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Quantum Algorithm for Spectral Measurement with a Lower Gate Count

Poulin, David and Kitaev, Alexei and Steiger, Damian S. and Hastings, Matthew B. and Troyer, Matthias (2018) Quantum Algorithm for Spectral Measurement with a Lower Gate Count. Physical Review Letters, 121 (1). Art. No. 010501. ISSN 0031-9007. doi:10.1103/PhysRevLett.121.010501.

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We present two techniques that can greatly reduce the number of gates required to realize an energy measurement, with application to ground state preparation in quantum simulations. The first technique realizes that to prepare the ground state of some Hamiltonian, it is not necessary to implement the time-evolution operator: any unitary operator which is a function of the Hamiltonian will do. We propose one such unitary operator which can be implemented exactly, circumventing any Taylor or Trotter approximation errors. The second technique is tailored to lattice models, and is targeted at reducing the use of generic single-qubit rotations, which are very expensive to produce by standard fault tolerant techniques. In particular, the number of generic single-qubit rotations used by our method scales with the number of parameters in the Hamiltonian, which contrasts with a growth proportional to the lattice size required by other techniques.

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Additional Information:© 2018 American Physical Society. (Received 22 December 2017; published 5 July 2018) We thank Thomas Häner for interesting discussions and Sergey Bravyi for feedback, and acknowledge support by the Swiss National Science Foundation, the NCCR QSIT, Canada’s NSERC, Caltech’s IQIM, and the Simons Foundation.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Swiss National Science Foundation (SNSF)UNSPECIFIED
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Simons FoundationUNSPECIFIED
Issue or Number:1
Record Number:CaltechAUTHORS:20180705-150616687
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:87568
Deposited By: George Porter
Deposited On:06 Jul 2018 14:23
Last Modified:15 Nov 2021 20:49

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