A summary of benchmarking results is shown in Fig. 4, with further details and results given in Methods and the Supplementary Information. The magnitude of errors in the most common individual operations, SPAM, 1Q and 2Q gates and MCMR, are shown in Fig. 4a,b. 1Q and 2Q gate errors are measured with Clifford RB50, SPAM errors are measured with repeated SPAM and MCMR crosstalk is measured with a state decay test51. Furthermore, transport operations induce small memory errors owing to magnetic field spatiotemporal inhomogeneities. The magnitudes of these errors are measured as a function of time with a variant of interleaved RB22,52 and shown in Fig. 4c. The stochastic Pauli error components of the 2Q gate are measured with cycle benchmarking (CB)53 and plotted in Fig. 4d. A summary of all component errors measured and averaged over all locations is given in Fig. 4i.

The random Clifford circuits benchmark is a slight variation from ref. 49 and run with N = 98 qubit circuits with a variable number of layers. Each layer contains an independent random 1Q Clifford unitary on every qubit, followed by a maximally entangling 2Q gate on N/2 uniformly random pairs of qubits, followed by a fixed number of MCMR operations performed on a uniformly random subset of qubits. We use stabilizer tracking to perform all measurements, both mid-circuit and final, in a Pauli basis such that the outcome ideally has a deterministic parity (Methods). We measure the average circuit success probability as a function of both the number of layers and the number of MCMR operations per layer. We fit the results to a decay model to estimate an effective 2Q gate error and an effective MCMR error. The effective 2Q (MCMR) errors are the magnitudes of simple depolarizing (bit-flip) channels that would best fit the data in the absence of all other errors. The data are shown in Fig. 4e,f, with further details in the Supplementary Information.

The mirror benchmarking of the random circuits benchmark procedure follows exactly the description in ref. 14. The results of mirror benchmarking on random quantum circuits are shown in Fig. 4g. The fidelity reported at each depth gives an accurate estimate of the fidelity achievable by running (unmirrored) random circuits at that depth. Figure 4h shows the expected classical per-sample cost to simulate RCS at various circuit depths using optimized tensor network contraction (and under various assumptions on available memory). Costs are reported both in years of exascale compute time and in power requirements to classically sample at the same rate that Helios can (assuming state-of-the-art GPU power consumption of 1011 FLOPS W−1). Further details on the circuits used, estimation of fidelity from mirror benchmarking and assumptions involved in the reported classical simulation costs can be found in Methods.

Outlook

In this manuscript, we reported on how Helios operates and its current performance. Even at this early stage in its life cycle, Helios exhibits state-of-the-art capabilities at the scale of roughly 100 qubits. Like its predecessors Quantinuum H1 and H2, we expect the performance of Helios to improve over time. Examples of relatively straightforward performance improvements include: (1) fewer gate errors, as our two-qubit gate error model suggests that the 2Q gate error could be cut in half; (2) smaller memory errors using dynamic decoupling strategies54; and (3) reduced circuit times from both faster transport operations55,56,57 and better compilation methods.

Beyond these performance improvements, increasing clock speed is one scaling challenge for the QCCD platform. In this work, we begin to address this issue through a fundamental architectural shift by parallelizing operations12. Previous generations, H1 and H2, used the same space for ground-state cooling and gating operations, with cooling operations being up to two orders of magnitude slower21,22. Helios, on the other hand, spreads the cooling operation over space to allow ions to spend less time in the zones used for 2Q gates. By increasing the ratio of cooling zones to gate zones, future QCCD-based QPUs can optimize the processor zone complexity while simultaneously increasing the clock speed.

Although we do not yet fully understand the power or limitations of Helios, the combination of a new qubit choice, device architecture and control software runtime already represents substantial progress in the push for more powerful devices, scalable architectures and capabilities for fault-tolerant computation. Helios is far beyond the simulation abilities of classical computers, as evidenced by the RCS demonstration described above, and well poised to expand the set of tasks best suited for contemporary quantum computers. Indeed, as reported in refs. 36,37,38, Helios is already enabling advancements in quantum simulations of superconductivity and in cryptographic protocols to generate certified randomness.

Looking further ahead, the successful integration of the four-way junction29 paves the way for much larger QCCD processors. Junction-based architectures should allow QCCD machines to maintain all-to-all connectivity for large numbers of qubits, opening the design space for fault tolerance to high-efficiency encodings58, transversal logic59,60, low-overhead magic state factories61 and single-shot error correction62,63,64,65,66,67,68,69,70,71,72,73,74,75,76.

Methods

Quantum operations

The 1Q and 2Q gates are implemented with pairs of 515-nm laser beams separated by the approximately 8.04 GHz qubit frequency splitting. The 1Q gates, \({U}_{1{\rm{Q}}}(\theta ,\phi )={{\rm{e}}}^{(-{\rm{i}}\theta /2)(\cos \phi X+\sin \phi Y)}\), are implemented with co-propagating laser beams for improved phase stability of the Raman interaction and minimal sensitivity to the thermal motion of the ions. 1Q Z-rotations, RZ(θ) = e−iZθ/2, are implemented by phase changes in software tracking and applied to the next 1Q gate scheduled. The 2Q gates are implemented with beams intersecting the quantum logic zones at 90° to each other such that the difference k-vector is parallel to the crystal axis (Fig. 2e). The 2Q gate protocol is based on the Mølmer–Sørensen interaction using wrapper pulses to remove optical phase sensitivity21,77, yielding a native 2Q gate RZZ(θ) = e−iZZθ/2. The gate angle θ is specified by the user and is varied by adjusting the detuning and duration of the gate. Gate infidelities have been shown to improve for smaller angles22 but here we only benchmark the perfect entangler RZZ(π/2).

