Abstract
The advent of cloud quantum computing has led to the rapid development of quantum algorithms. In particular, it is necessary to study variational quantum-classical hybrid algorithms, which are executable on noisy intermediate-scale quantum (NISQ) computers. Evaluations of observables appear frequently in the variational quantum-classical hybrid algorithms for NISQ computers. By speeding up the evaluation of observables, it is possible to realize a faster algorithm and save resources of quantum computers. Grouping of observables with separable measurements has been conventionally used, and the grouping with entangled measurements has also been proposed recently by several teams. In this paper, we show that entangled measurements enhance the efficiency of evaluation of observables, both theoretically and experimentally, by taking into account the covariance effect, which may affect the quality of evaluation of observables. We also propose using a part of entangled measurements for grouping to keep the depth of extra gates constant. Our proposed method is expected to be used in conjunction with other related studies. We hope that entangled measurements would become crucial resources, not only for joint measurements but also for quantum information processing.
Highlights
It has been reported that many researchers have been working tirelessly to build a fault-tolerant quantum computer and quantum algorithms for years
We focus on variational quantum eigensolver (VQE), which is a quantum-classical hybrid algorithm proposed by Peruzzo et al.[8] to compute eigenvalues and eigenvectors of matrices such as Hamiltonians
We presented the efficient evaluation of Pauli strings with a part of entangled measurements
Summary
It has been reported that many researchers have been working tirelessly to build a fault-tolerant quantum computer and quantum algorithms for years. Quantum computers can be used to evaluate the expectation values of Pauli strings 〈ψ(θ)∣Piψ(θ)〉. Algorithms require a large number of executions of quantum circuits to evaluate the expectation values of observables. ● Inner iteration: to evaluate the expectation value of a Pauli string through sampling. The inner iteration evaluates Pauli strings as an expectation value with multiple samples This requires O(ε−2) samples for the statistical error ε. If Pauli strings are commutative, it computer, the expectation value of a quantum observable A can implies that they are compatible; i.e., they are jointly measurable. Kandala et al.[2] addressed the grouping of qubit Hamiltonians using TPB and analyzed the distribution of the standard error of its expectation value computational basis is available in a quantum computer. Proof-of-concept demonstration of a simple Hamiltonian on real quantum computers
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