Single-shot number-resolved detection of microwave photons with error mitigation

TL;DR

This paper demonstrates a high-fidelity, single-shot microwave photon number-resolving detector capable of distinguishing up to 15 photons, employing error mitigation techniques that significantly improve measurement accuracy and scalability.

Contribution

The authors implement a novel single-shot photon number-resolving detector in circuit QED and develop an error mitigation protocol based on a hidden Markov model.

Findings

Achieved photon number resolution up to 15 photons with high fidelity.

Reduced measurement error from 13.5% to 1.1% through bias mitigation.

Demonstrated scalable error mitigation for multi-mode systems.

Abstract

Single-photon detectors are ubiquitous and integral components of photonic quantum cryptography, communication, and computation. Many applications, however, require not only detecting the presence of any photons, but distinguishing the number present with a single shot. Here, we implement a single-shot, high-fidelity photon number-resolving detector of up to 15 microwave photons in a cavity-qubit circuit QED platform. This detector functions by measuring a series of generalized parity operators which make up the bits in the binary decomposition of the photon number. Our protocol consists of successive, independent measurements of each bit by entangling the ancilla with the cavity, then reading out and resetting the ancilla. Photon loss and ancilla readout errors can flip one or more bits, causing nontrivial errors in the outcome, but these errors have a traceable form which can be captured in a simple hidden Markov model. Relying on the independence of each bit measurement, we mitigate biases in ensembles of measurements, showing good agreement with the predictions of the model. The mitigation improves the average total variation distance error of Fock states from $13.5\%$ to $1.1\%$. We also show that the mitigation is efficiently scalable to an $M$-mode system provided that the errors are independent and sufficiently small. Our work motivates the development of new algorithms that utilize single-shot, high-fidelity PNR detectors.