Efficient Classical Computation of Quantum Mean Values for Shallow QAOA Circuits
The Quantum Approximate Optimization Algorithm (QAOA), which is a variational quantum algorithm, aims to give sub-optimal solutions of combinatorial optimization problems. It is widely believed that QAOA has the potential to demonstrate application-level quantum advantages in the noisy intermediate-...
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Main Authors | , , , , , , , , , , , |
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Format | Journal Article |
Language | English |
Published |
21.12.2021
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Subjects | |
Online Access | Get full text |
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Summary: | The Quantum Approximate Optimization Algorithm (QAOA), which is a variational
quantum algorithm, aims to give sub-optimal solutions of combinatorial
optimization problems. It is widely believed that QAOA has the potential to
demonstrate application-level quantum advantages in the noisy
intermediate-scale quantum(NISQ) processors with shallow circuit depth. Since
the core of QAOA is the computation of expectation values of the problem
Hamiltonian, an important practical question is whether we can find an
efficient classical algorithm to solve quantum mean value in the case of
general shallow quantum circuits. Here, we present a novel graph decomposition
based classical algorithm that scales linearly with the number of qubits for
the shallow QAOA circuits in most optimization problems except for complete
graph case. Numerical tests in Max-cut, graph coloring and
Sherrington-Kirkpatrick model problems, compared to the state-of-the-art
method, shows orders of magnitude performance improvement. Our results are not
only important for the exploration of quantum advantages with QAOA, but also
useful for the benchmarking of NISQ processors. |
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DOI: | 10.48550/arxiv.2112.11151 |