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Quantum Linear System Solver Based on Time-optimal Adiabatic Quantum Computing and Quantum Approximate Optimization Algorithm
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DOI：10.1145/3498331.png)
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We demonstrate that with an optimally tuned scheduling function, adiabatic quantum computing (AQC) can readily solve a quantum linear system problem (QLSP) with O(kappa poly(log(kappa/epsilon))) runtime, where kappa is the condition number, and epsilon is the target accuracy. This is near optimal with respect to both kappa and epsilon, and is achieved without relying on complicated amplitude amplification procedures that are difficult to implement. Our method is applicable to general non-Hermitian matrices, and the cost as well as the number of qubits can be reduced when restricted to Hermitian matrices, and further to Hermitian positive definite matrices. The success of the time-optimal AQC implies that the quantum approximate optimization algorithm (QAOA) with an optimal control protocol can also achieve the same complexity in terms of the runtime. Numerical results indicate that QAOA can yield the lowest runtime compared to the time-optimal AQC, vanilla AQC, and the recently proposed randomization method.
Keyword:
Quantum linear system problem
adiabatic quantum computing
quantum approximate optimization algorithm
期刊
A
IF:
6.8
论文数:
542
被引数:
508
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