Unitary circuit synthesis for tomography of generalized coherent states
Abstract
We present a method that outputs a sequence of simple unitary operations to prepare a given quantum state that is a generalized coherent state. Our method takes as inputs the expectation values of some relevant observables. Such expectations can be estimated by performing projective measurements on $$\mathcal{O}$$(M^{3}log(M/δ)/ε^{2}) copies of the state, where M is the dimension of an associated Lie algebra, ε is a precision parameter, and 1  δ is the required confidence level. The method can be implemented on a classical computer and runs in time $$\mathcal{O}$$(M^{4}log(M/ε)). It provides $$\mathcal{O}$$(Mlog(M/ε)) simple unitaries that form the sequence. The overall complexity is then polynomial in M, being very efficient in cases where M is significantly smaller than the Hilbert space dimension, as for some fermion algebras. When the algebra of relevant observables is given by certain Pauli matrices, each simple unitary may be easily decomposed into twoqubit gates. We discuss applications to efficient quantum state tomography and classical simulations of quantum circuits. $$\mathcal{O}$$
 Authors:

 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1574752
 Alternate Identifier(s):
 OSTI ID: 1573100
 Report Number(s):
 LAUR1830016
Journal ID: ISSN 00222488; TRN: US2001297
 Grant/Contract Number:
 89233218CNA000001
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Mathematical Physics
 Additional Journal Information:
 Journal Volume: 60; Journal Issue: 11; Journal ID: ISSN 00222488
 Publisher:
 American Institute of Physics (AIP)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Computer Science; Information Science; Mathematics; Quantum tomography, quantum information, quantum computing
Citation Formats
Somma, Rolando Diego. Unitary circuit synthesis for tomography of generalized coherent states. United States: N. p., 2019.
Web. doi:10.1063/1.5121549.
Somma, Rolando Diego. Unitary circuit synthesis for tomography of generalized coherent states. United States. https://doi.org/10.1063/1.5121549
Somma, Rolando Diego. Mon .
"Unitary circuit synthesis for tomography of generalized coherent states". United States. https://doi.org/10.1063/1.5121549. https://www.osti.gov/servlets/purl/1574752.
@article{osti_1574752,
title = {Unitary circuit synthesis for tomography of generalized coherent states},
author = {Somma, Rolando Diego},
abstractNote = {We present a method that outputs a sequence of simple unitary operations to prepare a given quantum state that is a generalized coherent state. Our method takes as inputs the expectation values of some relevant observables. Such expectations can be estimated by performing projective measurements on $\mathcal{O}$(M3log(M/δ)/ε2) copies of the state, where M is the dimension of an associated Lie algebra, ε is a precision parameter, and 1  δ is the required confidence level. The method can be implemented on a classical computer and runs in time $\mathcal{O}$(M4log(M/ε)). It provides $\mathcal{O}$(Mlog(M/ε)) simple unitaries that form the sequence. The overall complexity is then polynomial in M, being very efficient in cases where M is significantly smaller than the Hilbert space dimension, as for some fermion algebras. When the algebra of relevant observables is given by certain Pauli matrices, each simple unitary may be easily decomposed into twoqubit gates. We discuss applications to efficient quantum state tomography and classical simulations of quantum circuits. $\mathcal{O}$},
doi = {10.1063/1.5121549},
journal = {Journal of Mathematical Physics},
number = 11,
volume = 60,
place = {United States},
year = {2019},
month = {11}
}
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