Quantum Computing with Very Noisy Devices

Abstract

In theory, quantum computers can efficiently simulate quantum physics, factor large numbers and estimate integrals, thus solving otherwise intractable computational problems. In practice, quantum computers must operate with noisy devices called ``gates'' that tend to destroy the fragile quantum states needed for computation. The goal of fault-tolerant quantum computing is to compute accurately even when gates have a high probability of error each time they are used. Here we give evidence that accurate quantum computing is possible with error probabilities above 3% per gate, which is significantly higher than what was previously thought possible. However, the resources required for computing at such high error probabilities are excessive. Fortunately, they decrease rapidly with decreasing error probabilities. If we had quantum resources comparable to the considerable resources available in today's digital computers, we could implement non-trivial quantum computations at error probabilities as high as 1% per gate.

47 pages

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• Statistical Mechanics of Monitored Dissipative Random Circuits
• Uniaxial dynamical decoupling for an open quantum system
• Decoding Merged Color-Surface Codes and Finding Fault-Tolerant Clifford Circuits Using Solvers for Satisfiability Modulo Theories
• Correcting low-frequency noise with continuous measurement
• Greenberger-Horne-Zeilinger state protocols for fully connected qubit networks
• Ion-trap quantum information processing: experimental status
• Conditions for Equivalent Noise Sensitivity of Geometric and Dynamical Quantum Gates
• Measurement-free fault-tolerant logical zero-state encoding of the distance-three nine-qubit surface code in a one-dimensional qubit array
• Bacon-Shor code with continuous measurement of non-commuting operators
• Actis: A Strictly Local Union-Find Decoder
• Scalable noise characterization of syndrome-extraction circuits with averaged circuit eigenvalue sampling
• Robust measurement of wave function topology on NISQ quantum computers
• Implications of Electronics Constraints for Solid-State Quantum Error Correction and Quantum Circuit Failure Probability
• Constant depth fault-tolerant Clifford circuits for multi-qubit large block codes
• Stability thresholds and calculation techniques for fast entangling gates on trapped ions
• Benchmarking Quantum State Transfer on Quantum Devices using Spatio-Temporal Steering
• Comparative study of quantum error correction strategies for the heavy-hexagonal lattice
• Optimal correction of concatenated fault-tolerant quantum codes
• Computation with Coherent States via Teleportations to and from a Quantum Bus
• Toward a more economical cluster state quantum computation
• Scalable Quantum Networks based on Few-Qubit Registers
• Feasibility of single-shot realizations of conditional three-qubit gates in exchange-coupled qubit arrays with local control
• Ultra-fast two-qubit ion gate using sequences of resonant pulses
• Combating quasiparticle poisoning with multiple Majorana fermions in a periodically-driven quantum wire
• Extracting randomness from magic quantum states
• Nonstabilizerness in open XXZ spin chains: Universal scaling and dynamics
• Exponential Families for Bayesian Quantum Process Tomography
• Mitigating errors in logical qubits
• Generalised state spaces and non-locality in fault tolerant quantum computing schemes
• Contextual bound states for qudit magic state distillation
• A tunable rf SQUID manipulated as flux and phase qubit
• Eliminating qubit type cross-talk in the $\text{omg}$ protocol
• Parity-encoding-based quantum computing with Bayesian error tracking
• Gottesman Types for Quantum Programs
• Randomized Benchmarking of Clifford Operators
• Leveraging Qubit Loss Detection in Fault Tolerant Quantum Algorithms
• Quantum dot state initialization by control of tunneling rates
• Physical requirements for scaling up network-based biocomputation
• Concatenation Schemes for Topological Fault-tolerant Quantum Error Correction
• Upper bounds on fault tolerance thresholds of noisy Clifford-based quantum computers
• Robust engineering of maximally entangled states by identical particle interferometry
• Parallel syndrome extraction with shared flag qubits for Calderbank-Shor-Steane codes of distance three
