skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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 $$\mathcal{O}$$(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 two-qubit gates. We discuss applications to efficient quantum state tomography and classical simulations of quantum circuits. $$\mathcal{O}$$

Authors:
ORCiD logo [1]
  1. 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):
LA-UR-18-30016
Journal ID: ISSN 0022-2488; 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 0022-2488
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. doi:10.1063/1.5121549.
Somma, Rolando Diego. Mon . "Unitary circuit synthesis for tomography of generalized coherent states". United States. doi: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 two-qubit 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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Save / Share:

Works referenced in this record:

Coherent states: Theory and some applications
journal, October 1990


Efficient Solvability of Hamiltonians and Limits on the Power of Some Quantum Computational Models
journal, November 2006


Nature and measure of entanglement in quantum phase transitions
journal, October 2004


Diagonalization in Compact Lie Algebras and a New Proof of a Theorem of Kostant
journal, October 1993

  • Wildberger, N. J.
  • Proceedings of the American Mathematical Society, Vol. 119, Issue 2
  • DOI: 10.2307/2159953

Unconditionally verifiable blind quantum computation
journal, July 2017


Classical Verification of Quantum Computations
conference, October 2018

  • Mahadev, Urmila
  • 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)
  • DOI: 10.1109/FOCS.2018.00033

Simulating physical phenomena by quantum networks
journal, April 2002


Lower bounds for the fidelity of entangled-state preparation
journal, November 2006


Probability Inequalities for Sums of Bounded Random Variables
journal, March 1963

  • Hoeffding, Wassily
  • Journal of the American Statistical Association, Vol. 58, Issue 301
  • DOI: 10.2307/2282952

Generalizations of entanglement based on coherent states and convex sets
journal, September 2003


Efficient quantum state tomography
journal, December 2010

  • Cramer, Marcus; Plenio, Martin B.; Flammia, Steven T.
  • Nature Communications, Vol. 1, Issue 1
  • DOI: 10.1038/ncomms1147

Coherent and Incoherent States of the Radiation Field
journal, September 1963


Quantum Simulations of Physics Problems
journal, June 2003

  • Somma, Rolando; Ortiz, Gerardo; Knill, Emanuel
  • International Journal of Quantum Information, Vol. 01, Issue 02
  • DOI: 10.1142/s0219749903000140

Permutationally Invariant Quantum Tomography
journal, December 2010