Data-centric machine learning in quantum information science

Abstract

We propose a series of data-centric heuristics for improving the performance of machine learning systems when applied to problems in quantum information science. In particular, we consider how systematic engineering of training sets can significantly enhance the accuracy of pre-trained neural networks used for quantum state reconstruction without altering the underlying architecture. We find that it is not always optimal to engineer training sets to exactly match the expected distribution of a target scenario, and instead, performance can be further improved by biasing the training set to be slightly more mixed than the target. This is due to the heterogeneity in the number of free variables required to describe states of different purity, and as a result, overall accuracy of the network improves when training sets of a fixed size focus on states with the least constrained free variables. For further clarity, we also include a ``toy model'' demonstration of how spurious correlations can inadvertently enter synthetic data sets used for training, how the performance of systems trained with these correlations can degrade dramatically, and how the inclusion of even relatively few counterexamples can effectively remedy such problems.

Demonstration of machine-learning-enhanced Bayesian quantum state estimation

“…Previous work considering the selection of prior distributions for Bayesian reconstruction has often defaulted to standard distributions based on fair sampling according to the Bures [28] or Hilbert-Schmidt [29] measures. Unfortunately, these distributions are, on average, significantly more mixed than many relevant experimental scenarios and hence have motivated the use of alternatives such as the Mai-Alquier (MA) distribution [22], which can be tuned to favor lower-rank states than those obtained on average from Bures or Hilbert-Schmidt metrics [16,26]. Recent results show that manually tuning the MA distribution with even very coarse knowledge, such as the mean state purity expected in an experimental scenario, can improve the performance of Bayesian reconstruction methods [26].…”

“…Significant recent research effort has focused on leveraging ML to perform quantum state reconstruction. While different results reveal that ML-based reconstruction has potential advantages over conventional approaches when reconstructing data that include experimental errors, missing measurements, or high statistical noise, the primary motivator has been to reduce computation times [16]. In particular, ML methods that utilize pre-trained networks effectively 'frontload' expensive computations into training the network so that, once trained, it can perform inference indefinitely without further computationally intensive training [30].…”

“…The density matrix is calculated for all 1000 runs using Bayesian inference with ML-based and Bures priors. As in the previous section, the red curve in figure 4(a) is the reconstruction using the ML prior with µ = 25 and α 0 = 11.6, but now utilizing a neural network trained on MA-distributed states with α = 0.4 to infer ρ ML , motivated by previous work that found this distribution balances reconstruction fidelity across the purity spectrum of arbitrary two-qubit states [16,26]. Even though we test inference on experimental data in this section, we still train our neural network using simulated data in order to avoid the inclusion of false correlations from experimental error and keep our system more general; simulated data are often significantly more accessible than comparable quantities of accurately labeled experimental data.…”

“…However, given the substantial experimental challenges associated with collecting measurements of high-dimensional quantum systems, the computational resources involved with state reconstruction have only relatively recently become a significant bottleneck in their own right [1,2]. Various approaches for performing state estimation given a set of measurement results have appeared in the literature, including maximum likelihood estimation (MLE) [2][3][4][5][6], compressive sensing [7,8], machine learning (ML) [9][10][11][12][13][14][15][16][17], and Bayesian inference [18][19][20][21][22][23][24]. The existing inference methods define a trade-space between different characteristics such as general applicability and assumptions about the system, computation time, and accuracy guarantees.…”

“…While the former has shown some promise in terms of improving efficiency [22,23], it is conceptually unsatisfying, as in principle all prior information should enter through the prior distribution. On the other hand, current approaches for including prior information through direct engineering of prior distributions are coarse and rely on assumptions about a system that may change over time, such as the expected rank of output states, while also requiring manual tuning [16,26].…”