Simplifying errors by symmetry and randomisation

Tue, 14 Nov 2023 00:00:00 +0000

We present a set of methods to generate less complex error channels by quantum circuit parallelisation. The resulting errors are simplified as a consequence of their symmetrisation and randomisation. Initially, the case of a single error channel is analysed; these results are then generalised to multiple error channels. Error simplification for each method is shown to be either constant, linear, or exponential in terms of system size. Finally, example applications are provided, along with experiments run on superconducting quantum hardware and numerical simulation. These applications are: (1) reducing the sample complexity of matrix-inversion measurement error mitigation by error symmetrisation, (2) improving the effectiveness of noise-estimation circuit error mitigation by error randomisation, and (3) improving the predictability of noisy circuit performance by error randomisation.

Mitigating errors by quantum verification and post-selection

Sat, 27 Nov 2021 00:00:00 +0000

Correcting errors due to noise in quantum circuits run on current and near-term quantum hardware is essential for any convincing demonstration of quantum advantage. Indeed, in many cases it has been shown that noise renders quantum circuits efficiently classically simulable, thereby destroying any quantum advantage potentially offered by an ideal (noiseless) implementation of these circuits. Although the technique of quantum error correction (QEC) allows to correct these errors very accurately, QEC usually requires a large overhead of physical qubits which is not reachable with currently available quantum hardware. This has been the motivation behind the field of quantum error mitigation, which aims at developing techniques to correct an important part of the errors in quantum circuits, while also being compatible with current and near-term quantum hardware. In this work, we present a technique for quantum error mitigation which is based on a technique from quantum verification, the so-called accreditation protocol, together with post-selection. Our technique allows for correcting the expectation value of an observable $O$, which is the output of multiple runs of noisy quantum circuits, where the noise in these circuits is at the level of preparations, gates, and measurements. We discuss the sample complexity of our procedure and provide rigorous guarantees of errors being mitigated under some realistic assumptions on the noise. Our technique also allows for time dependant behaviours, as we allow for the output states to be different between different runs of the accreditation protocol. We validate our findings by running our technique on currently available quantum hardware.

James Mills | LIP6 - Équipe QI

Simplifying errors by symmetry and randomisation

Mitigating errors by quantum verification and post-selection