Predicting Gibbs-State Expectation Values with Pure Thermal Shadows
- URL: http://arxiv.org/abs/2206.05302v4
- Date: Mon, 26 Jun 2023 13:03:25 GMT
- Title: Predicting Gibbs-State Expectation Values with Pure Thermal Shadows
- Authors: Luuk Coopmans, Yuta Kikuchi, and Marcello Benedetti
- Abstract summary: We propose a quantum algorithm that can predict $M$ linear functions of an arbitrary Gibbs state with only $mathcalO(logM)$ experimental measurements.
We show that the algorithm can be successfully employed as a subroutine for training an eight-qubit fully connected quantum Boltzmann machine.
- Score: 1.4050836886292868
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The preparation and computation of many properties of quantum Gibbs states is
essential for algorithms such as quantum semidefinite programming and quantum
Boltzmann machines. We propose a quantum algorithm that can predict $M$ linear
functions of an arbitrary Gibbs state with only $\mathcal{O}(\log{M})$
experimental measurements. Our main insight is that for sufficiently large
systems we do not need to prepare the $n$-qubit mixed Gibbs state explicitly
but, instead, we can evolve a random $n$-qubit pure state in imaginary time.
The result then follows by constructing classical shadows of these random pure
states. We propose a quantum circuit that implements this algorithm by using
quantum signal processing for the imaginary time evolution. We numerically
verify the efficiency of the algorithm by simulating the circuit for a
ten-spin-1/2 XXZ-Heisenberg model. In addition, we show that the algorithm can
be successfully employed as a subroutine for training an eight-qubit fully
connected quantum Boltzmann machine.
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