Faster Stochastic First-Order Method for Maximum-Likelihood Quantum State Tomography

• URL: http://arxiv.org/abs/2211.12880v1
• Date: Wed, 23 Nov 2022 11:35:47 GMT
• Title: Faster Stochastic First-Order Method for Maximum-Likelihood Quantum State Tomography
• Authors: Chung-En Tsai and Hao-Chung Cheng and Yen-Huan Li
• Abstract summary: In quantum state tomography, the sample size and dimension grow exponentially with the number of qubits. We propose an algorithm called mirror descent with the Burg-likelihood entropy. To the best of our knowledge, this is currently the fastest, first-order method for maximum-likelihood quantum state tomography.
• Score: 10.758021887982782
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 gradient descent for modern machine learning, to compute the maximum-likelihood estimate. To this end, we propose an algorithm called stochastic mirror descent with the Burg entropy. Its expected optimization error vanishes at a $O ( \sqrt{ ( 1 / t ) d \log t } )$ rate, where $d$ and $t$ denote the dimension and number of iterations, respectively. Its per-iteration time complexity is $O ( d^3 )$, independent of the sample size. To the best of our knowledge, this is currently the computationally fastest stochastic first-order method for maximum-likelihood quantum state tomography.

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