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arxiv 1909.05500 v3 pith:S4ZQRDMQ submitted 2019-09-12 quant-ph cs.NAmath.NA

Quantum linear system solver based on time-optimal adiabatic quantum computing and quantum approximate optimization algorithm

classification quant-ph cs.NAmath.NA
keywords quantumkappaepsilonmatricesruntimetime-optimaladiabaticalgorithm
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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 $\mathcal{O}(\kappa~\text{poly}(\log(\kappa/\epsilon)))$ runtime, where $\kappa$ is the condition number, and $\epsilon$ is the target accuracy. This is near optimal with respect to both $\kappa$ and $\epsilon$. 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.

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Cited by 5 Pith papers

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    quant-ph 2024-06 accept novelty 7.0

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  5. Nonisothermal global-pressure exactness in fractured multiphase flow with aperture feedback

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