Unrolling SVT to obtain computationally efficient SVT for n-qubit
quantum state tomography
- URL: http://arxiv.org/abs/2212.08852v1
- Date: Sat, 17 Dec 2022 11:42:57 GMT
- Title: Unrolling SVT to obtain computationally efficient SVT for n-qubit
quantum state tomography
- Authors: Siva Shanmugam, Sheetal Kalyani
- Abstract summary: We present a machine learning approach to estimate the quantum state of n-qubit systems by unrolling the iterations of SVT.
We show that our proposed LQST with very few layers reconstructs the density matrix with much better fidelity than the SVT algorithm.
We also demonstrate the reconstruction of the quantum Bell state from an informationally incomplete set of noisy measurements.
- Score: 13.203765985718201
- License: http://creativecommons.org/licenses/by-nc-sa/4.0/
- Abstract: Quantum state tomography aims to estimate the state of a quantum mechanical
system which is described by a trace one, Hermitian positive semidefinite
complex matrix, given a set of measurements of the state. Existing works focus
on estimating the density matrix that represents the state, using a compressive
sensing approach, with only fewer measurements than that required for a
tomographically complete set, with the assumption that the true state has a low
rank. One very popular method to estimate the state is the use of the Singular
Value Thresholding (SVT) algorithm. In this work, we present a machine learning
approach to estimate the quantum state of n-qubit systems by unrolling the
iterations of SVT which we call Learned Quantum State Tomography (LQST). As
merely unrolling SVT may not ensure that the output of the network meets the
constraints required for a quantum state, we design and train a custom neural
network whose architecture is inspired from the iterations of SVT with
additional layers to meet the required constraints. We show that our proposed
LQST with very few layers reconstructs the density matrix with much better
fidelity than the SVT algorithm which takes many hundreds of iterations to
converge. We also demonstrate the reconstruction of the quantum Bell state from
an informationally incomplete set of noisy measurements.
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