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arXiv:2610.07393

Benchmarking exchange-only control of a 48-spin singlet manifold

HRL Quantum Team, Microsoft Collaborators, :, Stephen Carr, Matt Abbitt, Michael Abraham, Edwin Acuna, I. Alverado, Carter Andrews, Hussein Anton, Katherine M. Beech, Aaron J. Bluestone, Jacob Z. Blumoff, Matthew G. Borselli, Brydon Boyd, Jacob T. Boyer, Peter Brewer, Steven L. Brown, Joseph D. Broz, Tyler A. Cain, John B. Carpenter, Faustin W. Carter, Brittany Carter, Matthew D. Chambers, James M. Chappell, Kevin C. Chen, Edward H. Chen, Maxwell D. Choi, Matthew N. H. Chow, Justin E. Christensen, Aaron M. Chronister, Andrew M. Clapper, Michael D. Cornelius, Gregory M. Crosswhite, Stanislav Culaclii, Erik S. Daniel, Dominic Daprano, John K. David, Charles R. Elliott, Kevin Eng, Colin P. Feeney, David J. Fialkow, Dylan H. Finestone, Bryan H. Fong, Richie Fu, Zachary A. Geiger, Bradley W. Greene, Rafael Guerra-Fuentes, Hrayr K. Gurgenian, Alex Hamill, Brooke M. Hardesty, Jim W. Harrington, Alex Hirman, Donald A. Hitko, Silas Hoffman, Dominic Holloman, Daniel R. Hulbert, Jake Hundley, Clayton A. C. Jackson, Paul C. Jerger, B. Johnson, Aaron M. Jones, Michael P. Jura, Adour V. Kabakian, Tyler Keating, Joseph Kerckhoff, Andrey A. Kiselev, Patrick W. Krantz, Thaddeus D. Ladd, Sanaaya Lakdawala, Elias Lawson-Fox, Alwina R. Liu, Dwight Luhman, Manny Macias, Theodore K. Macioce, Ryan M. Martin, Daniel S. Matic, Gavin C. Mazur, Ryan McGeehan, Olivia Means, Austin Meyer, Samuel Mumford, Tina Niknejad, Riley P. O'Neil, Andrew Pan, Winston Pouse, Eric M. Prophet, Matthew D. Reed, Marcus Rentie, Alec Roberson, Zechariah Rogers, Golam Sabbir, Spencer Sager, Christopher D. Sanborn, Jonathan Sanchez, Rachel H. Sarmiento, Christian J. Schnaible, Cole Scott, Aaron Smith, Daniel E. Smith, James Soash, Kevin C. Staley, Andrea Su, Bo Sun, Christopher M. Swank, Noah Swimmer, Charles Tahan, Bryan J. Thomas, Yessica Torres, Alan Tran, Ivan Tran, James R. van Meter, Franklin Vartanian, John Samuel Venker, Daniel Volya, Annette L. Wagner, Daniel R. Ward, Aaron J. Weinstein, Abigail L. Wessels, Thomas V. Westrick, Evan T. White, Randall M. White, Parker Williams, Catrina E. Wilson, Courtney P. Wilt, Matthew Wingert, Clifford S. YoungSciortino, Andrew Ziegler

quant-phSubmitted Oct 5, 2026• Announced Oct 7, 2026• 0 citations
arXivHTMLPDF

Abstract

Exchange-only quantum computing benefits from high fidelity and straightforward control afforded by the exchange interaction. However, independently controllable qubits must be encoded into subsystems of at least three electron spins, restricting computation to only a fraction of the available spin Hilbert space. The remaining states are treated as leakage and used only transiently in gate sequences. By contrast, a quantitative, system-wide measure of exchange-only performance can exploit the full available Hilbert space, including states conventionally treated as leakage. Here, we apply this approach to arrays of up to 48 electron spins, accessing a total-spin-zero Hilbert space with dimension exceeding $2^{40}$. Measurements of out-of-time-order correlators (OTOCs) reveal rich scrambling dynamics and demonstrate access to regimes relevant to quantum computational advantage. Using generalized forms of cross-entropy and mirror randomized benchmarking, we also assess the aggregate performance of the full exchange-only system per fundamental two-body interaction: the two-spin exchange. We obtain an effective system-level error of $3 \times 10^{-4}$ per exchange, incorporating the complete experimental control sequence and all associated noise sources. This value is up to an order of magnitude lower than those reported from comparable benchmarks on other platforms at the time of writing.

