Always-On Quantum Error Tracking with Continuous Parity Measurements
arXiv:1907.08882 · doi:10.22331/q-2020-11-04-358
Abstract
We investigate quantum error correction using continuous parity measurements to correct bit-flip errors with the three-qubit code. Continuous monitoring of errors brings the benefit of a continuous stream of information, which facilitates passive error tracking in real time. It reduces overhead from the standard gate-based approach that periodically entangles and measures additional ancilla qubits. However, the noisy analog signals from continuous parity measurements mandate more complicated signal processing to interpret syndromes accurately. We analyze the performance of several practical filtering methods for continuous error correction and demonstrate that they are viable alternatives to the standard ancilla-based approach. As an optimal filter, we discuss an unnormalized (linear) Bayesian filter, with improved computational efficiency compared to the related Wonham filter introduced by Mabuchi [New J. Phys. 11, 105044 (2009)]. We compare this optimal continuous filter to two practical variations of the simplest periodic boxcar-averaging-and-thresholding filter, targeting real-time hardware implementations with low-latency circuitry. As variations, we introduce a non-Markovian ``half-boxcar'' filter and a Markovian filter with a second adjustable threshold; these filters eliminate the dominant source of error in the boxcar filter, and compare favorably to the optimal filter. For each filter, we derive analytic results for the decay in average fidelity and verify them with numerical simulations.
arXiv comment34 pages, 7 figures, published version
References in corpus (39)
- Charge insensitive qubit design derived from the Cooper pair box
- Good Quantum Error-Correcting Codes Exist
- Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
- A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
- A Theory of Fault-Tolerant Quantum Computation
- Realization of Three-Qubit Quantum Error Correction with Superconducting Circuits
- Simple Quantum Error Correcting Codes
- Detecting arbitrary quantum errors via stabilizer measurements on a sublattice of the surface code
- Procedure for systematically tuning up crosstalk in the cross resonance gate
- A simple all-microwave entangling gate for fixed-frequency superconducting qubits
- Deterministic entanglement of superconducting qubits by parity measurement and feedback
- Observation of measurement-induced entanglement and quantum trajectories of remote superconducting qubits
- Implementing a strand of a scalable fault-tolerant quantum computing fabric
- Continuous quantum error correction via quantum feedback control
- Mapping the optimal route between two quantum states
- Effective Hamiltonian models of the cross-resonance gate
- Robust concurrent remote entanglement between two superconducting qubits
- Observing quantum state diffusion by heterodyne detection of fluorescence
- Operation and intrinsic error budget of a two-qubit cross-resonance gate
- Prediction, Retrodiction, and The Amount of Information Stored in the Present
- Quantum error correction for continuously detected errors
- A practical scheme for error control using feedback
- Tunable joint measurements in the dispersive regime of cavity QED
- Parity meter for charge qubits: an efficient quantum entangler
- Quantum Zeno effect in the strong measurement regime of circuit quantum electrodynamics
- Quadratic Quantum Measurements
- High fidelity feed-back assisted parity measurement in circuit QED
- Entanglement genesis under continuous parity measurement
- Quantum trajectories and their statistics for remotely entangled quantum bits
- Parity detection and entanglement with a Mach-Zehnder interferometer
- Qubit Parity Measurement by Parametric Driving in Circuit QED
- Error correcting Bacon-Shor code with continuous measurement of noncommuting operators
- On-demand maximally entangled states with a parity meter and continuous feedback
- Method for quantum-jump continuous-time quantum error correction
- Three-qubit direct dispersive parity measurement with Tunable Coupling Qubits
- Multi-Qubit Joint Measurements in Circuit QED: Stochastic Master Equation Analysis
- Quantum error correction benchmarks for continuous weak parity measurements
- Towards a heralded eigenstate preserving measurement of multi-qubit parity in circuit QED
- Quantum error correction using weak measurements
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- A Fault-Tolerant Honeycomb Memory
- Experimental demonstration of continuous quantum error correction
- Machine Learning for Continuous Quantum Error Correction on Superconducting Qubits
- Continuous quantum error correction for evolution under time-dependent Hamiltonians
- Entanglement-Preserving Limit Cycles from Sequential Quantum Measurements and Feedback
- Stabilizing two-qubit entanglement with dynamically decoupled active feedback
- Optimal Zeno Dragging for Quantum Control: A Shortcut to Zeno with Action-based Scheduling Optimization
- A Logarithmic Bayesian Approach to Quantum Error Detection
- Measurement based estimator scheme for continuous quantum error correction
- Noise-Canceling Quantum Feedback: non-Hermitian Dynamics with Applications to State Preparation and Magic State Distillation
- CDJ-Pontryagin Optimal Control for General Continuously Monitored Quantum Systems