SPAM is achieved in 137Ba+ with a combination of lasers at 493 nm, 614 nm, 650 nm and 1,762 nm, with preparation accomplished by means of narrow-band optical pumping9,78. The 1,762-nm laser is locked to a narrow linewidth cavity to facilitate high-fidelity mapping pulses between the S1/2 ground state and the D5/2 state (Extended Data Fig. 1). The standard measurement protocol first maps the |F = 1, mf = 0⟩ qubit state to the D5/2 manifold with several π pulses to different levels in D5/2. Then the 493-nm and 650-nm lasers are turned on to induce fluorescence from all S1/2 states. Furthermore, the 1,762-nm laser is used to protect neighbouring qubits from measurement crosstalk errors (Extended Data Fig. 1b) and enables a ternary (three-outcome) measurement to detect leakage population (Extended Data Fig. 1c) without the use of ancillas or 2Q gates79,80,81.

The QCCD architecture relies on mid-circuit recooling of ions, achieved here with sympathetic cooling applied to 171Yb+ ions co-trapped with the 137Ba+ qubit ions. The 171Yb+ ion is chosen because of its similar mass to 137Ba+ and for the established and straightforward methods for qubit control and state measurement82. The cooling is performed with lasers tuned near the S1/2 to P1/2 transition of 171Yb+ at 369 nm.

To load ions into the QCCD, we photoionize both species from cold atomic beams produced by an atomic source similar to ref. 22, based on a neutral atom magneto-optical trap83,84. Other hardware details, including implementation of all quantum operations, are described in the Supplementary Information.

The Helios runtime software

Many of the Guppy13 programs for the applications discussed in the ‘Benchmarking’ use the features outlined in the section ‘Real-time compilation of sorting and gates’. Moreover, quantum error correction programs can use dynamic allocation and de-allocation of virtual ancilla qubits without worrying about physical qubit mappings of the ancilla qubits or the precise control flow of the quantum error correction program. Furthermore, any programming language compiling to QIR85, such as Q#86, Qiskit87, OpenQASM 2.0/3.0 (refs. 88,89), Cirq90 and CUDA-Q91, can use QIR adaptive profile features to implement these control flow constructs for programs executing on Helios.

An example of high-level operations enabled by the Helios runtime is the ‘gate streaming’ used in ref. 37. In the Guppy program executed on Helios for this work, a section of the program performs a remote procedure call out to a classical server that is separate from the control system but which is allowed to communicate with the control system through a networking interface92. The information transmitted to the control system by the classical server is the measurement basis for each qubit. If a qubit needs no change in measurement basis, then the runtime receives no 1Q gate to apply before measurement. In the case that a whole row of BY or YB crystals on the top or bottom legs needs no basis change, the Helios runtime will not perform any extraneous transport to address these qubits. Notably, this reduces the overall shot time, improving the critical latency times in that application. Efficient gate streaming would be impossible without the real-time identification of qubits provided by the runtime.

As mentioned in the section ‘Real-time compilation of sorting and gates’, the Helios runtime has four main responsibilities to perform for programs executing on Helios. Responsibility (1) is performed using a model of the physical QPU state as the program runs and determining efficient mappings from virtual qubits to physical qubits. Regardless of the state of the trap when a qubit allocation request is made, a simple algorithm identifies the qubit closest to the quantum operation zone. If an unallocated qubit is in the quantum operation zone, then it is used. Otherwise, a qubit in the storage ring that is unallocated and closest to the junction is allocated. If no allocatable qubits are in the storage ring or quantum operation zone, then all qubits are ‘flushed’ back into the storage ring and then an unallocated qubit closest to the junction is allocated.

Responsibilities (2) and (3) are performed by identifying which quantum logic operations can be done in parallel by storing them in sets contained in a data structure we refer to as a ‘slice’. Sequences of slices are accumulated into another data structure that drives the sorting of each slice to execute the quantum logic operations within. Responsibility (4) is performed by carrying out an O(n) traversal over the ring storage to determine which two pairs in a slice have qubits closest to the cache. The runtime then assigns one pair to move to the top leg and the other to the bottom. Subsequently, the algorithm determines the smallest number of rotations needed to move the two pairs into BYYB crystals in both legs. This process is visualized in Fig. 2. This process repeats until either enough pairs are moved into the cache to fill a batch or no more pairs need to be sorted. Finally, the runtime dispatches the calculated sort by generating these operations as a queue of commands to lower-level control system software for performing transport operations and parallelized cooling, as outlined in the section ‘QCCD operation’. After all of the quantum logic operations have been executed in a given slice through repetitions of this sort, transport is generated to return the qubits back into the ring storage—and the sorting algorithm repeats for subsequent slices. For unconditional programs with no changes in program execution depending on mid-program measurement results, these responsibilities are calculated ‘ahead’ of the physical execution of the operations on the quantum processor and thus add no extra overhead to the time needed to run a program. However, when mid-program measurements are used to determine future quantum operations, submillisecond-scale latency can be added to calculate the above responsibilities for the next round future quantum operations while the qubit state is still live. The transport time savings can be on the several-millisecond timescale for sorting a single batch of qubits more efficiently based on feed-forward quantum operations and much larger quantities of time can be saved for programs with early-exit conditions.

