Journal
QUANTUM
Volume 4, Issue -, Pages -Publisher
VEREIN FORDERUNG OPEN ACCESS PUBLIZIERENS QUANTENWISSENSCHAF
DOI: 10.22331/q-2020-11-11-361
Keywords
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Funding
- Department of Energy [DESC0017867]
- Quantum Algorithm Teams Program [DE-AC02-05CH11231]
- Google Quantum Research Award
- Air Force Office of Scientific Research [FA9550-18-1-0095]
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We present a quantum eigenstate filtering algorithm based on quantum signal processing (QSP) and minimax polynomials. The algorithm allows us to efficiently prepare a target eigenstate of a given Hamiltonian, if we have access to an initial state with non-trivial overlap with the target eigenstate and have a reasonable lower bound for the spectral gap. We apply this algorithm to the quantum linear system problem (QLSP), and present two algorithms based on quantum adiabatic computing (AQC) and quantum Zeno effect respectively. Both algorithms prepare the final solution as a pure state, and achieves the near optimal (O) over tilde (dk, log(1/6)) query complexity for a d-sparse matrix, where k is the condition number, and epsilon is the desired precision. Neither algorithm uses phase estimation or amplitude amplification.
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