• Quasi-inversion of quantum and classical channels in finite dimensions
• Self-correction in Wegner's 3D Ising lattice gauge theory
• Limitations of Classically-Simulable Measurements for Quantum State Discrimination
• Low-temperature environments for quantum computation and quantum simulation
• Improving the performance of quantum approximate optimization for preparing non-trivial quantum states without translational symmetry
• Simulation of Grover's quantum search algorithm in a Ising nuclear spin chain quantum computer with first and second nearest neighbour couplings
• Using three-partite GHZ states for partial quantum error-detection in entanglement-based protocols
• Improving threshold for fault-tolerant color code quantum computing by flagged weight optimization
• New Limits on Fault-Tolerant Quantum Computation
• Multi-Qubit Joint Measurements in Circuit QED: Stochastic Master Equation Analysis
• Fault-tolerant conversion between adjacent Reed-Muller quantum codes based on gauge fixing
• Diagnostics of quantum-gate coherences via end-point-measurement statistics
• Coherent quantum effects through dispersive bosonic media
• Requirements for fault-tolerant quantum computation with cavity-QED-based atom-atom gates mediated by a photon with a finite pulse length
• Dynamically corrected gates for qubits with always-on Ising couplings: Error model and fault-tolerance with the toric code
• Voltage-Current curves for small Josephson junction arrays
• Variational Quantum Algorithms for Differential Equations on a Noisy Quantum Computer
• Quantumness and speedup limit of a qubit under transition frequency modulation
• Fault-tolerant linear optics quantum computation by error-detecting quantum state transfer
• Detrimental Decoherence
• Accurate Sampling with Noisy Forces from Approximate Computing
• Trapped-Ion Entangling Gates Robust Against Qubit Frequency Errors
• Error-correcting one-way quantum computation with global entangling gates
• Quantum error correction benchmarks for continuous weak parity measurements
• Message passing in fault tolerant quantum error correction
• Low-overhead magic state distillation with color codes
• A quantum computing concept for 1-D elastic wave simulation with exponential speedup
• Geometric Phase: a Diagnostic Tool for Entanglement
• Quantum process tomography of a Mølmer-Sørensen gate via a global beam
• Quantum Gates Robust to Secular Amplitude Drifts
• Low-depth random Clifford circuits for quantum coding against Pauli noise using a tensor-network decoder
• Fidelity-dissipation relations in quantum gates
• Concatenate codes, save qubits
• Trapped-ion quantum error-correcting protocols using only global operations
• Structured Error Recovery for Codeword-Stabilized Quantum Codes
• Many-Body Physics with Trapped Ions
• Qubit Coherent Control with Squeezed Light Fields
• An analytical error model for quantum computer simulation
• Fault-Tolerant Thresholds for Encoded Ancillae with Homogeneous Errors
• Accuracy threshold for postselected quantum computation
• High-fidelity two-qubit gates via dynamical decoupling of local 1/f noise at optimal point
• Edge local complementation for logical cluster states
• Clifford operations and homological codes for rotors and oscillators
• Efficient fault-tolerant code switching via one-way transversal CNOT gates
• Sculpting bosonic states with arithmetic subtractions
• Small Codes for Magic State Distillation
• Entanglement Generation by Communication using Phase-Squeezed Light with Photon Loss
• Reliable channel-adapted error correction: Bacon-Shor code recovery from amplitude damping
• Experimental Implementation of a Codeword Stabilized Quantum Code
• Onset of scrambling as a dynamical transition in tunable-range quantum circuits
• Bounding Fault-Tolerant Thresholds for Purification and Quantum Computation
• Fault-Tolerant Quantum Computation
• Hybrid magic state distillation for universal fault-tolerant quantum computation
• A lower bound on the space overhead of fault-tolerant quantum computation
• Bespoke Pulse Design for Robust Rapid Two-Qubit Gates with Trapped Ions
• Generation of graph-state streams
• High-Threshold Low-Overhead Fault-Tolerant Classical Computation and the Replacement of Measurements with Unitary Quantum Gates
• Quantum memory at an eigenstate phase transition in a weakly chaotic model
