Abstract
Many prominent quantum computing algorithms with applications in fields such as chemistry and materials science require a large number of measurements, which represents an important roadblock for future real-world use cases. We introduce a novel approach to tackle this problem through an adaptive measurement scheme. We present an algorithm that optimizes informationally complete positive operator-valued measurements (POVMs) on the fly in order to minimize the statistical fluctuations in the estimation of relevant cost functions. We show its advantage by improving the efficiency of the variational quantum eigensolver in calculating ground-state energies of molecular Hamiltonians with extensive numerical simulations. Our results indicate that the proposed method is competitive with state-of-the-art measurement-reduction approaches in terms of efficiency. In addition, the informational completeness of the approach offers a crucial advantage, as the measurement data can be reused to infer other quantities of interest. We demonstrate the feasibility of this prospect by reusing ground-state energy-estimation data to perform high-fidelity reduced state tomography.
Highlights
Quantum computing is a rapidly growing multidisciplinary field with a very clear objective: to understand if, and to what extent, it is possible to build computing machines able to perform tasks that are impossible for conventional computers
We focus on variational quantum algorithms, which have emerged recently as the most suited paradigm to tackle the classes of problems identified above [13,14] with approximate quantum computing
We introduce an algorithm for efficient observable estimation that exploits informationally complete generalized quantum measurements integrating three important
Summary
Quantum computing is a rapidly growing multidisciplinary field with a very clear objective: to understand if, and to what extent, it is possible to build computing machines able to perform tasks that are impossible for conventional (classical) computers. We focus on variational quantum algorithms, which have emerged recently as the most suited paradigm to tackle the classes of problems identified above [13,14] with approximate quantum computing These protocols are implemented by preparing a parametrized N -qubit trial state on a quantum device, extracting some observable quantities with suitable measurements, and processing such measurement outcomes using a classical optimizer. This cycle is repeated many times until it converges to a quantum state from which the desired approximate solution can be extracted This procedure can be used to solve problems in chemistry [15,16,17,18], for the design of new materials [19], and generally in every field of physics where one needs to extract the properties of many-body quantum correlated systems, e.g., interacting fermionic systems, which are typically hard to simulate on classical devices [20,21]. We describe the measurement problem in more detail and briefly mention the main approaches that have been proposed in the literature to tackle it
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