2000 character limit reached
Multiscale Quantum Approximate Optimization Algorithm (2312.06181v1)
Published 11 Dec 2023 in quant-ph
Abstract: The quantum approximate optimization algorithm (QAOA) is one of the canonical algorithms designed to find approximate solutions to combinatorial optimization problems in current noisy intermediate-scale quantum (NISQ) devices. It is an active area of research to exhibit its speedup over classical algorithms. The performance of the QAOA at low depths is limited, while the QAOA at higher depths is constrained by the current techniques. We propose a new version of QAOA that incorporates the capabilities of QAOA and the real-space renormalization group transformation, resulting in enhanced performance. Numerical simulations demonstrate that our algorithm can provide accurate solutions for certain randomly generated instances utilizing QAOA at low depths, even at the lowest depth. The algorithm is suitable for NISQ devices to exhibit a quantum advantage.
- Noisy intermediate-scale quantum algorithms. Reviews of Modern Physics, 94, 015005, 2022.
- A variational eigenvalue solver on a photonic quantum processor. Nature Communications, 5(1), July 2014.
- Demonstration of a small programmable quantum computer with atomic qubits. Nature, 536(7614):63, 2016.
- Digitized adiabatic quantum computing with a superconducting circuit. Nature, 534(7606):222, 2016.
- A quantum approximate optimization algorithm. arXiv preprint arXiv:1411.4028, 2014.
- Near-optimal quantum circuit for grover’s unstructured search using a transverse field. Phys. Rev. A, 95:062317, Jun 2017.
- Variational learning of grover’s quantum search algorithm. Physical Review A, 98(6):062333, 2018.
- Reachability deficits in quantum Approximate optimization Physical Review Letters, 124(9):090504, 2020
- Seth Lloyd. Quantum approximate optimization is computationally universal arXiv preprint arXiv:1812.11075, 2018.
- Quantum approximate optimization algorithm: performance, mechanism, and implementation on near-term devices newblockPhysical Review X, 10, 021067, 2020.
- Obstacles to variational quantum optimization from symmetry protection Physical Review Letters, 125(26):260505, 2020
- Quantum Approximate Optimization Algorithm Pseudo-Boltzmann States Physical Review Letters, 130, 050601, 2023.
- The quantum approximate optimization algorithm needs to see the whole graph: a typical case arXiv preprint arXiv:2004.09002, 2020.
- The quantum approximate optimization algorithm needs to see the whole graph: worst case examples arXiv preprint arXiv:2005.08747, 2020.
- Barren plateaus in quantum neural network training landscapes. Nature communications, 9(1):4812, 2018.
- Kenneth G. Wilson. The renormalization group: Critical phenomena and the Kondo problem. Reviews of Modern Physics, 47, 773, 1975.
- Steven R. White. Density matrix formulation for quantum renormalization groups. Physical Review Letters, 69(19):2863, 1992
- Steven R. White. Density-matrix algorithms for quantum renormalization groups. Physical Review B, 48, 10345, 1993
- Ulrich Schollwöck. The density-matrix renormalization group. Reviews of Modern Physics, 77, 259, 2005.
- G. Vidal. Entanglement Renormalization Physical Review Letters, 99, 220405, 2007.
- G. Vidal. A class of quantum many-body states that can be efficiently simulated Physical Review Letters, 101, 110501, 2008.
- G. Evenbly, G. Vidal. Algorithms for entanglement renormalization Physical Review B, 79, 144108, 2008.
- The unconstrained binary quadratic programming problem: a survey J Comb Optim, 28, 58-81, 2014
- Ulrich Schollwöck. The density-matrix renormalization group in the age of matrix product states Annals of Physics, 326, 96, 2011
- Aric A. Hagberg and Daniel A. Schult and Pieter J. Swart. Exploring Network Structure, Dynamics, and Function using NetworkX in Proceedings of the 7th Python in Science Conference, edited by G.Varoquaux, T. Vaught, and J. Millman (Pasadena, CA USA, 2008), pp. 11–15.
- See supplementary material for “Multiscale Quantum Approximate Optimization Algorithm”.
- Quantum approximate optimization algorithm for maxcut: A fermionic view. Physical Review A, 97(2):022304, 2018.
- Optimal quantum control with digitized Quantum Annealing arXiv preprint quant-ph/1911.12259, 2019.
- Billionnet Alain, Elloumi Sourour. Using a mixed integer quadratic programming solver for the unconstrained quadratic 0-1 problem Math. Program., Ser. A 109, 55–68, 2007.