Incoherent Approximation of Leakage in Quantum Error Correction
arXiv:2312.10277 · doi:10.1103/PhysRevApplied.23.054025
Abstract
Quantum error correcting codes typically do not account for quantum state transitions - leakage - out of the computational subspace. Since these errors can last for multiple detection rounds they can significantly contribute to logical errors. It is therefore important to understand how to numerically model them efficiently. Fully quantum simulations of leakage require more levels per leaked qubit, which substantially limits the system sizes that may be simulated. To address this, we introduce a Subspace Twirling Approximation (STA) on quantum channels that preserves the incoherence between the computational and leakage subspaces. The assumption of incoherence enables the quantum simulation of leakage at little computational overhead. We motivate the approximation's validity by showing that incoherence is achieved naturally during repeated stabilizer measurements. Additionally, we provide various simulation results which show that the STA yields accurate error correction statistics in the repetition and surface codes with physical error parameters.
v2: Renamed Random Phase Approximation (RPA) to Subspace Twirling Approximation (STA). Added further discussion in places, and other minor changes
References in corpus (55)
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- Charge insensitive qubit design derived from the Cooper pair box
- Review article: Linear optical quantum computing
- Quantifying Coherence
- Quantum Coherence as a Resource
- Improved Simulation of Stabilizer Circuits
- Suppressing quantum errors by scaling a surface code logical qubit
- Operational Resource Theory of Coherence
- State preservation by repetitive error detection in a superconducting quantum circuit
- Reference frames, superselection rules, and quantum information
- Simple pulses for elimination of leakage in weakly nonlinear qubits
- Exact and Approximate Unitary 2-Designs: Constructions and Applications
- The Flux Qubit Revisited to Enhance Coherence and Reproducibility
- Surface code quantum computing by lattice surgery
- A simple all-microwave entangling gate for fixed-frequency superconducting qubits
- Quantum Process Tomography: Resource Analysis of Different Strategies
- A tunable coupling scheme for implementing high-fidelity two-qubit gates
- Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask)
- Exponential suppression of bit or phase flip errors with repetitive error correction
- Stim: a fast stabilizer circuit simulator
- Realization of an Error-Correcting Surface Code with Superconducting Qubits
- Fidelity of quantum operations
- Demonstrating a Continuous Set of Two-qubit Gates for Near-term Quantum Algorithms
- Low-distance Surface Codes under Realistic Quantum Noise
- Analytic control methods for high fidelity unitary operations in a weakly nonlinear oscillator
- Measuring and Suppressing Quantum State Leakage in a Superconducting Qubit
- Quantum Process Tomography of a Universal Entangling Gate Implemented with Josephson Phase Qubits
- Realization of high-fidelity CZ and ZZ-free iSWAP gates with a tunable coupler
- Fault-tolerant quantum computation with long-range correlated noise
- Measurement-induced state transitions in a superconducting qubit: Beyond the rotating wave approximation
- Fault-Tolerant Quantum Computation For Local Non-Markovian Noise
- Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study
- Quantification and Characterization of Leakage Errors
- Microwave-induced coupling of superconducting qubits
- Leakage reduction in fast superconducting qubit gates via optimal control
- Towards Scalable Bosonic Quantum Error Correction
- Logical-qubit operations in an error-detecting surface code
- Reduced phase error through optimized control of a superconducting qubit
- Removing leakage-induced correlated errors in superconducting quantum error correction
- Tunable coupler for realizing a controlled-phase gate with dynamically decoupled regime in a superconducting circuit
- Coping with qubit leakage in topological codes
- Density-matrix simulation of small surface codes under current and projected experimental noise
- Overcoming leakage in scalable quantum error correction
- Measurement-Induced State Transitions in a Superconducting Qubit: Within the Rotating Wave Approximation
- Understanding the effects of leakage in superconducting quantum error detection circuits
- Constructing Smaller Pauli Twirling Sets for Arbitrary Error Channels
- Leakage detection for a transmon-based surface code
- A hardware-efficient leakage-reduction scheme for quantum error correction with superconducting transmon qubits
- Effects of noise on quantum error correction algorithms
- Leakage mitigation for quantum error correction using a mixed qubit scheme
- Handling Leakage with Subsystem Codes
- Avoiding leakage and errors caused by unwanted transitions in Lambda systems
- On the compatibility of quantum instruments
- Characterizing quantum instruments: from non-demolition measurements to quantum error correction
- Context Aware Fidelity Estimation