Universal programmable quantum circuit schemes to emulate an operator

Journal Article · Fri Dec 21 00:00:00 EST 2012 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4772185· OSTI ID:22099137

Daskin, Anmer; Grama, Ananth; Kollias, Giorgos ^[1]; Kais, Sabre ^[2]

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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)

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.

• OSTI ID: 22099137
• Journal Information: Journal of Chemical Physics, Vol. 137, Issue 23; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

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