Related papers

Spin singlets are useful

Silas Hoffman, Edward H. Chen, Matthew Brooks +6 more

We evaluate the utility of the spin-zero manifold of an exchange-coupled array of $N$ spins for tasks in quantum computation and quantum simulation. Since pairs of electrons can be readily initialized into a product state of singlets in semiconducting quantum dot arrays, the full spin-zero manifold is available with exchange-only control, providing a Hilbert space of approximate dimension $2^N/(N/2)^{3/2}$, asymptotically close to the $2^N$ dimension of the full spin Hilbert space. Leveraging the spin-zero manifold enables larger computational space in a given array compared to traditional exchange-only control, in which spin arrays are organized into modular units of $n$ spins comprising $N/n$ encoded qubits, limiting to the exponentially smaller Hilbert dimension $2^{N/n}$. Here we focus on benchmarking metrics for this resource utilization by generalizing cross-entropy benchmarking, mirror benchmarking, and out-of-time-ordered correlators to this system. We show that operating in the spin-zero manifold can accelerate the realization of computational quantum advantage applications in semiconductor-based spin qubits.

quant-pharXiv:2607.06672•Jul 9, 2026•0 citations

Singlet-Only Always-On Gapless Exchange Qubits with Baseband Control

Nathan L. Foulk, Silas Hoffman, Katharina Laubscher +1 more

We propose a singlet-only always-on gapless exchange (SAGE) spin qubit that encodes a single qubit in the spins of four electrons while allowing universal baseband control. While conventional exchange-only qubits suffer from magnetic-field-gradient-induced leakage and coherent errors due to local nuclear environments and variations in the g-factor, the SAGE qubit subspace is protected from coherent errors due to local magnetic field gradients, and leakage out of the computational subspace is energetically suppressed due to the exchange interactions between electrons being always on. Consequently, we find that when magnetic gradient noise dominates over charge noise, coherence times and single-qubit gate infidelities of the SAGE qubit improve by an order of magnitude compared to conventional exchange-only qubits. Moreover, using realistic parameters, two-qubit gates can be performed with a single interqubit exchange pulse with times comparable in duration to conventional exchange-only qubits but with a significantly simplified pulse sequence.

arXiv:2501.18589•Physical Review Letters•Aug 11, 2025•2 citations

Measurement-Free Encoded-Qubit Control and a Two-Local Qutrit Obstruction in a Spin-2 AKLT Plaquette

Boris Batenin, Andrei Preece

Can an encoded quantum state be controlled continuously without repeated measurements to prevent leakage? This study gives a constructive answer for a four-spin-2 AKLT plaquette, where a three-dimensional singlet code sits inside a 625-dimensional physical Hilbert space. The result combines an exact restriction with a coherent control scheme: strictly leakage-free two-site Hamiltonians cannot provide universal control of the full encoded qutrit, yet two explicitly constructed interactions enable universal single-qubit control without intermediate measurements or postselection within a two-dimensional subspace. The classification begins with the complete physical leakage map for all six spin pairs and exchange polynomials through degree four. Exact rational calculations establish rank L = 6 and dim ker L = 18 for the 255 × 24 matrix. Despite this large family of leakage-cancelling combinations, every accessible logical Hamiltonian obeys [A, R] = 0, where R is a fixed geometric involution. Its two-dimensional and one-dimensional eigenspaces therefore remain separate, obstructing universal SU(3) control. The restriction extends to arbitrary anisotropic two-site Hamiltonians that preserve the code. Within the rotationally invariant pair-polynomial model, interactions confined to the four plaquette edges act only as logical scalars; noncommuting protected controls require at least three pair supports and polynomial degree three. The constructive solution uses quadratic and cubic exchange Hamiltonians acting simultaneously on three pairs, including a diagonal link. Their coefficients cancel physical leakage exactly, so QH₂P = QH₃P = 0 throughout the full system, with P projecting onto the code and Q onto its complement. Their logical generators satisfy Lie(iA, iB) ≅ u(2) ⊕ u(1), allowing arbitrary coherent qubit gates while preserving the code at every intermediate time. The manuscript supplies exact certificates and verification procedures, together with operator-norm and calibration-error bounds that make the engineering requirements explicit. The practical opportunity is to remove intermediate code-check measurements from this control scheme; demonstrating a hardware advantage requires calibrated simultaneous interactions, including the diagonal channel, and measured gate fidelity and latency.

