QVECTOR: an algorithm for device-tailored quantum error correction

Abstract

Current approaches to fault-tolerant quantum computation will not enable useful quantum computation on near term devices of 50 to 100 qubits. Leading proposals, such as the color code and surface code schemes, must devote a large fraction of their physical quantum bits to quantum error correction. Building from recent quantum machine learning techniques, we propose an alternative approach to quantum error correction aimed at reducing this overhead, which can be implemented in existing quantum hardware and on a myriad of quantum computing architectures. This method aims to optimize the average fidelity of encoding and recovery circuits with respect to the actual noise in the device, as opposed to that of an artificial or approximate noise model. The quantum variational error corrector (QVECTOR) algorithm employs a quantum circuit with parameters that are variationally-optimized according to processed data originating from quantum sampling of the device, so as to learn encoding and error-recovery gate sequences. We develop this approach for the task of preserving quantum memory and analyze its performance with simulations. We find that, subject to phase damping noise, the simulated QVECTOR algorithm learns a three-qubit encoding and recovery which extend the effective T 2 of a quantum memory six-fold. Subject to a continuous-time amplitude-plus phase-damping noise model on five qubits, the simulated QVECTOR algorithm learns encoding and decoding circuits which exploit the coherence among Pauli errors in the noise model to outperform the five-qubit stabilizer code and any other scheme that does not leverage such coherence. Both of these schemes can be implemented with existing hardware.

Efficient diagnostics for quantum error correction

“…We have shown how experimental data from NR, even limited data, can be used to successfully predict the logical performance of FT architectures based on concatenated codes. It can be used to precisely and efficiently estimate the resource overhead required to achieve a target logical error rate [2,50,51] for implementing quantum algorithms. Along with informing the choice of an optimal code for an underlying physical noise process, the logical estimator provides directives for other components in a FT scheme, such as a decoder.…”

Toward a quantum computing algorithm to quantify classical and quantum correlation of system states

“…Among the different approaches to quantum computing, NISQ devices, which include relatively low-depth quantum circuits by hybrid variational quantumclassical algorithms, have recently received a lot of attention. Hybrid algorithms have been designed in a way that uses resources such as quantum and classical to solve problems specific optimization tasks that are not accessible to traditional classical computers [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52]. One of the most important advantages of this method is that it requires a small number of qubits (contain from 10 to 10 3 of qubits) to run with high gate fidelity and not fault-tolerant error correction [37].…”

Quantum Pure State Tomography via Variational Hybrid Quantum-Classical Method

“…HQC approach is a novel attempt versus full-quantum computation [31,32]. It has found many successful applications ranging from quantum chemistry simulation [33,34], quantum optimal control [35,36], and quantum error correction [37] to quantum state diagonalization [38].…”