Exact and efficient Lanczos method on a quantum computer
نویسندگان
چکیده
We present an algorithm that uses block encoding on a quantum computer to exactly construct Krylov space, which can be used as the basis for Lanczos method estimate extremal eigenvalues of Hamiltonians. While classical has exponential cost in system size represent states systems, our efficient achieves this polynomial time and memory. The construction presented is exact sense resulting space identical method, so only approximation with respect due finite sample noise. This possible because, unlike previous methods, does not require simulating real or imaginary evolution. provide explicit error bound ground state energy presence For successful efficiently, requirement input problem overlap initial true must $\Omega(1/\text{poly}(n))$ $n$ qubits.
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ژورنال
عنوان ژورنال: Quantum
سال: 2023
ISSN: ['2521-327X']
DOI: https://doi.org/10.22331/q-2023-05-23-1018