Component-level benchmarks

SPAM

It is difficult to differentiate state preparation errors from measurement errors93, although from detailed modelling of 137Ba+ qubits, we expect state preparation errors to be the largest contributor9.

We measure SPAM errors by preparing 16 qubits in the eight operation zones in the |0⟩ or |1⟩ states and measuring each qubit. For any given shot, the state preparations are randomized among the different qubits, but we ensure that each qubit is prepared in each state for the same total number of shots. We run two experiments: standard measurement that ideally differentiates |0⟩ from |1⟩ but falsely returns |1⟩ in the event that the qubit has leaked and a ternary measurement, shown in Extended Data Fig. 1c, that ideally differentiates |0⟩, |1⟩ and leaked states. For both experiments, we take 4,000 shots per state preparation.

For the standard measurement, we measure errors of 5.2(9) × 10−4 and 1.4(5) × 10−4 when preparing |0⟩ and |1⟩, respectively. Because this measurement protocol mistakenly detects leaked states as |1⟩, the reported error for preparing and measuring |1⟩ will not catch all errors9. For the ternary measurement, we find an average leakage probability of 8(3) × 10−4 and, in the event of non-leakage, we measure SPAM errors of 1.0(1) × 10−3 and 1.3(1) × 10−3 for |0⟩ and |1⟩, respectively. Although the ternary measurement reveals more information as it can detect leakage, it also has a larger SPAM error owing to a larger number of shelving pulses involved. The SPAM errors reported in Fig. 4a,b,i are averaged between the two state preparations. We actively make a trade-off between SPAM fidelity and MCMR crosstalk by reducing laser powers and detection times. SPAM is performed much less frequently than gating, leading to a lower relevant importance in the circuit despite being a large error in Fig. 4a,b,i.

1Q gates

1Q gate errors are mainly caused by spontaneous emission during the Raman gate, laser phase and intensity noise and finite qubit coherence. Notably, spontaneous emission causes leakage outside the computational subspace. We quantify 1Q gate errors by Clifford RB50 (Supplementary Information).

We follow the methods in ref. 94 to account for leakage in the 1Q infidelity estimate. The ternary measurement allows us to measure the leakage population at the end of every circuit without the use of ancilla qubits (as done in ref. 22). We estimate the rate of leakage per 1Q Clifford rL by the rate at which the measured leakage population increases with sequence length. The probability of observing the expected computational state decays exponentially owing to non-leakage errors as p(l) = A(1 − r)l + 1/2 for sequence length l, in which A and r are fit parameters. The reported 1Q error is the Clifford average infidelity ϵavg,1Q = r/2 + r (ref. 94).

Extended Data Fig. 2 shows the success probability and the leaked population as a function of l, for all 16 qubits in the eight operation zones. We obtain a zone-averaged 1Q error of 2.5(1) × 10−5, which includes a leakage rate of 1.12(6) × 10−5. The error bars represent a one-sigma confidence interval obtained from bootstrapping95. The leakage rates and infidelities for each individual qubit are given in the Supplementary Information. The measured errors can be compared with our predictions from physical error models of 2.6(6) × 10−5 that account for measured laser intensity noise, calculated spontaneous emission and measured memory error.

Finally, we ran a statistical hypothesis test for correlated errors in the simultaneous 1QRB data. An error channel on several subsystems is correlated if it cannot be factored into a tensor product of individual error channels on each subsystem, and such correlated errors are a signature of crosstalk. We found no evidence of correlated errors at the 95% confidence level (Supplementary Information).

2Q gates

Errors in the RZZ(θ) gates are caused by spontaneous emission from the Raman lasers and experimental imperfections including laser phase and intensity noise at the position of the ion, thermal motion of the ions, voltage noise on the electrodes and imprecise calibrations of the gate parameters. We validate the performance of the maximally entangling RZZ(π/2) gate (referred to as the 2Q gate) using both Clifford 2QRB and CB. Further details of each implementation are in the Supplementary Information.

We again follow the methods in ref. 94 to account for leakage in the 2QRB infidelity estimate. The leaked population versus sequence length is used to extract a leakage rate per Clifford, which is rescaled into a leakage rate per 2Q gate rL,2Q, using the fact that there are 1.5 2Q gates per 2Q Clifford on average. We fit the success probability of the remaining population to the decay model p(l) = A(1 − r)l + 1/4, for sequence length l, in which A and r are fit parameters. The average infidelity of the non-leakage error component per Clifford is given by 3r/4, which is rescaled into an average infidelity per 2Q gate of r/2. The average infidelity per 2Q gate (including leakage) is then computed as ϵavg,2Q = r/2 + rL,2Q. We note that our rescaling of the error per Clifford into an error per 2Q neglects the errors from 1Q gates and memory errors during the 2QRB sequence, which we estimate to contribute 1.2(2) × 10−4 per 2Q gate.

The experimental 2QRB data are shown in Extended Data Fig. 3. We obtain a zone-averaged 2Q infidelity of ϵavg,2Q = 7.9(2) × 10−4, which includes a leakage rate of rL,2Q = 2.4(1) × 10−4. The leakage rates and infidelities for each individual qubit pair are given in the Supplementary Information. The leakage errors arise from both spontaneous emission error, which we measure to be 1.0(2) × 10−4 in agreement with the model in ref. 96, and from the leakage memory error (discussed in the section ‘Memory errors’). In total, we expect leakage to contribute 1.7(2) × 10−4 of the error.

