Quantum Algorithm for Spectral Measurement with a Lower Gate Count
Abstract
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.
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.Attached Files
Published - PhysRevLett.121.010501.pdf
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Additional details
- Eprint ID
- 87568
- Resolver ID
- CaltechAUTHORS:20180705-150616687
- Swiss National Science Foundation (SNSF)
- Natural Sciences and Engineering Research Council of Canada (NSERC)
- Institute for Quantum Information and Matter (IQIM)
- Simons Foundation
- Created
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2018-07-06Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field
- Caltech groups
- Institute for Quantum Information and Matter