Towards new solutions for scientific computing: the case of Julia

Tomasi, Maurizio; Giordano, Mosè

doi:10.48550/arxiv.1812.01219

Cited by 1 publication

(1 citation statement)

References 2 publications

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“…To check the validity of our filter analysis, we numerically implement continuous measurements of the 3-bit code, the linear Bayesian filter, and the three boxcar filter variations in the programming language julia [56]. To do this efficiently, we first pick a target bit-flip rate µ to test, such that µτ ∈ [10 −6 , 10 −3 ] with τ being the reference timescale for the numerics (set to 1 for convenience).…”

Section: Numerical Simulationsmentioning

confidence: 99%

Always-On Quantum Error Tracking with Continuous Parity Measurements

Mohseninia,

Yang,

Siddiqi

et al. 2019

Preprint

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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.

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Section: Numerical Simulationsmentioning

confidence: 99%