Maximum-Likelihood Quantum State Tomography by Soft-Bayes
Quantum state tomography (QST), the task of estimating an unknown quantum state given measurement outcomes, is essential to building reliable quantum computing devices. Whereas computing the maximum-likelihood (ML) estimate corresponds to solving a finite-sum convex optimization problem, the objective function is not smooth nor Lipschitz, so most existing convex optimization methods lack sample complexity guarantees; moreover, both the sample size and dimension grow exponentially with the number of qubits in a QST experiment, so a desired algorithm should be highly scalable with respect to the dimension and sample size, just like stochastic gradient descent. In this paper, we propose a stochastic first-order algorithm that computes an $\varepsilon$-approximate ML estimate in $O( ( D \log D ) / \varepsilon ^ 2 )$ iterations with $O( D^3 )$ per-iteration time complexity, where $D$ denotes the dimension of the unknown quantum state and $\varepsilon$ denotes the optimization error. Our algorithm is an extension of Soft-Bayes to the quantum setup.
Code (0)
등록된 구현이 없습니다.
Tasks
Learning TheoryQuantum State TomographySimilar Papers 제목 키워드 기반
Faster Stochastic First-Order Method for Maximum-Likelihood Quantum State Tomography
In maximum-likelihood quantum state tomography, both the sample size and dimension grow exponentially with the number of qubits. It is therefore desirable to develop a stochastic first-order method, just like stochastic …
Quantum State TomographySketch Tomography: Hybridizing Classical Shadow and Matrix Product State
We introduce Sketch Tomography, an efficient procedure for quantum state tomography based on the classical shadow protocol used for quantum observable estimations. The procedure applies to the case where the ground truth…
Quantum State Tomography with Conditional Generative Adversarial Networks
Quantum state tomography (QST) is a challenging task in intermediate-scale quantum devices. Here, we apply conditional generative adversarial networks (CGANs) to QST. In the CGAN framework, two duelling neural networks, …
Quantum State TomographyFast Quantum Process Tomography via Riemannian Gradient Descent
Constrained optimization plays a crucial role in the fields of quantum physics and quantum information science and becomes especially challenging for high-dimensional complex structure problems. One specific issue is tha…
Riemannian optimizationFast Minimization of Expected Logarithmic Loss via Stochastic Dual Averaging
Consider the problem of minimizing an expected logarithmic loss over either the probability simplex or the set of quantum density matrices. This problem includes tasks such as solving the Poisson inverse problem, computi…
Quantum State Tomography