Our measured value of 7.9(2) × 10−4 can be compared with a total expected error per 2Q gate of 3.5(4) × 10−4, which we predict from an error budget consisting of spontaneous emission errors, memory error and 1Q pulse errors plus other characterized experimental sources of noise, such as laser phase and intensity noise, thermal motion of the ions and imprecise calibrations. The discrepancy of the measured 2Q error with predicted value could be explained by several factors, including higher leakage error in the operational zones owing to finite extinction of the resonant detection beams present, non-thermal motional distributions, crosstalk or other unaccounted for effects.

Just as with the 1QRB data, we performed a statistical test for the presence of correlated errors in the 2QRB data and found no notable evidence of correlated errors between different qubit pairs (Supplementary Information).

We also perform 2QCB (ref. 53) to estimate a partial Pauli error model for the 2Q gate in each operation zone, with the experimental and theoretical details provided in the Supplementary Information. Extended Data Fig. 4 shows the expectation value decays and estimated Pauli error channels for each qubit pair. We find that the zone-averaged infidelity is 8.1(2) × 10−4, which includes a leakage rate of 1.14(4) × 10−4. The error channel is dominated by IZ and ZI errors, which modelling suggests is caused by laser phase noise, spontaneous emission and electrode voltage noise. We note that our estimate of leakage rate per 2Q gate from 2QCB is about a factor of two smaller than the estimate from 2QRB.

Memory errors

Qubits not being gated incur memory errors owing to magnetic field inhomogeneities, with their impact being heavily dependent on the circuit structure and its specific transport schedule. As a figure of merit, we define the depth-n memory error to be the average infidelity per qubit after randomly pairing all qubits, performing the transport and cooling operations that would be required to apply 2Q gates on all pairs (but no actual gate operations) and repeating this process n times.

We measure memory error with a variant of 1QRB that interleaves random transport between 1Q Clifford gates, referred to as transport-1QRB22,52. Our method here differs from ref. 22 in that we partition the 98 qubits into groups in which the qubits in each group have a random 1Q Clifford operation applied after every k rounds of depth-1 transport operations on all qubits (Supplementary Information). The qubits in the different groups will have a different amount of transport and idle time between Clifford operations, which allows us to extract how memory errors scale with the number of depth-1 transport operations for random circuits.

We run transport-1QRB circuits on the 98 qubits in four groups of 25 or 24 qubits, with k ∈ {1, 2, 4, 8} transport operations between Cliffords. Furthermore, we use the ternary measurement to extract any leakage errors during transport. Extended Data Fig. 5a,b shows the measured decay in transport-1QRB for computational and ternary measurements, respectively. The decay curves are clustered into four groups determined by k. By fitting the decay curves and accounting for the leakage rate using the same procedure as in the section ‘1Q gates’, we obtain the Clifford infidelity for each qubit.

Extended Data Figure 5c shows a plot of the Clifford infidelity as a function of the number of depth-1 transport operations, averaged over all qubits in the corresponding group. The expected scaling of memory error with delay time varies depending on the timescale of the noise sources97. For this reason, we fit the memory error versus l to a quadratic equation a + bl + cl2, in which b and c capture the linear memory error rate (from fast noise) and quadratic memory error parameter (from slow noise), respectively52.

From the fit to the data, we infer a linear memory error rate of 5(1) × 10−4 and a quadratic memory error parameter of 7(2) × 10−5. We find that the leakage error scales linearly with the number of transport operations, with a rate of 4.0(2) × 10−4, and accounts for nearly all of the linear memory error. The expected coherent error from typical drift in magnetic fields between calibrations (every roughly 5 s) of approximately 10 μG is 3 × 10−5 in a depth-1 circuit. The remaining coherent error may be explained by imperfections in the phase-tracking routine or other unaccounted sources of noise.

MCMR crosstalk

We measure MCMR crosstalk errors by preparing 16 qubits in the eight operation zones, while the remaining 80 qubits are stored in the ring. A single (‘target’) qubit in each operation zone is measured and reset repeatedly, while the other 90 (‘spectator’) qubits are prepared in the |0⟩ or |1⟩. Crosstalk errors on spectator qubits result from absorbing stray measurement or reset light. The resulting spontaneous emission can lead to incoherence owing to bit-flip, leakage or dephasing errors. Using the ternary measurement at the end allows us to differentiate bit-flip rates from leakage rates to get a more detailed picture of the crosstalk error channel. We find a per MCMR crosstalk error of 1.3(1) × 10−5, with crosstalk in individual operation zones reported in Fig. 4a. Further details are provided in the Supplementary Information.

System-level benchmarks

Random Clifford circuits with mid-circuit measurements

Reference 98 introduced circuits with random Clifford layers as a scalable system-level benchmark called binary randomized benchmarking. An extension allowing for MCMRs was given in ref. 49, called quantum instrument randomized benchmarking. Our circuits are constructed similarly to those in ref. 49, with a few small modifications (Supplementary Information).

In our implementation, a length l circuit on N qubits with nm MCMRs per layer consists of the following for each layer:

A distinct uniformly random 1Q Clifford is applied to each qubit.

The N qubits are uniformly randomly paired into \(\lfloor \frac{N}{2}\rfloor \) qubit pairs and the 2Q gate RZZ(π/2) is applied to each pair, with Pauli twirling applied to the 2Q gates.

A uniformly random subset of nm qubits is sampled and, for each qubit, a 1Q Clifford is applied to prepare a measurement in a particular Pauli basis, followed by a MCMR operation.

