Reliable Quantum Certification of Bosonic Code Preparations

TL;DR

This paper introduces efficient methods for certifying Bosonic code states in continuous-variable quantum computing using Gaussian measurements, enabling reliable verification of complex quantum states with reduced resource overhead.

Contribution

It develops a Gaussian measurement-based certification approach for Bosonic code states, applicable to various cat and GKP states, improving reliability and efficiency over traditional tomography.

Findings

Effective certification of Bosonic code states using Gaussian measurements.

Applicable to multiple types of cat and GKP states.

Sample complexity is significantly reduced, enabling scalable verification.

Abstract

Bosonic fault tolerant quantum computing requires preparations of Bosonic code states like cat states and GKP states with high fidelity and reliable quantum certification of these states. Although many proposals on preparing these states have been developed, few investigation has been done on how to reliably certify these experimental states. In this paper, we develop approaches to certify whether a continuous-variable state falls inside a certain Bosonic qubit code space by detecting a witness using Gaussian measurements. Our results can be applied to certification of various cat codes including two-component cat states, four-component cat states, and squeezed two-component cat states as well as Gottesman-Kitaev-Preskill codes. Then we further apply our approach to certify resource states in continuous-variable universal fault tolerant measurement-based quantum computing and quantum outputs of instantaneous quantum polynomial circuits, which can be used to show quantum supremacy. The sample complexity of our approach is efficient in terms of number of modes, so significantly reducing overhead compared to quantum state tomography in certification of many-mode quantum states.