Nested Quantum Annealing Correction

TL;DR

This paper introduces a scalable error correction scheme for quantum annealing that encodes logical qubits into large physical qubit groups, improving performance by effectively lowering the system's temperature.

Contribution

It proposes a novel nested error-correcting encoding for quantum annealing that enhances performance and reduces effective temperature, demonstrating experimental improvements on a D-Wave device.

Findings

Performance improves with larger code size C

Effective temperature decreases as C increases

Error correction enhances quantum annealing scalability

Abstract

We present a general error-correcting scheme for quantum annealing that allows for the encoding of a logical qubit into an arbitrarily large number of physical qubits. Given any Ising model optimization problem, the encoding replaces each logical qubit by a complete graph of degree $C$, representing the distance of the error-correcting code. A subsequent minor-embedding step then implements the encoding on the underlying hardware graph of the quantum annealer. We demonstrate experimentally that the performance of a D-Wave Two quantum annealing device improves as $C$ grows. We show that the performance improvement can be interpreted as arising from an effective increase in the energy scale of the problem Hamiltonian, or equivalently, an effective reduction in the temperature at which the device operates. The number $C$ thus allows us to control the amount of protection against thermal and control errors, and in particular, to trade qubits for a lower effective temperature that scales as $C^{-\eta}$, with $\eta \leq 2$. This effective temperature reduction is an important step towards scalable quantum annealing.