Quantum expectation-value estimation by computational basis sampling
- URL: http://arxiv.org/abs/2112.07416v2
- Date: Mon, 5 Sep 2022 14:15:54 GMT
- Title: Quantum expectation-value estimation by computational basis sampling
- Authors: Masaya Kohda, Ryosuke Imai, Keita Kanno, Kosuke Mitarai, Wataru
Mizukami, Yuya O. Nakagawa
- Abstract summary: A practical obstacle is the necessity of a large number of measurements for statistical convergence.
We propose an algorithm to estimate the expectation value based on its approximate expression as a weighted sum of classically-tractable matrix elements.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Measuring expectation values of observables is an essential ingredient in
variational quantum algorithms. A practical obstacle is the necessity of a
large number of measurements for statistical convergence to meet requirements
of precision, such as chemical accuracy in the application to quantum chemistry
computations. Here we propose an algorithm to estimate the expectation value
based on its approximate expression as a weighted sum of classically-tractable
matrix elements with some modulation, where the weight and modulation factors
are evaluated by sampling appropriately prepared quantum states in the
computational basis on quantum computers. Each of those states is prepared by
applying a unitary transformation consisting of at most N CNOT gates, where N
is the number of qubits, to a target quantum state whose expectation value is
evaluated. Our algorithm is expected to require fewer measurements than
conventional methods for a required statistical precision of the expectation
value when the target quantum state is concentrated in particular computational
basis states. We provide numerical comparisons of our method with existing ones
for measuring electronic ground state energies (expectation values of
electronic Hamiltonians for the lowest-energy states) of various small
molecules. Numerical results show that our method can reduce the numbers of
measurements to obtain the ground state energies for a targeted precision by
several orders of magnitudes for molecules whose ground states are
concentrated. Our results provide another route to measure expectation values
of observables, which could accelerate the variational quantum algorithms.
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