Suppressing quantum errors by scaling a surface code logical qubit

Abstract

Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical qubits, where increasing the number of physical qubits enhances protection against physical errors. However, introducing more qubits also increases the number of error sources, so the density of errors must be sufficiently low in order for logical performance to improve with increasing code size. Here, we report the measurement of logical qubit performance scaling across multiple code sizes, and demonstrate that our system of superconducting qubits has sufficient performance to overcome the additional errors from increasing qubit number. We find our distance-5 surface code logical qubit modestly outperforms an ensemble of distance-3 logical qubits on average, both in terms of logical error probability over 25 cycles and logical error per cycle ($2.914\%\pm 0.016\%$ compared to $3.028\%\pm 0.023\%$). To investigate damaging, low-probability error sources, we run a distance-25 repetition code and observe a $1.7\times 10^{-6}$ logical error per round floor set by a single high-energy event ($1.6\times 10^{-7}$ when excluding this event). We are able to accurately model our experiment, and from this model we can extract error budgets that highlight the biggest challenges for future systems. These results mark the first experimental demonstration where quantum error correction begins to improve performance with increasing qubit number, illuminating the path to reaching the logical error rates required for computation.

arXiv commentMain text: 6 pages, 4 figures. v2: Update author list, references, Fig. S12, Table IV

