Quantum Approximate Optimization for Hard Problems in Linear Algebra
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Ajinkya Borle, Vincent E. Elfving and Samuel J. Lomonaco, Quantum Approximate Optimization for Hard Problems in Linear Algebra, https://arxiv.org/abs/2006.15438
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Abstract
The Quantum Approximate Optimization Algorithm (QAOA) by Farhi et al. is a quantum computational framework for solving quantum or classical optimization tasks. Here, we explore using QAOA for Binary Linear Least Squares (BLLS); a problem that can serve as a building block of several other hard problems in linear algebra. Most of the previous efforts in quantum computing for solving these problems were done using the quantum annealing paradigm. For the scope of this work, our experiments were done on the QISKIT simulator and an IBM Q 5 qubit machine. We highlight the possibilities of using QAOA and QAOA-like variational algorithms for solving such problems, where trial solutions can be obtained directly as samples, rather than being amplitude-encoded in the quantum wavefunction. Our simulations show that Simulated Annealing can outperform QAOA for BLLS at a circuit depth of p≤3 for the probability of sampling the ground state. Finally, we point out some of the challenges involved in current-day experimental implementations of this technique on a cloud-based quantum computer