Introduction to Quantum Algorithms for Physics and Chemistry

  1. Sabre Kais
  1. Man-Hong Yung1,2,
  2. James D. Whitfield2,3,4,
  3. Sergio Boixo2,5,
  4. David G. Tempel2,6 and
  5. Alán Aspuru-Guzik2

Published Online: 21 MAR 2014

DOI: 10.1002/9781118742631.ch03

Quantum Information and Computation for Chemistry: Advances in Chemical Physics Volume 154

Quantum Information and Computation for Chemistry: Advances in Chemical Physics Volume 154

How to Cite

Yung, M.-H., Whitfield, J. D., Boixo, S., Tempel, D. G. and Aspuru-Guzik, A. (2014) Introduction to Quantum Algorithms for Physics and Chemistry, in Quantum Information and Computation for Chemistry: Advances in Chemical Physics Volume 154 (ed S. Kais), John Wiley & Sons, Inc., Hoboken, New Jersey. doi: 10.1002/9781118742631.ch03

Editor Information

  1. Purdue University, QEERI, Qatar Santa Fe Institute

Author Information

  1. 1

    Center for Quantum Information, Institute for Interdisciplinary Information, Sciences, Tsinghua University, Beijing 100084, P. R. China

  2. 2

    Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, MA 02138, USA

  3. 3

    NEC Laboratories America, 4 Independence Way, Princeton, NJ 08540, USA

  4. 4

    Department of Physics, Columbia University, 538 West 120th Street, New York, NY 10027, USA

  5. 5

    Google, 340 Main St, Venice, CA 90291, USA

  6. 6

    Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA

Publication History

  1. Published Online: 21 MAR 2014
  2. Published Print: 14 FEB 2014

Book Series:

  1. Advances in Chemical Physics

Book Series Editors:

  1. Stuart A. Rice and
  2. Aaron R. Dinner

Series Editor Information

  1. Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois

ISBN Information

Print ISBN: 9781118495667

Online ISBN: 9781118742631

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Keywords:

  • chemistry;
  • digital quantum simulation;
  • physics;
  • quantum algorithms;
  • quantum computational complexity;
  • Suzuki–Trotter formulas

Summary

This chapter introduces the basic concepts of digital quantum simulation. The study of the computational complexity of problems in quantum simulation helps us better understand how quantum computers can surpass classical computers. The chapter briefly summarizes a few important examples of complexity classes of decision problems. Quantum algorithms are procedures for applying elementary quantum logic gates to complete certain unitary transformations of the input state. The steps involved in carrying out a digital quantum simulation consist of three parts: state preparation, time evolution, and measurement of observables. The chapter provides an overview of state preparation and simulation of time evolution. The use of Suzuki–Trotter formulas in quantum simulation for time-independent sparse Hamiltonians is reviewed. The chapter reviews a method to effect nondestructive measurements of constants of the motion within the adiabatic model.