To classically verify correct circuit outputs, we track a random initial stabilizer through the circuit (Supplementary Information). The parity of the evolved stabilizer defines a success/failure trial. For the purpose of fidelity estimation, the average success probability is rescaled into a quantity called the polarization98, defined as ypol = 2psucc − 1. A polarization of 1 corresponds to perfect success, whereas a polarization of 0 corresponds to 50% success, or random guessing. A plot of ypol(l, nm) versus l for different values of nm is shown in Fig. 4e. Let F(nm) be the process fidelity per circuit layer as a function of nm. We estimate F(nm) by fitting the polarization to an exponential decay model. Figure 4f shows a plot of F(nm) versus nm. We note that the layer fidelity actually increases slightly (with overlapping error bars) as nm increases from 8 to 16. This is explained by the fact that a batch of 16 measurements in the operation zones uses the protected measure scheme (explained in Fig. 1b), which protects against MCMR crosstalk in the operation zones.

To see whether the results are consistent with our component benchmarks, we first compute an effective 2Q gate error ϵeff,2Q from the nm = 0 data, using

$$F({n}_{{\rm{m}}}=0)={(1-5{{\epsilon }}_{{\rm{eff}},2{\rm{Q}}}/4)}^{\left\lfloor \frac{N}{2}\right\rfloor },$$

(1)

in which the factor 5/4 comes from the conversion between process and average fidelity99. The effective 2Q gate error includes errors from 2Q gates, 1Q gates and memory errors and can be thought of as the infidelity of a 2Q depolarizing channel that would best fit the data in the absence of all other errors. We find ϵeff,2Q = 1.7(2) × 10−3, whereas an accounting of 2Q and memory errors according to

$${{\epsilon }}_{{\rm{eff}},2{\rm{Q}}}=\frac{4}{5}\left(\left(\frac{5}{4}\right){{\epsilon }}_{{\rm{avg}},2{\rm{Q}}}+2\left(\frac{3}{2}\right){{\epsilon }}_{{\rm{mem}}}\right)$$

(2)

predicts 2.2(1) × 10−3 (Supplementary Information). We attribute the fact that the effective 2Q error is smaller than what the component errors predict to improvements in the gates and memory errors between the times when the component and random Clifford circuit benchmarks were run.

We next compute an effective MCMR error ϵeff,MCMR by best-fitting the F(nm) versus nm data to the heuristic formula

$$F({n}_{{\rm{m}}})={(1-5{{\epsilon }}_{{\rm{eff}},2{\rm{Q}}}/4)}^{\left\lfloor \frac{N}{2}\right\rfloor }{(1-3{{\epsilon }}_{{\rm{eff}},{\rm{MCMR}}}/2)}^{{n}_{{\rm{m}}}}$$

(3)

together with our computed value of ϵeff,2Q. We find ϵeff,MCMR = 2.4(5) × 10−3. By comparison, adding the component-level SPAM, MCMR crosstalk and memory errors, we predict an effective MCMR error of 2.5(1) × 10−3 (Supplementary Information). We conclude that the data from our random Clifford with MCMR circuits is consistent with our measured component-level errors. We remark that our method of comparison is heuristic and a rigorous methodology for comparing component-level to system-level benchmarking performance is an open problem.

RCS mirror benchmarking

RCS is a system-level benchmark assessing how effectively a quantum computer can generate computationally complex quantum states15. Like binary randomized benchmarking, RCS examines the extent to which quantum circuits obtain the performance expected from component-level benchmarks. At the same time, because the classical difficulty of sampling from the outputs of random quantum circuits has been extremely well studied over the past decade100, RCS provides a well-vetted benchmark for the computational power of a quantum computer.

By making use of the arbitrary connectivity of the Helios quantum computer, we consider RCS with circuit geometries constructed from colourings of random regular graphs14: a layer depth-l random circuit is constructed by interleaving l layers of 2Q RZZ(π/2) gates (each layer containing N/2 2Q gates) with l + 1 layers of Haar-random 1Q gates (each layer containing N 1Q gates). Although the fidelity of such circuits can in principle be inferred by running them and performing cross-entropy benchmarking101, evaluating the cross-entropy requires exact simulation of the circuits in question and is infeasible except for small depth or qubit number. To estimate the expected state fidelity in RCS (and therefore the anticipated performance in cross-entropy benchmarking), we follow the strategy of refs. 14,102,103,104,105 and infer the fidelity of a layer depth-l circuit by computing the return-probability FMB of a ‘mirrored’ layer depth-l/2 circuit, with the second (mirrored) half of the circuit using randomized compiling to prevent unintended cancellation of coherent errors. The randomness for randomized compilation is sampled in real time at the start of each shot and the corresponding random 1Q gates are compiled on the fly (with the existing Haar-random 1Q gates), resulting in only one physical 1Q gate per qubit per layer. Following ref. 14, we also initialize each mirrored circuit into a random computational basis state to prevent unequal SPAM errors between the two basis states from biasing the fidelity estimate. At each depth, we execute between 1,000 and 2,500 shots spread evenly across 100 random circuit connectivities. As well as the mirrored random circuits run to assess RCS performance, we also directly sampled the output of a single (unmirrored) random circuit of depth d = 26. That circuit is included in ref. 106, along with 2,500 sampled bitstrings from Helios.