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• Effect of Etching Methods on Dielectric Losses in Transmons
• Parallel Logical Measurements via Quantum Code Surgery
• Optimizing the frequency positioning of tunable couplers in a circuit QED processor to mitigate spectator effects on quantum operations
• Geometric Quantum Gates of Non-closed Paths Under Counterdiabatic Driving
• Topological Degeneracy Induced Flat Bands in two-Dimensional Holed Systems
• A cat qubit stabilization scheme using a voltage biased Josephson junction
• Flux-Trapping Fluxonium Qubit
• Thermal masses and trapped-ion quantum spin models: a self-consistent approach to Yukawa-type interactions in the $\lambda {\varphi }^4$ model
• Error Crafting in Mixed Quantum Gate Synthesis
• Exact diagonalization study of double quantum dots in parallel geometry in zero-bandwidth limit
• Unified Architecture for Quantum Lookup Tables
• Performance-centric roadmap for building a superconducting quantum computer
• Break-even point of the quantum repetition code
• Leakage Mobility in Superconducting Qubits as a Leakage Reduction Unit
• Error mitigation of entangled states using brainbox quantum autoencoders
• Towards self-correcting quantum codes for neutral atom arrays
• Generating Compilers for Qubit Mapping and Routing
• Overhead in Quantum Circuits with Time-Multiplexed Qubit Control
• Mitigating Measurement Crosstalk via Pulse Shaping
• Investigation of tantalum films growth for coplanar resonators with internal quality factors above ten million
• Topological stabilizer models on continuous variables
• Noise cross-correlations from single-shot measurements
• Entanglement dynamics and performance of two-qubit gates for superconducting qubits under non-Markovian effects
• Fault-tolerant interfaces for modular quantum computing on diverse qubit platforms
• Optimal number of stabilizer measurement rounds in an idling surface code patch
• Mitigating Errors in Analog Quantum Simulation by Hamiltonian Reshaping or Hamiltonian Rescaling
• Accurate Leakage Speculation for Quantum Error Correction
• Concurrent Fermionic Simulation Gate
• Experimental measurement and a physical interpretation of quantum shadow enumerators
• Type-Based Verification of Connectivity Constraints in Lattice Surgery
• Measurement Schemes for Quantum Linear Equation Solvers
• Error-mitigated initialization of surface codes with non-Pauli stabilizers
• Error-mitigated Geometric Quantum Control over an Oscillator
• Suppressing decoherence in quantum state transfer with unitary operations
• Geometrical Approach to Logical Qubit Fidelities of Neutral Atom CSS Codes
• Granular Aluminum kinetic inductance nonlinearity
• Generalized Parity Measurements and Efficient Large Multi-component Cat State Preparation with Quantum Signal Processing
• High-fidelity initialization a logical qubit with multiple injections
• No-go theorem for environment-assisted invariance in non-unitary dynamics
• Fault-tolerant Quantum Error Correction Using a Linear Array of Emitters
• Circuit-level fault tolerance of cat codes
• Reduced Sampling Overhead for Probabilistic Error Cancellation by Pauli Error Propagation
• Approximate Quantum Error Correction with 1D Log-Depth Circuits
• Hardness results for decoding the surface code with Pauli noise
• Efficient learning and optimizing non-Gaussian correlated noise in digitally controlled qubit systems
• Integrating Entanglement Purification into All-Photonic Quantum Repeaters
• Quantum Error Correction with Superpositions of Squeezed Fock States
• Universal quantum computation via scalable measurement-free error correction
• Robust shaped pulses for arrays of superconducting or semiconductor spin qubits with fixed Ising coupling
• Stabilizer codes for Heisenberg-limited many-body Hamiltonian estimation
• Non-Topological Edge-Localized Yu-Shiba-Rusinov States in CrBr${}_3$/NbSe${}_2$ Heterostructures
• Benchmarking non-Clifford gates using only Pauli twirling group
• Clifford Transformations for Fermionic Quantum Systems: From Paulis to Majoranas to Fermions
• Effects of valley splitting on resonant-tunneling readout of spin qubits
• Decay of transmon qubit in a broadband one-dimensional cavity
• Fault-Tolerant Encoding of Logical Qudits in Spin Systems
• Single-Period Floquet Control of Bosonic Codes with Quantum Lattice Gates
• Systematic Characterization of Transmon Qubit Stability with Thermal Cycling
• Network Requirements for Distributed Quantum Computation
• Spin amplification in realistic systems
• iSwitch: QEC on Demand via In-Situ Encoding of Bare Qubits for Ion Trap Architectures
• Decoder Dependence in Surface-Code Threshold Estimation under Digitized Hybrid Continuous-Variable and Discrete Noise
• The toric code under antiferromagnetic isotropic Heisenberg interactions
• Overflow-Safe Polylog-Time Parallel Minimum-Weight Perfect Matching Decoder: Toward Experimental Demonstration
• Passive leakage removal unit based on a disordered transmon array
• Weakly Fault-Tolerant Computation in a Quantum Error-Detecting Code
• From equivalent Lagrangians to inequivalent open quantum system dynamics
• Logical operations with a dynamical qubit in Floquet-Bacon-Shor code
• Feedforward suppression of readout-induced faults in quantum error correction
• Q-Cluster: Quantum Error Mitigation Through Noise-Aware Unsupervised Learning
• The perfect entangler spectrum as a tool to analyze crosstalk
• Unfolding the Toric Code Model with Emergent Qubits
• Mitigating state transition errors during readout with a synchronized flux pulse
• Classical representation of local Clifford operators
• Snowflake: A Distributed Streaming Decoder
• Maximal device-independent randomness in every dimension
• Bayesian inference of general noise-model parameters from the syndrome statistics of surface codes
• Geometric and holonomic quantum computation
• Low-rank optimal control of quantum devices
• Conceptual study of a two-layer silicon pixel detector to tag the passage of muons from cosmic sources through quantum processors
• Soft information decoding with superconducting qubits
• Qubit-efficient quantum combinatorial optimization solver
• GPU-Accelerated Syndrome Decoding for Quantum LDPC Codes below the 63 $\mu$s Latency Threshold
• Chaos and quantum regimes in $n$-photon driven, dissipative bosonic chains
• Optimizing Compilation for Distributed Quantum Computing via Clustering and Annealing
• Symmetry in Multi-Qubit Correlated Noise Errors Enhances Surface Code Thresholds
• Scalable and fault-tolerant preparation of encoded k-uniform states
• Incoherent Approximation of Leakage in Quantum Error Correction
• On the interpretability of neural network decoders
• Simulated-annealing decoder for the XZZX code with greedy-matching initialization
• Comparison of spin-qubit architectures for quantum error-correcting codes
• Quantum-optical reset with classical memory
• Neural Decoders for Universal Quantum Algorithms