High-threshold and low-overhead fault-tolerant quantum memory

Abstract

Quantum error correction becomes a practical possibility only if the physical error rate is below a threshold value that depends on a particular quantum code, syndrome measurement circuit, and decoding algorithm. Here we present an end-to-end quantum error correction protocol that implements fault-tolerant memory based on a family of LDPC codes with a high encoding rate that achieves an error threshold of $0.8\%$ for the standard circuit-based noise model. This is on par with the surface code which has remained an uncontested leader in terms of its high error threshold for nearly 20 years. The full syndrome measurement cycle for a length-$n$ code in our family requires $n$ ancillary qubits and a depth-7 circuit composed of nearest-neighbor CNOT gates. The required qubit connectivity is a degree-6 graph that consists of two edge-disjoint planar subgraphs. As a concrete example, we show that 12 logical qubits can be preserved for nearly one million syndrome cycles using 288 physical qubits in total, assuming the physical error rate of $0.1\%$. We argue that achieving the same level of error suppression on 12 logical qubits with the surface code would require nearly 3000 physical qubits. Our findings bring demonstrations of a low-overhead fault-tolerant quantum memory within the reach of near-term quantum processors.

numerical results are revised after fixing a bug in the simulation software

References in corpus (38)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Topological quantum memory
• Suppressing quantum errors by scaling a surface code logical qubit
• Elucidating Reaction Mechanisms on Quantum Computers
• Realizing Repeated Quantum Error Correction in a Distance-Three Surface Code
• Building logical qubits in a superconducting quantum computing system
• Controlling the spontaneous emission of a superconducting transmon qubit
• High threshold universal quantum computation on the surface code
• Sparse Graph Codes for Quantum Error-Correction
• The Future of Quantum Computing with Superconducting Qubits
• Realization of an Error-Correcting Surface Code with Superconducting Qubits
• A universal gate for fixed-frequency qubits via a tunable bus
• Quantum LDPC codes with positive rate and minimum distance proportional to n^{1/2}
• Quantum Computer Systems for Scientific Discovery
• Impact of ionizing radiation on superconducting qubit coherence
• Laser-annealing Josephson junctions for yielding scaled-up superconducting quantum processors
• Demonstration of weight-four parity measurements in the surface code architecture
• Protecting superconducting qubits from external sources of loss and heat
• Tradeoffs for reliable quantum information storage in 2D systems
• Decoding Across the Quantum LDPC Code Landscape
• Tunable Coupling Architecture for Fixed-frequency Transmons
• Logical-qubit operations in an error-detecting surface code
• Balanced Product Quantum Codes
• Constructions and Noise Threshold of Hyperbolic Surface Codes
• Quantum Algorithm for Obtaining the Energy Spectrum of Molecular Systems
• Quantum "hyperbicycle" low-density parity check codes with finite rate
• Low-overhead fault-tolerant quantum computing using long-range connectivity
• Quantum accuracy threshold for concatenated distance-3 codes
• Constant-overhead quantum error correction with thin planar connectivity
• High contrast qubit interactions using multimode cavity QED
• Fault-tolerant quantum computing with color codes
• Noise Analysis for High-Fidelity Quantum Entangling Gates in an Anharmonic Linear Paul Trap
• TLS Dynamics in a Superconducting Qubit Due to Background Ionizing Radiation
• Algebraic Methods for Quantum Codes on Lattices
• Quantifying nonlocality: how outperforming local quantum codes is expensive
• Errors in stimulated-Raman-induced logic gates in ${}^{133}$Ba${}^{+}$
• Spacetime codes of Clifford circuits
• Quantum two-block group algebra codes

Cited by in corpus (185)

• Logical quantum processor based on reconfigurable atom arrays
• Quantum error correction below the surface code threshold
• IBM Quantum Computers: Evolution, Performance, and Future Directions
• A tweezer array with 6100 highly coherent atomic qubits
• Operating semiconductor quantum processors with hopping spins
• Universal quantum operations and ancilla-based readout for tweezer clocks
• High-coherence superconducting qubits made using industry-standard, advanced semiconductor manufacturing
• Decoding algorithms for surface codes