The fidelity of RCS as a function of depth inferred in this manner is reported in Fig. 4g. We perform a least-squares best fit to the gate-counting model from ref. 14,

$${F}_{{\rm{GC}}}(l)={(1-{p}_{{\rm{SPAM}}})}^{N}{\left(1-\frac{5}{4}{{\epsilon }}_{{\rm{eff}},2{\rm{Q}}}\right)}^{\frac{N}{2}(l-\delta )}.$$

(4)

Here N = 98, δ = 1.12 is a correction to effective circuit layer depth from boundary effects in mirror circuits14, pSPAM is the effective SPAM error and ϵeff,2Q is the effective average 2Q error rate, which includes effects from 1Q, 2Q and memory errors as in the previous section. From the fit, we estimate pSPAM = 5.3(51) × 10−4 and ϵeff,2Q = 2.00(6) × 10−3. This effective 2Q error is also consistent with the estimate obtained from random Clifford circuits as well as component benchmarks reported in Fig. 4i.

The task of sampling from the output distribution induced by running forward (unmirrored) circuits is well defined for either quantum or classical computers. In either case, the quality of samples can be judged by statistical tests, with the linear cross-entropy test being a widely used standard15. As mentioned above, the linear cross-entropy score of the quantum data is expected to agree closely (for the circuits run here) with the overall circuit fidelity estimated from mirror benchmarking results at comparable depth14. For the high scores achievable with Helios (hitting a minimum of about 3.5% at depth 26), there is no known classical strategy to score well on the linear cross-entropy test without performing (nearly) exact simulation of the circuits in question14, with the most efficient strategy for doing so being tensor-network contraction.

The reported costs in Fig. 4h are for optimized tensor-network contraction assuming so-called ‘embarrassing parallelization’ (by means of slicing) into independent computations involving various amounts of available memory (corresponding to cotengra contraction widths of \({\mathcal{W}}=30\), 49 and 54) and were obtained using (sliced) simulated annealing built into cotengra107. We note that the contraction–cost optimization performed here is only approximate and the costs could certainly be mildly improved by providing the optimization heuristics with more computational power. However, we do not expect such improvements to change the overall conclusion that Helios can produce states at high global fidelity for which the (classical) sampling cost is vastly beyond the capabilities of existing supercomputers.

Data availability

Component benchmarking data are available from the Quantinuum hardware specifications repository at https://github.com/Quantinuum/quantinuum-hardware-specifications. The data used in this paper are available from the Helios paper data repository at https://github.com/Quantinuum/Helios-paper-data.

Code availability

The custom code used to generate and analyse the tests in this paper is available from the Helios paper data repository at https://github.com/Quantinuum/Helios-paper-data.

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Acknowledgements

We thank the entire Quantinuum team for numerous contributions that enabled this work. We specifically thank J. Ross for editing the image in Fig. 1.

Funding

The contributions of the Sandia National Laboratories authors were funded in part by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Quantum Testbed Pathfinder programme. T.P. acknowledges support from an Office of Advanced Scientific Computing Research Early Career Award. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC (NTESS), a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration (NNSA) under contract DE-NA0003525. This written work is authored by an employee of NTESS. The employee, not NTESS, owns the right, title and interest in and to the written work and is responsible for its contents. Any subjective views or opinions that might be expressed in the written work do not necessarily represent the views of the U.S. Government. The publisher acknowledges that the U.S. Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this written work or allow others to do so, for U.S. Government purposes. The Department of Energy will provide public access to results of federally sponsored research in accordance with the Department of Energy Public Access Plan.

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Authors and Affiliations

Quantinuum, Broomfield, CO, USA

Anthony Ransford, M. S. Allman, J. P. Campora III, Samuel F. Cooper, Robert D. Delaney, Joan M. Dreiling, Brian Estey, Caroline Figgatt, Alex Hall, Akhil Isanaka, Colin J. Kennedy, Ivaylo S. Madjarov, Karl Mayer, Annie J. Park, Adam P. Reed, Riley Ancona, Liz Argueta, Benjamin Arkin, Leonardo Ascarrunz, William Baker, Corey Barnes, John Bartolotta, Jordan Berg, Ryan Besand, Bryce Bjork, Paul Blanchard, Matt Bohn, Daniel Y. Botamanenko, Robert Boutelle, Natalie Brown, Grant T. Buckingham, William Cody Burton, Varis Carey, Joe Chambers, Jia Wen Chan, Victor E. Colussi, Steven Crepinsek, Andrew Cureton, Daniel Davis, Matthew DeCross, Conor Delaney, Davide DelVento, B. J. DeSalvo, Jason Dominy, Sydney Drotar, Neal Erickson, Stephen Erickson, Bruce Evans, Tyler Evans, Maya I. Fabrikant, Andrew Fischer, Cameron Foltz, Michael Foss-Feig, David Francois, Brad Freyberg, Charles Gao, Robert Garay, Jane Garvin, David M. Gaudiosi, Christopher N. Gilbreth, Josh Giles, Erin Glynn, Jeff Graves, Azure Hansen, David Hayes, Tyler Hilbun, Kyle Hoffman, Ian M. Hoffman, Jack Houlton, Jared Hout, Ross Hutson, Ryan T. Jacobs, Trent Jacobs, Jacob Johansen, Loren Jones, Sydney Julian, Ryo Kondo, Chang Kong, Asa Kosto, David Liefer, Michelle Lollie, Dominic Lucchetti, Christian Lytle, Andrew Malm, Spencer Mather, Brian Mathewson, Lauren McCaffrey, Hannah McDougall, Robin Mendoza, David B. Miller, Michael Mills, Louis Narmour, Nhung Nguyen, Lora Nugent, Jeremy Parks, Zach Peters, Jessie Petricka, Juan M. Pino, Frank Polito, Andrew C. Potter, Gabriel Price, McKinley Pugh, Noah Ratcliff, Daisy Raymondson, Peter Rhodes, Conrad Roman, Ciaran Ryan-Anderson, Peter Schow, Peter Shevchuk, Peter Siegfried, Kartik Singhal, Thomas Skripka, Ben Spaun, R. Tucker Sprenkle, Paul Stoufer, Mariel Tader, Raanan Tobey, Anh Tran, Tam Tran, Jim Walker, Quinn Wolf, Jian Zheng, Kristen Zuraski, Charles H. Baldwin, Alex Chernoguzov, John P. Gaebler, Steven J. Sanders, Brian Neyenhuis, Russell Stutz & Justin G. Bohnet

