2013
DOI: 10.1137/120871997
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Abstract: A large number of problems in science can be solved by preparing a specific eigenstate of some Hamiltonian H. The generic cost of quantum algorithms for these problems is determined by the inverse spectral gap of H for that eigenstate and the cost of evolving with H for some fixed time. The goal of spectral gap amplification is to construct a Hamiltonian H' with the same eigenstate as H but a bigger spectral gap, requiring that constant-time evolutions with H' and H are implemented with nearly the same cost. W… Show more

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Cited by 40 publications
(53 citation statements)
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“…Roughly speaking, linear dispersion is achieved by discretizing a one-dimensional analogue of Dirac's equation rather than discretizing the one-dimensional Schrödinger equation. Similar ideas have been used previously in [27,35]. Consider the Hamiltonian…”
Section: Dispersionless Discretizationmentioning
confidence: 99%
“…Roughly speaking, linear dispersion is achieved by discretizing a one-dimensional analogue of Dirac's equation rather than discretizing the one-dimensional Schrödinger equation. Similar ideas have been used previously in [27,35]. Consider the Hamiltonian…”
Section: Dispersionless Discretizationmentioning
confidence: 99%
“…Dickson and Amin [15] show analytically that in the case of Maximum Independent Set, there must always exist an adiabatic path for which the exponentially small gaps of [2] do not occur. Somma and Boixo [31] show that sometimes the final Hamiltonian can be transformed in a way that preserves the ground state but (quadratically) amplifies g.…”
Section: Theoretical Underpinningsmentioning
confidence: 99%
“…In certain situations, the energy gaps can be amplified [68], but not in a general case considered here. Moreover, as Figure 5 indicates, minimal energy gaps of studied processes correspond to s = 1 1 and thus cannot be avoided by a different ASP path.…”
Section: Møller-plesset Type Of Initial Hamiltoniansmentioning
confidence: 82%