•Oct 28, 2026•0 citations

Operating two exchange-only qubits in parallel

Mateusz Tomasz Mądzik, Florian Luthi, Gian Giacomo Guerreschi +38 more

Semiconductors are among the most promising platforms to implement large-scale quantum computers, as advanced manufacturing techniques allow fabrication of large quantum dot arrays1. Various qubit encodings can be used to store and manipulate quantum information on these quantum dot arrays. Regardless of qubit encoding, precise control over the exchange interaction between electrons confined in quantum dots in the array is critical. Furthermore, it is necessary to execute high-fidelity quantum operations concurrently to make full use of the limited coherence of individual qubits. Here we demonstrate the parallel operation of two exchange-only qubits, consisting of six quantum dots in a linear arrangement. Using randomized benchmarking (RB) techniques, we show that issuing pulses on the five barrier gates to modulate exchange interactions in a maximally parallel way maintains the quality of qubit control relative to sequential operation. The techniques developed to perform parallel exchange pulses can be readily adapted to other quantum-dot-based encodings. Moreover, we show the first, to our knowledge, experimental demonstrations of an iSWAP gate for exchange-only qubits and of a charge-locking Pauli spin blockade (PSB) readout method. The results are validated using cross-entropy benchmarking (XEB)2, a technique useful for performance characterization of larger quantum computing systems; here it is used for the first time on a quantum system based on semiconductor technology. Parallel operation of two exchange-only qubits consisting of six quantum dots arranged linearly is shown to be achievable and maintains qubit control quality compared with sequential operation, with potential for use in scaled quantum computing.

arXiv:2504.01191•Nature•Nov 26, 2025•5 citations

Demonstration of an always-on exchange-only spin qubit

Joseph Broz, Jesse C. Hoke, Edwin Acuna +1 more

Abstract In conventional exchange-only (EO) spin qubit demonstrations, quantum gates have been implemented using sequences of individually pulsed pairwise exchange interactions with only one exchange coupling active at a time. Alternatively, multiple non-commuting exchange interactions can be pulsed simultaneously, reducing circuit depths and providing protection against leakage. We demonstrate high-fidelity quantum control of an always-on exchange-only (AEON) qubit, operated using simultaneous exchange pulses in a triangular quantum dot (QD) array. We use blind randomized benchmarking to characterize the performance of the full AEON single-qubit Clifford gate set, achieving an average Clifford gate fidelity F C1 = 99.86%. Extensions of this work may enable more efficient EO two-qubit entangling gates as well as the implementation of native i -Toffoli gates in Loss-DiVincenzo single-spin qubits.

Nature Communications•Apr 3, 2026•1 citation

Hardware-Efficient Exchange-Only QML: Singlet-Triplet Spin Chains via Inter-pair Coupling without Magnetic Gradients

Yuichiro Minato

Standard universal quantum computing using exchange-only qubits typically requires three physical spins per logical qubit, leading to significant hardware overhead. Conversely, two-spin units offer higher density but rely on local magnetic field gradients for control, increasing integration complexity. In this paper, we propose a resource-efficient quantum machine learning (QML) architecture that achieves high expressibility using minimal two-spin units and Heisenberg exchange interactions alone, without any magnetic gradients. We shift the paradigm from universal gate-based control to utilizing the intrinsic, time-domain dynamics of a spin chain as a learning resource. Numerical simulations on MNIST digit classification demonstrate that the symmetry-protected constraints of isolated spin pairs are bypassed by leveraging inter-pair exchange coupling. This interference-mediated state mixing significantly enhances the expressibility of the Hilbert space. The model reaches a test-set accuracy of 90.9% +/- 0.2% over five independent seeds on the full 10,000-image MNIST test set. Under an identical linear readout, the trained quantum feature map (88.1%) clearly outperforms a classical linear baseline on the same PCA inputs (83.2%) as well as an untrained (reservoir-style) version of the same dynamics (53.0%), demonstrating that the learned, input-dependent exchange pulses implement a genuinely non-linear and trainable feature map. The protocol is also robust to experimentally relevant imperfections: accuracy remains at 89.9% under 10% quasi-static pulse-area noise and at 89.8% when every observable is estimated from 10^3 measurement shots. These findings suggest that competitive QML can be executed on the simplest possible semiconductor spin-chain hardware, bypassing the need for leakage-prone encodings or complex micro-magnet integration.

