### Abstract

Given a set of quantum gates and a target unitary operation, the most elementary task of quantum compiling is the identification of a sequence of the gates that approximates the target unitary to a determined precision. The Solovay-Kitaev theorem provides an elegant solution which is based on the construction of successively tighter "nets" around unity comprised of successively longer sequences of gates. The procedure for the construction of the nets, according to this theorem, requires accessibility to the inverse of the gates as well. In this work, we propose a method for constructing nets around unity without this requirement. The algorithmic procedure is applicable to sets of gates which are diffusive enough, in the sense that sequences of moderate length cover the space of unitary matrices in a uniform way. We prove that the number of gates sufficient for reaching a precision scales as log(1)log3/log2 while the precompilation time is increased as compared to that of the Solovay-Kitaev algorithm by the exponential factor 3/2.

Original language | English |
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Article number | 012325 |

Journal | Physical Review A |

Volume | 98 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jul 24 2018 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A*,

*98*(1), [012325]. https://doi.org/10.1103/PhysRevA.98.012325

**Quantum compiling with diffusive sets of gates.** / Zhiyenbayev, Y.; Akulin, V. M.; Mandilara, Aikaterini.

Research output: Contribution to journal › Article

*Physical Review A*, vol. 98, no. 1, 012325. https://doi.org/10.1103/PhysRevA.98.012325

}

TY - JOUR

T1 - Quantum compiling with diffusive sets of gates

AU - Zhiyenbayev, Y.

AU - Akulin, V. M.

AU - Mandilara, Aikaterini

PY - 2018/7/24

Y1 - 2018/7/24

N2 - Given a set of quantum gates and a target unitary operation, the most elementary task of quantum compiling is the identification of a sequence of the gates that approximates the target unitary to a determined precision. The Solovay-Kitaev theorem provides an elegant solution which is based on the construction of successively tighter "nets" around unity comprised of successively longer sequences of gates. The procedure for the construction of the nets, according to this theorem, requires accessibility to the inverse of the gates as well. In this work, we propose a method for constructing nets around unity without this requirement. The algorithmic procedure is applicable to sets of gates which are diffusive enough, in the sense that sequences of moderate length cover the space of unitary matrices in a uniform way. We prove that the number of gates sufficient for reaching a precision scales as log(1)log3/log2 while the precompilation time is increased as compared to that of the Solovay-Kitaev algorithm by the exponential factor 3/2.

AB - Given a set of quantum gates and a target unitary operation, the most elementary task of quantum compiling is the identification of a sequence of the gates that approximates the target unitary to a determined precision. The Solovay-Kitaev theorem provides an elegant solution which is based on the construction of successively tighter "nets" around unity comprised of successively longer sequences of gates. The procedure for the construction of the nets, according to this theorem, requires accessibility to the inverse of the gates as well. In this work, we propose a method for constructing nets around unity without this requirement. The algorithmic procedure is applicable to sets of gates which are diffusive enough, in the sense that sequences of moderate length cover the space of unitary matrices in a uniform way. We prove that the number of gates sufficient for reaching a precision scales as log(1)log3/log2 while the precompilation time is increased as compared to that of the Solovay-Kitaev algorithm by the exponential factor 3/2.

UR - http://www.scopus.com/inward/record.url?scp=85050456187&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85050456187&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.98.012325

DO - 10.1103/PhysRevA.98.012325

M3 - Article

AN - SCOPUS:85050456187

VL - 98

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 1

M1 - 012325

ER -