Error-corrected quantum annealing with hundreds of qubits

Abstract

Quantum information processing offers dramatic speedups, yet is susceptible to decoherence, whereby quantum superpositions decay into mutually exclusive classical alternatives, thus robbing quantum computers of their power. This makes the development of quantum error correction an essential aspect of quantum computing. So far, little is known about protection against decoherence for quantum annealing, a computational paradigm aiming to exploit ground-state quantum dynamics to solve optimization problems more rapidly than is possible classically. Here we develop error correction for quantum annealing and experimentally demonstrate it using antiferromagnetic chains with up to 344 superconducting flux qubits in processors that have recently been shown to physically implement programmable quantum annealing. We demonstrate a substantial improvement over the performance of the processors in the absence of error correction. These results pave the way towards large-scale noise-protected adiabatic quantum optimization devices, although a threshold theorem such as has been established in the circuit model of quantum computing remains elusive.

Performance of two different quantum annealing correction codes

“…We have shown that these differences translate into performance gains as expected, i.e., both a higher energy boost and a lower operating temperature result in improved success probabilities. This conclusion has immediate implications for the design of future quantum annealing devices: despite results indicating that thermal effects can assist AQC [48], and our (and previous [24,31,40]) results supporting the notion that error correction can tolerate thermal excitations, significant performance gains are to be realized via the straightforward mechanisms of cooling and increasing the energy scale.…”

“…The observation that error correction for AQC or quantum annealing is designed to tolerate excitations has of course been made before, e.g., in Refs. [24,31,40]. …”

“…Work on the first generation D-Wave 1 (DW1) "Rainier" and second generation D-Wave 2 (DW2) "Vesuvius" processors has already demonstrated that error correction can substantially benefit quantum annealing [40][41][42]. Namely, it was shown that even a relatively simple quantum repetition code incorporating energy penalty terms and a decoding procedure, can significantly improve the success probability of finding ground states, as well as overcome precision issues in the specification of the Ising Hamiltonian.…”

Dissipative universal Lindbladian simulation

“…Simulation of highly non-trivial properties of matter as topological order [22] and non-abelian synthetic gauge fields [23] can also be accomplished by dissipative means. Finally, all forms of QIP that encode information in the ground state of a time-dependent Hamiltonian, e.g., open system adiabatic quantum computation and quantum annealing, also benefit from dissipation and relaxation to negate thermally driven errors [24][25][26].In particular in [27] it has been shown that quantum information can be encoded in the set of steady states (SSS) of a sufficiently symmetric strongly dissipative system and manipulated coherently by an effective dissipation-projected Hamiltonian. The latter is of geometric nature and is robust against some types of Hamiltonian and dissipative perturbations [28].…”

Hamiltonian gadgets with reduced resource requirements

“…For instance, the gadgets from [3] were used by Bravyi, DiVincenzo, Loss and Terhal [11] to show that one can combine the use of subdivision and 3-to 2-body gadgets to recursively reduce a k-body Hamiltonian to 2-body, which is useful for simulating quantum many-body Hamiltonians. We note that these gadgets solve a different problem than the type of many-body operator simulations considered previously [17,18] for gate model quantum computation, where the techniques developed therein are not directly applicable to our situation.While recent progress in the experimental implementation of adiabatic quantum processors [19][20][21][22] suggests the ability to perform sophisticated adiabatic quantum computing experiments, the perturbative gadgets require very large values of ∆. This places high demands on experimental control precision by requiring that devices enforce very large couplings between ancilla qubits while still being able to resolve couplings from the original problem -even though those fields may be orders of magnitude smaller than ∆.…”