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

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.

References in corpus (20)

• Synthesis of Quantum Logic Circuits
• Quantum-state preparation with universal gate decompositions
• Universal Algorithm for Optimal Estimation of Quantum States from Finite Ensembles
• Simulating positive-operator-valued measures with projective measurements
• A divide-and-conquer algorithm for quantum state preparation
• Optimal randomness certification from one entangled bit
• Machine learning method for state preparation and gate synthesis on photonic quantum computers
• Realization of single-qubit positive operator-valued measurement via a one-dimensional photonic quantum walk
• Deterministic realization of collective measurements via photonic quantum walks
• Spherical Code Key Distribution Protocols for Qubits
• Optimising shadow tomography with generalised measurements
• Device-Independent Certification of a Nonprojective Qubit Measurement
• A two-qubit Bell inequality for which POVM measurements are relevant
• General implementation of all possible positive-operator-value measurements of single photon polarization states
• Simulating all quantum measurements using only projective measurements and postselection
• Double sparse quantum state preparation
• Realization of POVMs using measurement-assisted programmable quantum processors
• Implementation of a general single-qubit positive operator-valued measure on a circuit-based quantum computer
• Implementation of generalized measurements on a qudit via quantum walks
• Universal quantum state preparation via revised greedy algorithm

Cited by in corpus (4)

• High-fidelity, multi-qubit generalized measurements with dynamic circuits
• Enhanced quantum state preparation via stochastic prediction of neural network
• Efficient fidelity estimation: Alternative derivation and related applications
• General measurements with limited resources and their application to quantum unambiguous state discrimination