Quantinuum, Cambridge, UK

Jake Arkinstall, Pablo Andres-Martinez, Will Angenent, Agustíin Borgna, John Children, Vanya Eccles, Alec Edgington, Lukas Heidemann, Ariana Hlavaty, Isobel Hooper, Melf Johannsen, Aidan Keay, Mark Koch, Alan Lawrence, Callum MacPherson, Richard Morrison, Craig Roy, Fernando Betanzo Sanchez, George Sangiolo, Tatiana Sawadski, Henry Semenenko, Seyon Sivarajah, Travis H. Thompson, Sam White, Douglas Wilson & Chester Wringe

Quantinuum, Brooklyn Park, MN, USA

Ali A. Husain, Nathaniel Q. Burdick, David Deen, James Hostetter, Daniel Maxwell, Timothy A. Peterson, Andrew Schaffer, Jon Sedlacek, Lucas Sletten, Stephen F. Taylor, Grahame Vittorini, Curtis Volin & Garrett R. Williams

Quantinuum, London, UK

Nikhil Kotibhaskar & Alistair R. Milne

Quantinuum, Plymouth, MN, USA

Molly P. Andersen, Matt Blain, Christopher J. Carron, Joe Davies, Christopher T. Ertsgaard, Jay Esposito, Bob Higashi, Bob Horning, Ryan Jung, Todd Klein, Scott Olson, Daniel Ouellette, Matthias Preidl & Susan Shore

Quantum Performance Laboratory, Sandia National Laboratories, Albuquerque, NM, USA