quant-pharXiv:2608.29017•Sep 1, 2026•0 citations
Exchange-only quantum computing benefits from high fidelity and straightforward control afforded by the exchange interaction. However, independently controllable qubits must be encoded into subsystems of at least three electron spins, restricting computation to only a fraction of the available spin Hilbert space. The remaining states are treated as leakage and used only transiently in gate sequences. By contrast, a quantitative, system-wide measure of exchange-only performance can exploit the full available Hilbert space, including states conventionally treated as leakage. Here, we apply this approach to arrays of up to 48 electron spins, accessing a total-spin-zero Hilbert space with dimension exceeding 2402^{40}240. Measurements of out-of-time-order correlators (OTOCs) reveal rich scrambling dynamics and demonstrate access to regimes relevant to quantum computational advantage. Using generalized forms of cross-entropy and mirror randomized benchmarking, we also assess the aggregate performance of the full exchange-only system per fundamental two-body interaction: the two-spin exchange. We obtain an effective system-level error of 3×10−43 \times 10^{-4}3×10−4 per exchange, incorporating the complete experimental control sequence and all associated noise sources. This value is up to an order of magnitude lower than those reported from comparable benchmarks on other platforms at the time of writing.
We evaluate the utility of the spin-zero manifold of an exchange-coupled array of NNN spins for tasks in quantum computation and quantum simulation. Since pairs of electrons can be readily initialized into a product state of singlets in semiconducting quantum dot arrays, the full spin-zero manifold is available with exchange-only control, providing a Hilbert space of approximate dimension 2N/(N/2)3/22^N/(N/2)^{3/2}2N/(N/2)3/2, asymptotically close to the 2N2^N2N dimension of the full spin Hilbert space. Leveraging the spin-zero manifold enables larger computational space in a given array compared to traditional exchange-only control, in which spin arrays are organized into modular units of nnn spins comprising N/nN/nN/n encoded qubits, limiting to the exponentially smaller Hilbert dimension 2N/n2^{N/n}2N/n. Here we focus on benchmarking metrics for this resource utilization by generalizing cross-entropy benchmarking, mirror benchmarking, and out-of-time-ordered correlators to this system. We show that operating in the spin-zero manifold can accelerate the realization of computational quantum advantage applications in semiconductor-based spin qubits.
We propose a singlet-only always-on gapless exchange (SAGE) spin qubit that encodes a single qubit in the spins of four electrons while allowing universal baseband control. While conventional exchange-only qubits suffer from magnetic-field-gradient-induced leakage and coherent errors due to local nuclear environments and variations in the g-factor, the SAGE qubit subspace is protected from coherent errors due to local magnetic field gradients, and leakage out of the computational subspace is energetically suppressed due to the exchange interactions between electrons being always on. Consequently, we find that when magnetic gradient noise dominates over charge noise, coherence times and single-qubit gate infidelities of the SAGE qubit improve by an order of magnitude compared to conventional exchange-only qubits. Moreover, using realistic parameters, two-qubit gates can be performed with a single interqubit exchange pulse with times comparable in duration to conventional exchange-only qubits but with a significantly simplified pulse sequence.
Can an encoded quantum state be controlled continuously without repeated measurements to prevent leakage? This study gives a constructive answer for a four-spin-2 AKLT plaquette, where a three-dimensional singlet code sits inside a 625-dimensional physical Hilbert space. The result combines an exact restriction with a coherent control scheme: strictly leakage-free two-site Hamiltonians cannot provide universal control of the full encoded qutrit, yet two explicitly constructed interactions enable universal single-qubit control without intermediate measurements or postselection within a two-dimensional subspace. The classification begins with the complete physical leakage map for all six spin pairs and exchange polynomials through degree four. Exact rational calculations establish rank L = 6 and dim ker L = 18 for the 255 × 24 matrix. Despite this large family of leakage-cancelling combinations, every accessible logical Hamiltonian obeys [A, R] = 0, where R is a fixed geometric involution. Its two-dimensional and one-dimensional eigenspaces therefore remain separate, obstructing universal SU(3) control. The restriction extends to arbitrary anisotropic two-site Hamiltonians that preserve the code. Within the rotationally invariant pair-polynomial model, interactions confined to the four plaquette edges act only as logical scalars; noncommuting protected controls require at least three pair supports and polynomial degree three. The constructive solution uses quadratic and cubic exchange Hamiltonians acting simultaneously on three pairs, including a diagonal link. Their coefficients cancel physical leakage exactly, so QH₂P = QH₃P = 0 throughout the full system, with P projecting onto the code and Q onto its complement. Their logical generators satisfy Lie(iA, iB) ≅ u(2) ⊕ u(1), allowing arbitrary coherent qubit gates while preserving the code at every intermediate time. The manuscript supplies exact certificates and verification procedures, together with operator-norm and calibration-error bounds that make the engineering requirements explicit. The practical opportunity is to remove intermediate code-check measurements from this control scheme; demonstrating a hardware advantage requires calibrated simultaneous interactions, including the diagonal channel, and measured gate fidelity and latency.
