Ioannis Petrongonas | Searcharxiv

arXiv2024

Optimal Discrimination of Mixed Symmetric Multi-mode Coherent States

We find the optimal measurement for distinguishing between symmetric multi-mode phase-randomized coherent states. A motivation for this is that phase-randomized coherent states can be used for quantum communication, including quantum cryptography. The so-called square-root measurement is optimal for pure symmetric states, but is not always optimal for mixed symmetric states. When phase-randomizing a multi-mode coherent state, the state becomes a mixture of pure multi-mode states with different total photon numbers. We find that the optimal measurement for distinguishing between any set of phase-randomised coherent states can be realised by first counting the total number of photons, and then distinguishing between the resulting pure states in the corresponding photon-number subspace. If the multi-mode coherent states we started from are symmetric, then the optimal measurement in each subspace is a square-root measurement. The overall optimal measurement in the cases we consider is also a square-root measurement. In some cases, we are able to present a simple linear optical circuit that realizes the overall optimal measurement.

quant-ph↗

arXiv2024

Adiabatic quantum computing with parameterized quantum circuits

Adiabatic quantum computing is a universal model for quantum computing whose implementation using a gate-based quantum computer requires depths that are unreachable in the early fault-tolerant era. To mitigate the limitations of near-term devices, a number of hybrid approaches have been pursued in which a parameterized quantum circuit prepares and measures quantum states and a classical optimization algorithm minimizes an objective function that encompasses the solution to the problem of interest. In this work, we propose a different approach starting by analyzing how a small perturbation of a Hamiltonian affects the parameters that minimize the energy within a family of parameterized quantum states. We derive a set of equations that allow us to compute the new minimum by solving a constrained linear system of equations that is obtained from measuring a series of observables on the unperturbed system. We then propose a discrete version of adiabatic quantum computing that can be implemented in a near-term device while at the same time is insensitive to the initialization of the parameters and to other limitations hindered in the optimization part of variational quantum algorithms. We compare our proposed algorithm with the Variational Quantum Eigensolver on two classical optimization problems, namely MaxCut and Number Partitioning, and on a quantum-spin configuration problem, the Transverse-Field Ising Chain model, and confirm that our approach demonstrates superior performance.

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