Robin Blume-Kohout & Jordan Hines

Quantinuum K.K., Tokyo, Japan

Ross Duncan, Craig Holliman & Nathan K. Lysne

Quantum Performance Laboratory, Sandia National Laboratories, Livermore, CA, USA

Daniel Hothem, Timothy Proctor & Kevin Young

Authors

Anthony Ransford

M. S. Allman

Jake Arkinstall

J. P. Campora III

Samuel F. Cooper

Robert D. Delaney

Joan M. Dreiling

Brian Estey

Caroline Figgatt

Alex Hall

Ali A. Husain

Akhil Isanaka

Colin J. Kennedy

Nikhil Kotibhaskar

Ivaylo S. Madjarov

Karl Mayer

Alistair R. Milne

Annie J. Park

Adam P. Reed

Riley Ancona

Molly P. Andersen

Pablo Andres-Martinez

Will Angenent

Liz Argueta

Benjamin Arkin

Leonardo Ascarrunz

William Baker

Corey Barnes

John Bartolotta

Jordan Berg

Ryan Besand

Bryce Bjork

Matt Blain

Paul Blanchard

Robin Blume-Kohout

Matt Bohn

Agustíin Borgna

Daniel Y. Botamanenko

Robert Boutelle

Natalie Brown

Grant T. Buckingham

Nathaniel Q. Burdick

William Cody Burton

Varis Carey

Christopher J. Carron

Joe Chambers

Jia Wen Chan

John Children

Victor E. Colussi

Steven Crepinsek

Andrew Cureton

Joe Davies

Daniel Davis

Matthew DeCross

David Deen

Conor Delaney

Davide DelVento

B. J. DeSalvo

Jason Dominy

Sydney Drotar

Ross Duncan

Vanya Eccles

Alec Edgington

Neal Erickson

Stephen Erickson

Christopher T. Ertsgaard

Jay Esposito

Bruce Evans

Tyler Evans

Maya I. Fabrikant

Andrew Fischer

Cameron Foltz

Michael Foss-Feig

David Francois

Brad Freyberg

Charles Gao

Robert Garay

Jane Garvin

David M. Gaudiosi

Christopher N. Gilbreth

Josh Giles

Erin Glynn

Jeff Graves

Azure Hansen

David Hayes

Lukas Heidemann

Bob Higashi

Tyler Hilbun

Jordan Hines

Ariana Hlavaty

Kyle Hoffman

Ian M. Hoffman

Craig Holliman

Isobel Hooper

Bob Horning

James Hostetter

Daniel Hothem

Jack Houlton

Jared Hout

Ross Hutson

Ryan T. Jacobs

Trent Jacobs

Melf Johannsen

Jacob Johansen

Loren Jones

Sydney Julian

Ryan Jung

Aidan Keay

Todd Klein

Mark Koch

Ryo Kondo

Chang Kong

Asa Kosto

Alan Lawrence

David Liefer

Michelle Lollie

Dominic Lucchetti

Nathan K. Lysne

Christian Lytle

Callum MacPherson

Andrew Malm

Spencer Mather

Brian Mathewson

Daniel Maxwell

Lauren McCaffrey

Hannah McDougall

Robin Mendoza

David B. Miller

Michael Mills

Richard Morrison

Louis Narmour

Nhung Nguyen

Lora Nugent

Scott Olson

Daniel Ouellette

Jeremy Parks

Zach Peters

Timothy A. Peterson

Jessie Petricka

Juan M. Pino

Frank Polito

Andrew C. Potter

Matthias Preidl

Gabriel Price

Timothy Proctor

McKinley Pugh

Noah Ratcliff

Daisy Raymondson

Peter Rhodes

Conrad Roman

Craig Roy

Ciaran Ryan-Anderson

Fernando Betanzo Sanchez

George Sangiolo

Tatiana Sawadski

Andrew Schaffer

Peter Schow

Jon Sedlacek

Henry Semenenko

Peter Shevchuk

Susan Shore

Peter Siegfried

Kartik Singhal

Seyon Sivarajah

Thomas Skripka

Lucas Sletten

Ben Spaun

R. Tucker Sprenkle

Paul Stoufer

Mariel Tader

Stephen F. Taylor

Travis H. Thompson

Raanan Tobey

Anh Tran

Tam Tran

Grahame Vittorini

Curtis Volin

Jim Walker

Sam White

Garrett R. Williams

Douglas Wilson

Quinn Wolf

Chester Wringe

Kevin Young

Jian Zheng

Kristen Zuraski

Charles H. Baldwin

Alex Chernoguzov

John P. Gaebler

Steven J. Sanders

Brian Neyenhuis

Russell Stutz

Justin G. Bohnet

Contributions

A.R., C.J.K., A.P.R., A. Chernoguzov, J.P.G., R.S. and J.G.B. conceived and designed the system architecture. A.R., M.S.A., J.A., S.F.C., R.D.D., J.M.D., B. Estey, A. Hall, A.A.H., C.J.K., N.K., I.S.M., A.R.M., A.J.P., A.P.R., R.A., M.P.A., B.A., L.A., W.B., C.B., M. Blain, M. Bohn, D.Y.B., R. Boutelle, G.T.B., W.C.B., V.C., C.J.C., S.C., J. Davies, D. Davis, D. Deen, C.D., B.J.D., S.D., S.E., C.T.E., J.E., T.E., M.I.F., A.F., C. Foltz, D.F., D.M.G., J. Giles, E.G., J. Graves, B. Higashi, T.H., I.M.H., C.H., B. Horning, J. Hostetter, J. Houlton, J. Hout, R.T.J., T.J., J.J., L.J., S.J., R.J., T.K., R.K., C.K., M.L., N.K.L., C.L., A.M., S.M., D.M., L.M., H.M., R. Mendoza, D.B.M., M.M., N.N., L. Nugent, S.O., D.O., J. Parks, Z.P., T.A.P., J. Petricka, J.M.P., F.P., M. Preidl, M. Pugh, N.R., D.R., P.R., C. Roman, C. Roy, A.S., J.S., H.S., P. Shevchuk, S. Shore, P. Siegfried, L.S., B.S., R.T.S., P. Stoufer, S.F.T., T.H.T., R.T., A.T., T.T., C.V., G.R.W., Q.W., J.Z., K.Z., J.P.G. and J.G.B. contributed to the experimental work, including hardware development, operation, measurements and calibrations. M.S.A., J.A., J.P.C., C. Figgatt, A.I., P.A.-M., W.A., L. Argueta, L. Ascarrunz, J. Berg, B.B., P.B., A.B., J. Chambers, J.W.C., J. Children, D. DelVento, V.E., A.E., N.E., B. Evans, C. Foltz, D.F., B.F., R.G., J. Garvin, L.H., A. Hlavaty, K.H., I.H., M.J., A. Keay, M.K., A. Kosto, A.L., D. Liefer, D. Lucchetti, C.M., B.M., R. Morrison, L. Narmour, F.B.S., G.S., T. Sawadski, P. Schow, K.S., S. Sivarajah, T. Skripka, J.W., S.W., D.W., C.W. and A. Chernoguzov contributed to software and control-stack development. K.M., J. Bartolotta, R.B.-K., N.B., V.E.C., M.D., J. Dominy, M.F.-F., C.N.G., D. Hayes, J. Hines, D. Hothem, R.H., T.P., C.R.-A., M.T., K.Y. and C.H.B. contributed to theoretical work, benchmarking and data analysis. A.R., J.P.C., A.A.H., C.J.K., K.M., A.P.R., V.E.C., M.D., D. Hayes, J. Hines, D. Hothem, C.H.B., J.P.G. and J.G.B. wrote or substantially edited the manuscript. R. Besand, R.B.-K., N.Q.B., W.C.B., A. Cureton, R.D., S.E., M.F.-F., C.G., A. Hansen, D. Hayes, J. Hostetter, D. Lucchetti, A.M., B.M., L. Nugent, J. Parks, J.M.P., A.C.P., G.P., T.P., D.R., T. Skripka, B.S., R.T., G.V., K.Y., C.H.B., A. Chernoguzov, J.P.G., S.J.S., B.N., R.S. and J.G.B. supervised the project. All authors discussed the results and reviewed the manuscript.

Corresponding author

Correspondence to

Anthony Ransford.

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The authors declare no competing interests.

Peer review

Peer review information

Nature thanks Roee Ozeri, Arghavan Safavi-Naini and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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