Always-On Quantum Error Tracking with Continuous Parity Measurements

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.

A Fault-Tolerant Honeycomb Memory

“…The picture changes qualitatively if entanglement is instead generated using native two-body measurements -a context for which this code is optimized [1]. Direct two-body measurements have been proposed and demonstrated experimentally in circuit QED [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31], and are expected to be the native operation in Majorana-based architectures [1,14,32]. In this setting, we observe a honeycomb code threshold between 1.5% and 2.0% -by comparison, previous work reported a surface code threshold of 0.237% in the same error model [14] (but using a less accurate union-find decoder).…”

Machine Learning for Continuous Quantum Error Correction on Superconducting Qubits

“…However, in contrast to this theoretical idealization of instantaneous projections of the quantum state, experimental implementation of such measurements inherently involves performing weak measurements over finite time intervals [6], with the dispersive readouts in superconducting qubit architectures constituting the prime example of this in today's quantum technologies [7][8][9][10]. This has motivated the development of continuous quantum error correction (CQEC) [11][12][13][14], where the error syndrome operators are measured weakly in strength and continuously in time.…”

“…Previous theoretical work on CQEC has focused primarily on measurement signals that behave in an idealized manner [11][12][13], such that each sample is assumed to be i.i.d. Gaussian with a mean given by one of the syndrome eigenvalues.…”

“…In previous work, Ref. [12] compared the performance of a linear approximate Bayesian classifier and the double threshold model with one threshold fixed at y = 0 and another threshold at y > 0 in correcting the three-qubit bit-flip code for quantum memory. Ref.…”

Monitoring fast superconducting qubit dynamics using a neural network

“…Weak measurements allow the observer to reconstruct the dynamics of a quantum system, and to track the evolution of a wavefunction before its collapse to an eigenstate. For superconducting quantum circuits in particular, reconstructing individual quantum trajectories [1][2][3][4][5][6][7][8][9][10] has served as a tool to monitor quantum jumps [11][12][13][14], track diffusion statistics [15][16][17][18], generate entanglement via measurement [19,20], coherently control quantum evolution using feedback [21][22][23][24][25], and implement continuous quantum error correction [26][27][28][29]. In weak measurements with superconducting qubits coupled to a readout resonator, the dynamics of the latter are typically much faster than the former.…”