• Combining quantum processors with real-time classical communication
• A universal neutral-atom quantum computer with individual optical addressing and non-destructive readout
• Hunting for quantum-classical crossover in condensed matter problems
• Beyond NISQ: The Megaquop Machine
• Towards quantum computing for clinical trial design and optimization: A perspective on new opportunities and challenges
• Modular quantum processor with an all-to-all reconfigurable router
• Entangling four logical qubits beyond break-even in a nonlocal code
• Constructions and performance of hyperbolic and semi-hyperbolic Floquet codes
• Low-Overhead Transversal Fault Tolerance for Universal Quantum Computation
• Scalable Networking of Neutral-Atom Qubits: Nanofiber-Based Approach for Multiprocessor Fault-Tolerant Quantum Computer
• Benchmarking digital quantum simulations above hundreds of qubits using quantum critical dynamics
• Creating entangled logical qubits in the heavy-hex lattice with topological codes
• Localized statistics decoding for quantum low-density parity-check codes
• Toward a 2D Local Implementation of Quantum LDPC Codes
• High-fidelity single-spin shuttling in silicon
• High-rate quantum LDPC codes for long-range-connected neutral atom registers
• Quantum Natural Language Processing
• Architecture for fast implementation of qLDPC codes with optimized Rydberg gates
• LDPC-cat codes for low-overhead quantum computing in 2D
• A Spin-Optical Quantum Computing Architecture
• Hybrid Stabilizer Matrix Product Operator
• Demonstration of low-overhead quantum error correction codes
• Blueprint for all-to-all connected superconducting spin qubits
• Towards early fault tolerance on a 2$\times$N array of qubits equipped with shuttling
• Simultaneous Discovery of Quantum Error Correction Codes and Encoders with a Noise-Aware Reinforcement Learning Agent
• Fault-tolerant quantum algorithms for quantum molecular systems: A survey
• Compact quantum algorithms for time-dependent differential equations
• Many-hypercube codes: High-rate quantum error-correcting codes for high-performance fault-tolerant quantum computing
• Constant-Overhead Fault-Tolerant Bell-Pair Distillation using High-Rate Codes
• Long-Range $ZZ$ Interaction via Resonator-Induced Phase in Superconducting Qubits
• Data-driven decoding of quantum error correcting codes using graph neural networks
• Pauli path simulations of noisy quantum circuits beyond average case
• Machine-Learning-Assisted Photonic Device Development: A Multiscale Approach from Theory to Characterization
• Efficient Formal Verification of Quantum Error Correcting Programs
• Faster quantum chemistry simulations on a quantum computer with improved tensor factorization and active volume compilation
• Learning How to Dynamically Decouple
• Quantum Error Correction resilient against Atom Loss
• Distance-preserving stabilizer measurements in hypergraph product codes
• A Toffoli Gate Decomposition via Echoed Cross-Resonance Gates
• Lowering Connectivity Requirements For Bivariate Bicycle Codes Using Morphing Circuits
• Erasure Decoding for Quantum LDPC Codes via Belief Propagation with Guided Decimation
• Comparative study of quantum error correction strategies for the heavy-hexagonal lattice
• Cross-cap defects and fault-tolerant logical gates in the surface code and the honeycomb Floquet code
• Fault-tolerant hyperbolic Floquet quantum error correcting codes
• Fault-tolerant logical measurements via homological measurement
• Stabilizer Entanglement Distillation and Efficient Fault-Tolerant Encoders
• Non-Local Multi-Qubit Quantum Gates via a Driven Cavity
• Improved Belief Propagation Decoding Algorithms for Surface Codes
• Partial Syndrome Measurement for Hypergraph Product Codes
• Linear-optical quantum computation with arbitrary error-correcting codes
• Graph Neural Networks for Enhanced Decoding of Quantum LDPC Codes
• A quantum computing concept for 1-D elastic wave simulation with exponential speedup
• Modeling error correction with Lindblad dynamics and approximate channels
• Quantum Kernel Learning for Small Dataset Modeling in Semiconductor Fabrication: Application to Ohmic Contact
• Time-Efficient Logical Operations on Quantum Low-Density Parity Check Codes
• Hybrid cat-transmon architecture for scalable, hardware-efficient quantum error correction
• Teleportation and Entanglement Swapping of Continuous Quantum Variables of Microwave Radiation
• Fault-tolerant compiling of classically hard IQP circuits on hypercubes
• Resource Analysis of Low-Overhead Transversal Architectures for Reconfigurable Atom Arrays
