- Y Lu, JY Sim, J Suzuki, B-G Englert, and HK Ng,
*Direct estimation of minimum gate fidelity*, Phys Rev A 102, 022410 (2020); arXiv:2004.02422.

**Abstract**With the current interest in building quantum computers, there is a strong need for accurate and efficient characterization of the noise in quantum gate implementations. A key measure of the performance of a quantum gate is the minimum gate fidelity, i.e., the fidelity of the gate, minimized over all input states. Conventionally, the minimum fidelity is estimated by first accurately reconstructing the full gate process matrix using the experimental procedure of quantum process tomography (QPT). Then, a numerical minimization is carried out to find the minimum fidelity. QPT is, however, well known to be costly, and it might appear that we can do better, if the goal is only to estimate one single number. In this work, we propose a hybrid numerical-experimental scheme that employs a numerical gradient-free minimization (GFM) and an experimental target-fidelity estimation procedure to directly estimate the minimum fidelity without reconstructing the process matrix. We compare this to an alternative scheme, referred to as QPT fidelity estimation, that does use QPT, but directly employs the minimum gate fidelity as the termination criterion. Both approaches can thus be considered as direct estimation schemes. General theoretical bounds suggest a significant resource savings for the GFM scheme over QPT fidelity estimation; numerical simulations for specific classes of noise, however, show that both schemes have similar performance, reminding us of the need for caution when using general bounds for specific examples. The GFM scheme, however, presents potential for future improvements in resource cost, with the development of even more efficient GFM algorithms.

- DJ Nott, M Seah, L Al-Labadi, M Evans, HK Ng, and B-G Englert,
*Using prior expansions for prior-data conflict checking*, Bayesian Anal 16, 203 (2021); arXiv:1902.10393.

**Abstract**Any Bayesian analysis involves combining information represented through different model components, and when different sources of information are in conflict it is important to detect this. Here we consider checking for prior-data conflict in Bayesian models by expanding the prior used for the analysis into a larger family of priors, and considering a marginal likelihood score statistic for the expansion parameter. Consideration of different expansions can be informative about the nature of any conflict, and extensions to hierarchically specified priors and connections with other approaches to prior-data conflict checking are discussed. Implementation in complex situations is illustrated with two applications. The first concerns testing for the appropriateness of a LASSO penalty in shrinkage estimation of coefficients in linear regression. Our method is compared with a recent suggestion in the literature designed to be powerful against alternatives in the exponential power family, and we use this family as the prior expansion for constructing our check. A second application concerns a problem in quantum state estimation, where a multinomial model is considered with physical constraints on the model parameters. In this example, the usefulness of different prior expansions is demonstrated for obtaining checks which are sensitive to different aspects of the prior.

- A Jayashankar, AM Babu, HK Ng, and P Mandayam,
*Finding good codes using the Cartan form*, Phys Rev A 101, 042307 (2020); arXiv:1911.02965.

**Abstract**We present a simple and fast numerical procedure to search for good quantum codes for storing logical qubits in the presence of independent per-qubit noise. In a key departure from past work, we use the worst-case fidelity as the figure of merit for quantifying code performance, a much better indicator of code quality than, say, entanglement fidelity. Yet, our algorithm does not suffer from inefficiencies usually associated with the use of worst-case fidelity. Specifically, using a near-optimal recovery map, we are able to reduce the triple numerical optimization needed for the search to a single optimization over the encoding map. We can further reduce the search space using the Cartan decomposition, focusing our search over the nonlocal degrees of freedom resilient against independent per-qubit noise, while not suffering much in code performance.