### 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^{-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.

Original language | English |
---|---|

Article number | 234112 |

Journal | Journal of Chemical Physics |

Volume | 137 |

Issue number | 23 |

DOIs | |

Publication status | Published - 21 Dec 2012 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

*Journal of Chemical Physics*,

*137*(23), [234112]. https://doi.org/10.1063/1.4772185

**Universal programmable quantum circuit schemes to emulate an operator.** / Daskin, Anmer; Grama, Ananth; Kollias, Giorgos; Kais, Sabre.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 137, no. 23, 234112. https://doi.org/10.1063/1.4772185

}

TY - JOUR

T1 - Universal programmable quantum circuit schemes to emulate an operator

AU - Daskin, Anmer

AU - Grama, Ananth

AU - Kollias, Giorgos

AU - Kais, Sabre

PY - 2012/12/21

Y1 - 2012/12/21

N2 - 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-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.

AB - 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-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.

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UR - http://www.scopus.com/inward/citedby.url?scp=84871939999&partnerID=8YFLogxK

U2 - 10.1063/1.4772185

DO - 10.1063/1.4772185

M3 - Article

C2 - 23267476

AN - SCOPUS:84871939999

VL - 137

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 23

M1 - 234112

ER -