Formulation of the Social Workers’ Problem in Quadratic Unconstrained Binary Optimization Form and Solve It on a Quantum Computer

The problem of social workers visiting their patients at home is a class of combinatorial optimization problems and belongs to the class of problems known as NP-Hard. These problems require heuristic techniques to provide an efficient solution in the best of cases. In this article, in addition to providing a detailed resolution of the social workers’ problem using the Quadratic Unconstrained Binary Optimization Problems (QUBO) formulation, an approach to mapping the inequality constraints in the QUBO form is given. Finally, we map it in the Hamiltonian of the Ising model to solve it with the Quantum Exact Solver and Variational Quantum Eigensolvers (VQE). The quantum feasibility of the algorithm will be tested on IBMQ computers.

Variational algorithms for linear algebra

Quantum algorithms have been developed for efficiently solving linear algebra tasks.However,they generally require deep circuits and hence universal fault-tolerant quantum computers.In this work,we propose variational algorithms for linear algebra tasks that are compatible with noisy intermediate-scale quantum devices.We show that the solutions of linear systems of equations and matrix–vector multiplications can be translated as the ground states of the constructed Hamiltonians.Based on the variational quantum algorithms,we introduce Hamiltonian morphing together with an adaptive ans?tz for efficiently finding the ground state,and show the solution verification.Our algorithms are especially suitable for linear algebra problems with sparse matrices,and have wide applications in machine learning and optimisation problems.The algorithm for matrix multiplications can be also used for Hamiltonian simulation and open system simulation.We evaluate the cost and effectiveness of our algorithm through numerical simulations for solving linear systems of equations.We implement the algorithm on the IBM quantum cloud device with a high solution fidelity of 99.95%.

Quantum computing for the Lipkin model with unitary coupled cluster and structure learning ansatz

We report a benchmark calculation for the Lipkin model in nuclear physics with a variational quantum eigensolver in quantum computing.Special attention is paid to the unitary coupled cluster(UCC)ansatz and structure learning(SL)ansatz for the trial wave function.Calculations with both the UCC and SL ansatz can reproduce the ground-state energy well;however,it is found that the calculation with the SL ansatz performs better than thatwith the UCC ansatz,and the SL ansatz has even fewer quantum gates than the UCC ansatz.