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Title: Universal programmable quantum circuit schemes to emulate an operator

Abstract

Unlike fixed designs, programmable circuit designs support an infinite number of operators. The functionality of a programmable circuit can be altered by simply changing the angle values of the rotation gates in the circuit. Here, we present a new quantum circuit design technique resulting in two general programmable circuit schemes. The circuit schemes can be used to simulate any given operator by setting the angle values in the circuit. This provides a fixed circuit design whose angles are determined from the elements of the given matrix-which can be non-unitary-in an efficient way. We also give both the classical and quantum complexity analysis for these circuits and show that the circuits require a few classical computations. For the electronic structure simulation on a quantum computer, one has to perform the following steps: prepare the initial wave function of the system; present the evolution operator U=e{sup -iHt} for a given atomic and molecular Hamiltonian H in terms of quantum gates array and apply the phase estimation algorithm to find the energy eigenvalues. Thus, in the circuit model of quantum computing for quantum chemistry, a crucial step is presenting the evolution operator for the atomic and molecular Hamiltonians in terms of quantum gatemore » arrays. Since the presented circuit designs are independent from the matrix decomposition techniques and the global optimization processes used to find quantum circuits for a given operator, high accuracy simulations can be done for the unitary propagators of molecular Hamiltonians on quantum computers. As an example, we show how to build the circuit design for the hydrogen molecule.« less

Authors:
; ;  [1];  [2]
  1. Department of Computer Science, Purdue University, West Lafayette, Indiana 47907 (United States)
  2. Department of Chemistry, Department of Physics and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 (United States)
Publication Date:
OSTI Identifier:
22099137
Resource Type:
Journal Article
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 137; Journal Issue: 23; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ACCURACY; ALGEBRA; ALGORITHMS; CALCULATION METHODS; CHEMISTRY; DECOMPOSITION; DESIGN; EIGENVALUES; ELECTRONIC STRUCTURE; EVOLUTION; HAMILTONIANS; HYDROGEN; MATRICES; OPTIMIZATION; QUANTUM COMPUTERS; SIMULATION; WAVE FUNCTIONS

Citation Formats

Daskin, Anmer, Grama, Ananth, Kollias, Giorgos, Kais, Sabre, and Qatar Environment and Energy Research Institute, Doha. Universal programmable quantum circuit schemes to emulate an operator. United States: N. p., 2012. Web. doi:10.1063/1.4772185.
Daskin, Anmer, Grama, Ananth, Kollias, Giorgos, Kais, Sabre, & Qatar Environment and Energy Research Institute, Doha. Universal programmable quantum circuit schemes to emulate an operator. United States. https://doi.org/10.1063/1.4772185
Daskin, Anmer, Grama, Ananth, Kollias, Giorgos, Kais, Sabre, and Qatar Environment and Energy Research Institute, Doha. Fri . "Universal programmable quantum circuit schemes to emulate an operator". United States. https://doi.org/10.1063/1.4772185.
@article{osti_22099137,
title = {Universal programmable quantum circuit schemes to emulate an operator},
author = {Daskin, Anmer and Grama, Ananth and Kollias, Giorgos and Kais, Sabre and Qatar Environment and Energy Research Institute, Doha},
abstractNote = {Unlike fixed designs, programmable circuit designs support an infinite number of operators. The functionality of a programmable circuit can be altered by simply changing the angle values of the rotation gates in the circuit. Here, we present a new quantum circuit design technique resulting in two general programmable circuit schemes. The circuit schemes can be used to simulate any given operator by setting the angle values in the circuit. This provides a fixed circuit design whose angles are determined from the elements of the given matrix-which can be non-unitary-in an efficient way. We also give both the classical and quantum complexity analysis for these circuits and show that the circuits require a few classical computations. For the electronic structure simulation on a quantum computer, one has to perform the following steps: prepare the initial wave function of the system; present the evolution operator U=e{sup -iHt} for a given atomic and molecular Hamiltonian H in terms of quantum gates array and apply the phase estimation algorithm to find the energy eigenvalues. Thus, in the circuit model of quantum computing for quantum chemistry, a crucial step is presenting the evolution operator for the atomic and molecular Hamiltonians in terms of quantum gate arrays. Since the presented circuit designs are independent from the matrix decomposition techniques and the global optimization processes used to find quantum circuits for a given operator, high accuracy simulations can be done for the unitary propagators of molecular Hamiltonians on quantum computers. As an example, we show how to build the circuit design for the hydrogen molecule.},
doi = {10.1063/1.4772185},
url = {https://www.osti.gov/biblio/22099137}, journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 23,
volume = 137,
place = {United States},
year = {2012},
month = {12}
}