• Topological error correction with a Gaussian cluster state
• Experimental demonstration of Pauli-frame randomization on a superconducting qubit
• The role of quantum measurements in physical processes and protocols
• Classically Replaceable Operations
• Lightcone Bounds for Quantum Circuit Mapping via Uncomplexity
• Fast Evolution of Single Qubit Gate in Non-Adiabatic Geometric Quantum Computing
• Efficient self-consistent learning of gate set Pauli noise
• Quantitative Treatment of Decoherence
• Cat-state generation and stabilization for a nuclear spin through electric quadrupole interaction
• Explicit error-correction scheme and code distance for bosonic codes with rotational symmetry
• Mesoscopic entanglement of noninteracting qubits using collective spontaneous emission
• Fault-tolerant ancilla preparation and noise threshold lower bounds for the 23-qubit Golay code
• Realization of Constant-Depth Fan-Out with Real-Time Feedforward on a Superconducting Quantum Processor
• An introduction to reliable quantum computation
• Quantum Circuit Discovery for Fault-Tolerant Logical State Preparation with Reinforcement Learning
• Adaptive Syndrome Extraction
• Experimental realization of quantum non-Markovianity through the convex mixing of Pauli semigroups on an NMR quantum processor
• Normalizer circuits and a Gottesman-Knill theorem for infinite-dimensional systems
• Advancing Quantum Otto Engine Performance via Additional Magnetic Field and Effective Negative Temperature
• Normalizer Circuits and Quantum Computation
• Fault-tolerant quantum computing with the parity code and noise-biased qubits
• Classes of topological qubits from low-dimensional quantum spin systems
• Weyl semimetallic state with antiferromagnetic order in Rashba-Hubbard model
• The impact of classical electronics constraints on a solid-state logical qubit memory
• Quantum error correction in the NISQ regime for sequential quantum computing
• Generating and verifying graph states for fault-tolerant topological measurement-based quantum computing in 2D optical lattices
• Reducing Quantum Error Correction Overhead with Versatile Flag-Sharing Syndrome Extraction Circuits
• Error correctable efficient quantum homomorphic encryption using Calderbank-Shor-Steane codes
• Estimating the bias of CX gates via character randomized benchmarking
• Effect of Ohmic environment on optimally controlled flux-biased phase qubit
• Generalized Number-Phase Lattice Encoding of a Bosonic Mode for Quantum Error Correction
• Susceptibility of Trapped-Ion Qubits to Low-Dose Radiation Sources
• Logical qubits with erasure conversion using metastable neutral atoms
• Demonstration of teleportation-based error correction in the IBM quantum computer
• Distance-four quantum codes with combined postselection and error correction
• On the Structure of Protocols for Magic State Distillation
• The resource cost of large scale quantum computing
• Harnessing Quantum Computing for Energy Materials: Opportunities and Challenges
• Fast quantum gate via Feshbach-Pauli blocking in a nanoplasmonic trap
• Computational quantum-classical boundary of complex and noisy quantum systems
• A Theory of Direct Randomized Benchmarking
• Improved performance of the Bacon-Shor code with Steane's syndrome extraction method
• Quantum noise modeling through Reinforcement Learning
• Quantum computation with noisy operations
• Postselection threshold against biased noise
• The simulation of distributed quantum algorithms
• Thresholds for post-selected quantum error correction from statistical mechanics
• Readout Error Mitigation for Mid-Circuit Measurements and Feedforward
• Gleipnir: Toward Practical Error Analysis for Quantum Programs (Extended Version)
• Quantum teleportation and computation with Rydberg atoms in an optical lattice
• Invested and Potential Magic Resources in Measurement-Based Quantum Computation
• Superconducting qubits in the millions: the potential and limitations of modularity
• Optimizing the Frequency of Quantum Error Correction using the [[7,1,3]] Steane Code
• A 3D lattice defect and efficient computations in topological MBQC
• Low-density parity-check representation of fault-tolerant quantum circuits
• Phase-controlled robust tripartite quantum entanglement in cavity-magnon optomechanics
• Harnessing Coding Theory for Reliable Network Quantum Communication