Semiconductors are among the most promising platforms to implement large-scale quantum computers, as advanced manufacturing techniques allow fabrication of large quantum dot arrays1. Various qubit encodings can be used to store and manipulate quantum information on these quantum dot arrays. Regardless of qubit encoding, precise control over the exchange interaction between electrons confined in quantum dots in the array is critical. Furthermore, it is necessary to execute high-fidelity quantum operations concurrently to make full use of the limited coherence of individual qubits. Here we demonstrate the parallel operation of two exchange-only qubits, consisting of six quantum dots in a linear arrangement. Using randomized benchmarking (RB) techniques, we show that issuing pulses on the five barrier gates to modulate exchange interactions in a maximally parallel way maintains the quality of qubit control relative to sequential operation. The techniques developed to perform parallel exchange pulses can be readily adapted to other quantum-dot-based encodings. Moreover, we show the first, to our knowledge, experimental demonstrations of an iSWAP gate for exchange-only qubits and of a charge-locking Pauli spin blockade (PSB) readout method. The results are validated using cross-entropy benchmarking (XEB)2, a technique useful for performance characterization of larger quantum computing systems; here it is used for the first time on a quantum system based on semiconductor technology. Parallel operation of two exchange-only qubits consisting of six quantum dots arranged linearly is shown to be achievable and maintains qubit control quality compared with sequential operation, with potential for use in scaled quantum computing.
Abstract In conventional exchange-only (EO) spin qubit demonstrations, quantum gates have been implemented using sequences of individually pulsed pairwise exchange interactions with only one exchange coupling active at a time. Alternatively, multiple non-commuting exchange interactions can be pulsed simultaneously, reducing circuit depths and providing protection against leakage. We demonstrate high-fidelity quantum control of an always-on exchange-only (AEON) qubit, operated using simultaneous exchange pulses in a triangular quantum dot (QD) array. We use blind randomized benchmarking to characterize the performance of the full AEON single-qubit Clifford gate set, achieving an average Clifford gate fidelity F C1 = 99.86%. Extensions of this work may enable more efficient EO two-qubit entangling gates as well as the implementation of native i -Toffoli gates in Loss-DiVincenzo single-spin qubits.
Standard universal quantum computing using exchange-only qubits typically requires three physical spins per logical qubit, leading to significant hardware overhead. Conversely, two-spin units offer higher density but rely on local magnetic field gradients for control, increasing integration complexity. In this paper, we propose a resource-efficient quantum machine learning (QML) architecture that achieves high expressibility using minimal two-spin units and Heisenberg exchange interactions alone, without any magnetic gradients. We shift the paradigm from universal gate-based control to utilizing the intrinsic, time-domain dynamics of a spin chain as a learning resource. Numerical simulations on MNIST digit classification demonstrate that the symmetry-protected constraints of isolated spin pairs are bypassed by leveraging inter-pair exchange coupling. This interference-mediated state mixing significantly enhances the expressibility of the Hilbert space. The model reaches a test-set accuracy of 90.9% +/- 0.2% over five independent seeds on the full 10,000-image MNIST test set. Under an identical linear readout, the trained quantum feature map (88.1%) clearly outperforms a classical linear baseline on the same PCA inputs (83.2%) as well as an untrained (reservoir-style) version of the same dynamics (53.0%), demonstrating that the learned, input-dependent exchange pulses implement a genuinely non-linear and trainable feature map. The protocol is also robust to experimentally relevant imperfections: accuracy remains at 89.9% under 10% quasi-static pulse-area noise and at 89.8% when every observable is estimated from 10^3 measurement shots. These findings suggest that competitive QML can be executed on the simplest possible semiconductor spin-chain hardware, bypassing the need for leakage-prone encodings or complex micro-magnet integration.