• Generalized toric codes on twisted tori for quantum error correction
• Spatially-Coupled QLDPC Codes
• Fault-Tolerant Stabilizer Measurements in Surface Codes with Three-Qubit Gates
• Quantum error correction for long chains of trapped ions
• Quantum computing for genomics: conceptual challenges and practical perspectives
• Quantum State Transfer via a Multimode Resonator
• Lift-Connected Surface Codes
• Demonstrating quantum error mitigation on logical qubits
• Low-overhead fault-tolerant quantum computation by gauging logical operators
• Efficient Frequency Allocation for Superconducting Quantum Processors Using Improved Optimization Techniques
• Network Operations Scheduling for Distributed Quantum Computing
• Adaptive Syndrome Extraction
• A spinless spin qubit
• Accelerating two-dimensional electronic spectroscopy simulations with a probe qubit protocol
• A Universal Circuit Set Using the $S_3$ Quantum Double
• Modular Architectures and Entanglement Schemes for Error-Corrected Distributed Quantum Computation
• Universal quantum processors in spin systems via robust local pulse sequences
• Classical product code constructions for quantum Calderbank-Shor-Steane codes
• Minimal Time Robust Control for Two Superconducting Qubits
• Low-Fidelity Entanglement Distillation with FIMAX
• Qudit vs. Qubit: Simulated performance of error correction codes in higher dimensions
• Non-Clifford and parallelizable fault-tolerant logical gates on constant and almost-constant rate homological quantum LDPC codes via higher symmetries
• Quantum error detection in qubit-resonator star architecture
• Synchronization for Fault-Tolerant Quantum Computers
• Calibrating quantum gates up to 52 qubits in a superconducting processor
• Coprime Bivariate Bicycle Codes and Their Layouts on Cold Atoms
• Reliable Quantum Memories with Unreliable Components
• Security Analysis of Ensemble-Based Quantum Token Protocol Under Advanced Attacks
• Exact results on finite size corrections for surface codes tailored to biased noise
• LSQCA: Resource-Efficient Load/Store Architecture for Limited-Scale Fault-Tolerant Quantum Computing
• Ensemble-Based Quantum Token Protocol Benchmarked on IBM Quantum Processors
• Degenerate quantum erasure decoding
• Heralding entangled optical photons from a microwave quantum processor
• Refining resource estimation for the quantum computation of vibrational molecular spectra through Trotter error analysis
• Magic Mirror on the Wall, How to Benchmark Quantum Error Correction Codes, Overall ?
• Logical Error Rates for the Surface Code Under a Mixed Coherent and Stochastic Circuit-Level Noise Model Inspired by Trapped Ions
• Low-loss liquid metal interconnects for superconducting quantum circuits
• Low-depth quantum error correction via three-qubit gates in Rydberg atom arrays
• Thresholds for post-selected quantum error correction from statistical mechanics
• Logical qubits with erasure conversion using metastable neutral atoms
• Distributed quantum error correction based on hyperbolic Floquet codes
• Quantum low-density parity-check codes for erasure-biased atomic quantum processors
• Sequency Hierarchy Truncation (SeqHT) for Adiabatic State Preparation and Time Evolution in Quantum Simulations
• Logical entanglement distribution between distant 2D array qubits
• Flying-cat parity checks for quantum error correction
• High-threshold, low-overhead and single-shot decodable fault-tolerant quantum memory
• Generalizing the matching decoder for the Chamon code
• On the energy barrier of hypergraph product codes
• Fault-tolerant quantum computation with constant overhead for general noise
• Cavity polariton blockade for non-local entangling gates with trapped atoms
• Qudit low-density parity-check codes
• Feasibility of Logical Bell State Generation in Memory Assisted Quantum Networks
• Universal graph representation of stabilizer codes
• High-speed and high-connectivity two-qubit gates in long chains of trapped ions
• Mitigating cosmic ray-like correlated events with a modular quantum processor
• Prospects for NMR Spectral Prediction on Fault-Tolerant Quantum Computers
• Low-density parity-check representation of fault-tolerant quantum circuits
• Achieving computational gains with quantum error-correction primitives: Generation of long-range entanglement enhanced by error detection
• New Quantum MDS Codes with Flexible Parameters from Hermitian Self-Orthogonal GRS Codes
• Non-local resources for error correction in quantum LDPC codes