• Logical channel for heralded and pure loss with the Gottesman-Kitaev-Preskill code
• The Lie Algebra of XY-mixer Topologies and Warm Starting QAOA for Constrained Optimization
• Real-time decoding of stabilizer measurements in a bit-flip code
• Competition of decoherence and quantum speed limits for quantum-gate fidelity in the Jaynes-Cummings model
• Learning a quantum computer's capability
• Resource comparison of two surface code implementations of small angle Z rotations
• Single-shot quantum error correction with the three-dimensional subsystem toric code
• Fidelity of the Kitaev honeycomb model under a quench
• Syndrome decoding by quantum approximate optimization
• 1D Error Correcting Code for Majorana Qubits
• Error metric for non-trace-preserving quantum operations
• Fibonacci schemes of fault-tolerant quantum computation
• Error Channels and the Threshold for Fault-tolerant Quantum Computation
• An upper bound on quantum fault tolerant thresholds
• Transversal CNOT gate with multi-cycle error correction
• A note on threshold theorem of fault-tolerant quantum computation
• Spontaneous Raman scattering out of a metastable atomic qubit
• Corrupted sensing quantum state tomography
• Approaches to Quantum Error Correction
• Distributing Quantum Computations, Shot-wise
• A flow-map model for analyzing pseudothresholds in fault-tolerant quantum computing
• Finding the disjointness of stabilizer codes is NP-complete
• How Quantum Computers Can Fail
• Parallel Logical Measurements via Quantum Code Surgery
• Characterization of a quantum bus between two driven qubits
• Quantum Internet: Resource Estimation for Entanglement Routing
• GHZ-like states in the Qubit-Qudit Rabi Model
• On the Hardness of Measuring Magic
• Suppression of effective noise in Hamiltonian simulations
• Floquet Dynamical Decoupling at Zero Bias
• Third law of thermodynamics and the scaling of quantum computers
• Quantum Noise Sensing by generating Fake Noise
• An Upper Bound to the Number of Gates on Single Qubit within One Error-Correction Period of Quantum Computation
• Averaging gate approximation error and performance of Unitary Coupled Cluster ansatz in Pre-FTQC Era
• Quantum Computation and Communication in Bosonic Systems
• Enhancement of non-Stabilizerness within Indefinite Causal Order
• Noise tolerance via reinforcement: Learning a reinforced quantum dynamics
• A graph-state based synthesis framework for Clifford isometries
• Full quantum treatment of Rabi oscillation driven by a pulse train and its application in ion-trap quantum computation
• Quantum network protocol for qudits with use of quantum repeaters and Pauli Z-type operational errors
• Performance and Error Analysis of Knill's Postselection Scheme in a Two-Dimensional Architecture
• Structural encoding with classical codes for computational-basis bit-flip correction in the early fault-tolerant regime
• Flexible Fault Tolerant Gate Gadgets
• Subsystem many-hypercube codes: High-rate concatenated codes with low-weight syndrome measurements
• Non-Markovianity Benefits Quantum Dynamics Simulation
• Gottesman-Knill Limit on One-way Communication Complexity: Tracing the Quantum Advantage down to Magic Resources
• Quantum Computing Using Crossed Atomic Beams
• Fermionic Averaged Circuit Eigenvalue Sampling
• Feedforward suppression of readout-induced faults in quantum error correction
• Arbitrarily large violations of non-contextuality in single mode photon states with positive Wigner function
• Circuit-level fault tolerance of cat codes
• Optimized Clifford Noise Reduction: Theory, Simulations and Experiments
• Estimating Bell Diagonal states with separable measurements
• On the interpretability of neural network decoders
• Optical Quantum Computing
• Quantum Error Correction Codes for Truncated SU(2) Lattice Gauge Theories
• Speeding up Lindblad dynamics via time-rescaling engineering
• Channel Polarization of Two-dimensional-input Quantum Symmetric Channels
• Fault-tolerant and secure long-distance quantum communication via uncorrectable-error-injection
• Between Shor and Steane: A unifying construction for measuring error syndromes
• Notes on distinguishability of postselected computations
• Bayesian inference of general noise-model parameters from the syndrome statistics of surface codes
• Snowflake: A Distributed Streaming Decoder