Simulation of positive operator-valued measures and quantum instruments via quantum state preparation algorithms

TL;DR

This paper presents a simplified method for simulating positive operator-valued measures and quantum instruments on quantum systems of arbitrary dimension using quantum state preparation algorithms, demonstrated on IBM quantum processors.

Contribution

It introduces a straightforward approach to implement general quantum measurements and instruments without solving complex nonlinear equations, expanding practical capabilities in quantum simulation.

Findings

Successful implementation on IBM quantum processors

Simplified protocol avoids complex nonlinear equations

Applicable to systems of various dimensions (qubits, qutrits)

Abstract

In Ref. [Phys. Rev. A 100, 062317 (2019)], the authors reported an algorithm to implement, in a circuit-based quantum computer, a general quantum measurement (GQM) of a two-level quantum system, a qubit. Even though their algorithm seems right, its application involves the solution of an intricate non-linear system of equations in order to obtain the angles determining the quantum circuit to be implemented for the simulation. In this article, we identify and discuss a simple way to circumvent this issue and implement GQMs on any $d$-level quantum system through quantum state preparation algorithms. Using some examples for one qubit, one qutrit and two qubits, we illustrate the easy of application of our protocol. Besides, we show how one can utilize our protocol for simulating quantum instruments, for which we also give an example. All our examples are demonstrated using IBM's quantum processors.