• Non-Abelian Self-Correcting Quantum Memory and Transversal Non-Clifford Gate beyond the $n^{1/3}$ Distance Barrier
• Hybrid spin-phonon architecture for scalable solid-state quantum nodes
• Parallel Logical Measurements via Quantum Code Surgery
• Omnidirectional shuttling to avoid valley excitations in Si/SiGe quantum wells
• Generalized Parity Measurements and Efficient Large Multi-component Cat State Preparation with Quantum Signal Processing
• Geometrical Approach to Logical Qubit Fidelities of Neutral Atom CSS Codes
• Experimental measurement and a physical interpretation of quantum shadow enumerators
• Comparing Algorithms for Loading Classical Datasets into Quantum Memory
• Scalable Low-overhead Superconducting Non-local Coupler with Exponentially Enhanced Connectivity
• QUITS: A modular Qldpc code circUIT Simulator
• Lattice Surgery Compilation Beyond the Surface Code
• Hamiltonian Learning via Inverse Physics-Informed Neural Networks
• Tunable Hybrid-Mode Coupler Enabling Strong Interactions between Transmons at Centimeter-Scale Distance
• Performance-centric roadmap for building a superconducting quantum computer
• Towards self-correcting quantum codes for neutral atom arrays
• Magic tricycles: Efficient magic state generation with finite block-length quantum LDPC codes
• Accurate Leakage Speculation for Quantum Error Correction
• On The Stabilizer Formalism And Its Generalization
• Quantum LDPC codes from intersecting subsets
• Digital-Analog Simulations of Schrödinger Cat States in the Dicke-Ising Model
• Fully Parallelized BP Decoding for Quantum LDPC Codes Can Outperform BP-OSD
• All-to-all connectivity of Rydberg-atom-based quantum processors with messenger qubits
• Quantum Simulation of Nuclear Dynamics in First Quantization
• Reduced Sampling Overhead for Probabilistic Error Cancellation by Pauli Error Propagation
• Diversity Methods for Improving Convergence and Accuracy of Quantum Error Correction Decoders Through Hardware Emulation
• Informed Dynamic Scheduling for QLDPC Codes
• Feedforward suppression of readout-induced faults in quantum error correction
• Protocol for Purifying Noisy Preparation and Measurements of Qubits
• GPU-Accelerated Syndrome Decoding for Quantum LDPC Codes below the 63 $\mu$s Latency Threshold
• Quantum Gates via Dynamical Decoupling of Central Qubit on IBMQ and 15NV Center in Diamond
• Transversal architecture for megaquop-scale quantum simulation with neutral atoms
• Color code with a logical control-$S$ gate using transversal $T$ rotations
• Neural Decoders for Universal Quantum Algorithms
• Logical operations with a dynamical qubit in Floquet-Bacon-Shor code
• Subsystem many-hypercube codes: High-rate concatenated codes with low-weight syndrome measurements
• Quantum approximate optimization of finite-state bosonic systems
• Quantum memory based on concatenating surface codes and quantum Hamming codes
• qSIEVE: Efficient qLDPC Memory via Systolic Movement in Atom Arrays
• Decoding Correlated Errors in Quantum LDPC Codes
• Quantum Non-Demolition Measurements and Leggett-Garg inequality
• A graph-based approach to entanglement entropy of quantum error correcting codes
• Clifford Transformations for Fermionic Quantum Systems: From Paulis to Majoranas to Fermions
• Entanglemons: Cross-platform protected qubits from entanglement
• Improving the accuracy of circuit quantization using the electromagnetic properties of superconductors
• Fully Quantum Algorithm for the 1-dimensional linear Lattice Boltzmann Method
• Symmetry-enriched topological order and quasifractonic behavior in ${\mathbb{Z}}_N$ stabilizer codes
• Streaming Belief Propagation on Mixed-Alphabet Tanner Graphs for Practical Quantum Memory
• Quantum Error Correction Codes for Truncated SU(2) Lattice Gauge Theories
• Error Resilience of Fracton Codes and Near Saturation of Code-Capacity Threshold in Three Dimensions
• Exact and Efficient Stabilizer Simulation of Thermal-Relaxation Noise for Quantum Error Correction
• Decoder Dependence in Surface-Code Threshold Estimation under Digitized Hybrid Continuous-Variable and Discrete Noise
• Quantum-Enhanced Neural Exchange-Correlation Functionals
• Comparison of spin-qubit architectures for quantum error-correcting codes
• General many-body entanglement swapping protocol: opportunities for distributed quantum computing
• Roughening Transition in Quantum Circuits
• Kramers-protected hardware-efficient error correction with Andreev spin qubits
• Network Requirements for Distributed Quantum Computation
• iSwitch: QEC on Demand via In-Situ Encoding of Bare Qubits for Ion Trap Architectures