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.

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

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• Topological stabilizer models on continuous variables
• Weakly Fault-Tolerant Computation in a Quantum Error-Detecting Code
• Spin amplification in realistic systems
• Soft information decoding with superconducting qubits
• Maximal device-independent randomness in every dimension
• Comparison of spin-qubit architectures for quantum error-correcting codes
• Integrating Entanglement Purification into All-Photonic Quantum Repeaters
• Symmetry in Multi-Qubit Correlated Noise Errors Enhances Surface Code Thresholds
• Network Requirements for Distributed Quantum Computation
• Universal quantum computation via scalable measurement-free error correction
• iSwitch: QEC on Demand via In-Situ Encoding of Bare Qubits for Ion Trap Architectures
• Hardness results for decoding the surface code with Pauli noise
• Mitigating state transition errors during readout with a synchronized flux pulse
• Feedforward suppression of readout-induced faults in quantum error correction
• Q-Cluster: Quantum Error Mitigation Through Noise-Aware Unsupervised Learning
• Conceptual study of a two-layer silicon pixel detector to tag the passage of muons from cosmic sources through quantum processors
• Scalable and fault-tolerant preparation of encoded k-uniform states
• The perfect entangler spectrum as a tool to analyze crosstalk
• Robust shaped pulses for arrays of superconducting or semiconductor spin qubits with fixed Ising coupling
• Low-rank optimal control of quantum devices
• Approximate Quantum Error Correction with 1D Log-Depth Circuits
• Incoherent Approximation of Leakage in Quantum Error Correction
• GPU-Accelerated Syndrome Decoding for Quantum LDPC Codes below the 63 $\mu$s Latency Threshold
• Classical representation of local Clifford operators
• Chaos and quantum regimes in $n$-photon driven, dissipative bosonic chains
• Unfolding the Toric Code Model with Emergent Qubits
• Optimizing Compilation for Distributed Quantum Computing via Clustering and Annealing
• Logical operations with a dynamical qubit in Floquet-Bacon-Shor code
• On the interpretability of neural network decoders
• Fault-tolerant Quantum Error Correction Using a Linear Array of Emitters
• Simulated-annealing decoder for the XZZX code with greedy-matching initialization
• From equivalent Lagrangians to inequivalent open quantum system dynamics
• Quantum-optical reset with classical memory
• Passive leakage removal unit based on a disordered transmon array
• Neural Decoders for Universal Quantum Algorithms
• Reduced Sampling Overhead for Probabilistic Error Cancellation by Pauli Error Propagation
• Quantum Error Correction with Superpositions of Squeezed Fock States
• Benchmarking non-Clifford gates using only Pauli twirling group
• Clifford Transformations for Fermionic Quantum Systems: From Paulis to Majoranas to Fermions
• Decay of transmon qubit in a broadband one-dimensional cavity
• Fault-Tolerant Encoding of Logical Qudits in Spin Systems
• Efficient learning and optimizing non-Gaussian correlated noise in digitally controlled qubit systems
• Circuit-level fault tolerance of cat codes
• Single-Period Floquet Control of Bosonic Codes with Quantum Lattice Gates
• Effects of valley splitting on resonant-tunneling readout of spin qubits
• Bayesian inference of general noise-model parameters from the syndrome statistics of surface codes
• Snowflake: A Distributed Streaming Decoder
• Systematic Characterization of Transmon Qubit Stability with Thermal Cycling
• 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
• Non-Topological Edge-Localized Yu-Shiba-Rusinov States in CrBr${}_3$/NbSe${}_2$ Heterostructures
• Qubit-efficient quantum combinatorial optimization solver
• Stabilizer codes for Heisenberg-limited many-body Hamiltonian estimation