Fundamental thresholds of realistic quantum error correction circuits from classical spin models
arXiv:2104.04847 · doi:10.22331/q-2022-01-05-618
Abstract
Mapping quantum error correcting codes to classical disordered statistical mechanics models and studying the phase diagram of the latter has proven a powerful tool to study the fundamental error robustness and associated critical error thresholds of leading quantum error correcting codes under phenomenological noise models. In this work, we extend this mapping to admit realistic, multi-parameter faulty quantum circuits in the description of quantum error correcting codes. Based on the underlying microscopic circuit noise model, we first systematically derive the associated strongly correlated classical spin models. We illustrate this approach in detail for the example of a quantum repetition code in which faulty stabilizer readout circuits are periodically applied. Finally, we use Monte-Carlo simulations to study the resulting phase diagram of the associated interacting spin model and benchmark our results against a minimum-weight perfect matching decoder. The presented method provides an avenue to assess the fundamental thresholds of QEC codes and associated readout circuitry, independent of specific decoding strategies, and can thereby help guiding the development of near-term QEC hardware.
arXiv comment22 pages, 13 figures
References in corpus (59)
- Fault-tolerant quantum computation by anyons
- Topological quantum memory
- Superconducting Qubits: Current State of Play
- Quantum Error Correction for Quantum Memories
- Trapped-Ion Quantum Computing: Progress and Challenges
- Parallel Tempering: Theory, Applications, and New Perspectives
- State preservation by repetitive error detection in a superconducting quantum circuit
- Fault-tolerant quantum computation with high threshold in two dimensions
- Quantum Error Correction for Beginners
- Stabilizer Codes and Quantum Error Correction
- Operator Spreading in Random Unitary Circuits
- Topological Quantum Distillation
- Quantum computing with atomic qubits and Rydberg interactions: Progress and challenges
- Quantum error correction in a solid-state hybrid spin register
- Detecting arbitrary quantum errors via stabilizer measurements on a sublattice of the surface code
- Exponential suppression of bit or phase flip errors with repetitive error correction
- Fidelity benchmarks for two-qubit gates in silicon
- Semiconductor Qubits In Practice
- Repeated Quantum Error Detection in a Surface Code
- Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory
- Emergent statistical mechanics of entanglement in random unitary circuits
- Statistical mechanics of quantum error correcting codes
- Topological Computation without Braiding
- Loss Tolerant Optical Qubits
- Universal Finite Size Scaling Functions in the 3D Ising Spin Glass
- Thresholds for topological codes in the presence of loss
- Strong Resilience of Topological Codes to Depolarization
- Quantum Error Correction with the Toric-GKP Code
- Flag fault-tolerant error correction with arbitrary distance codes
- Repeated multi-qubit readout and feedback with a mixed-species trapped-ion register
- Fault-tolerant thresholds for quantum error correction with the surface code
- Fault-tolerant quantum computation with few qubits
- Error Threshold for Color Codes and Random 3-Body Ising Models
- Simulating Ising Spin Glasses on a Quantum Computer
- Simple universal models capture all classical spin physics
- Nishimori point in the 2D +/- J random-bond Ising model
- Statistical mechanical models for quantum codes with correlated noise
- Entanglement Stabilization using Parity Detection and Real-Time Feedback in Superconducting Circuits
- Error Correction and Degeneracy in Surface Codes Suffering Loss
- Triangular color codes on trivalent graphs with flag qubits
- A Quantum Approach to Classical Statistical Mechanics
- The cost of universality: A comparative study of the overhead of state distillation and code switching with color codes
- Introduction to Quantum Gate Set Tomography
- Phase Structure of the Random-Plaquette Z_2 Gauge Model: Accuracy Threshold for a Toric Quantum Memory
- Fault-tolerant quantum computing with color codes
- Very low overhead fault-tolerant magic state preparation using redundant ancilla encoding and flag qubits
- Classical spin models and the quantum stabilizer formalism
- Tricolored Lattice Gauge Theory with Randomness: Fault-Tolerance in Topological Color Codes
- On the Exact Evaluation of Certain Instances of the Potts Partition Function by Quantum Computers
- Unifying all classical spin models in a Lattice Gauge Theory
- Quantum algorithms for classical lattice models
- Topological color codes on Union Jack lattices: A stable implementation of the whole Clifford group
- Error tolerance of topological codes with independent bit-flip and measurement errors
- Twins Percolation for Qubit Losses in Topological Color Codes
- The U(1) Lattice Gauge Theory Universally Connects All Classical Models with Continuous Variables, Including Background Gravity
- Dual correspondence between classical spin models and quantum CSS states
- On maximum-likelihood decoding with circuit-level errors
- Towards a realistic GaAs-spin qubit device for a classical error-corrected quantum memory
- Analytical percolation theory for topological color codes under qubit loss
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