Decompositions of n-qubit Toffoli Gates with Linear Circuit Complexity

Toffoli gates are natural elements for the circuit model based quantum computation. We investigate general resource requirements for arbitrary n -qubit Toffoli gate. These resources consist of the nontrivial Clifford gate (CNOT), non-Clifford gate ( T gate), ancillary qubits, and circuit depth. To i...

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Published in:	International journal of theoretical physics Vol. 56; no. 7; pp. 2350 - 2361
Main Authors:	He, Yong, Luo, Ming-Xing, Zhang, E., Wang, Hong-Ke, Wang, Xiao-Feng
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.07.2017 Springer Nature B.V
Subjects:	Circuits Complexity Computation Decomposition Elementary Particles Gates Gates (circuits) Mathematical and Computational Physics Phase shift Physics Physics and Astronomy Quantum Field Theory Quantum Physics Qubits (quantum computing) Theoretical circuit complexity Toffoli gate Quantum circuit Clifford gates
ISSN:	0020-7748, 1572-9575
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Abstract	Toffoli gates are natural elements for the circuit model based quantum computation. We investigate general resource requirements for arbitrary n -qubit Toffoli gate. These resources consist of the nontrivial Clifford gate (CNOT), non-Clifford gate ( T gate), ancillary qubits, and circuit depth. To implement n -qubit Toffoli gates, we consider two cases: only one auxiliary qubit and unlimited auxiliary qubits. The key of the first case is to decompose an n -qubit Toffoli gate into the reduced Toffoli gate modulo phase shift using the Clifford gates and one ancillary qubit. With this construction, it only requires O ( n ) number of general resources for an n -qubit Toffoli gate. For the second case, an approximate Toffoli gate is constructed to obtain efficient decomposition of a Toffoli gate. The new decomposition can further reduce general resources except auxiliary qubits.
AbstractList	Toffoli gates are natural elements for the circuit model based quantum computation. We investigate general resource requirements for arbitrary n-qubit Toffoli gate. These resources consist of the nontrivial Clifford gate (CNOT), non-Clifford gate (T gate), ancillary qubits, and circuit depth. To implement n-qubit Toffoli gates, we consider two cases: only one auxiliary qubit and unlimited auxiliary qubits. The key of the first case is to decompose an n-qubit Toffoli gate into the reduced Toffoli gate modulo phase shift using the Clifford gates and one ancillary qubit. With this construction, it only requires O(n) number of general resources for an n-qubit Toffoli gate. For the second case, an approximate Toffoli gate is constructed to obtain efficient decomposition of a Toffoli gate. The new decomposition can further reduce general resources except auxiliary qubits. Toffoli gates are natural elements for the circuit model based quantum computation. We investigate general resource requirements for arbitrary n -qubit Toffoli gate. These resources consist of the nontrivial Clifford gate (CNOT), non-Clifford gate ( T gate), ancillary qubits, and circuit depth. To implement n -qubit Toffoli gates, we consider two cases: only one auxiliary qubit and unlimited auxiliary qubits. The key of the first case is to decompose an n -qubit Toffoli gate into the reduced Toffoli gate modulo phase shift using the Clifford gates and one ancillary qubit. With this construction, it only requires O ( n ) number of general resources for an n -qubit Toffoli gate. For the second case, an approximate Toffoli gate is constructed to obtain efficient decomposition of a Toffoli gate. The new decomposition can further reduce general resources except auxiliary qubits.
Author	Wang, Hong-Ke Luo, Ming-Xing Zhang, E. He, Yong Wang, Xiao-Feng
Author_xml	– sequence: 1 givenname: Yong surname: He fullname: He, Yong email: heyongmath@163.com organization: Department of Mathematics and Physics, Chongqing University of Science and Technology – sequence: 2 givenname: Ming-Xing surname: Luo fullname: Luo, Ming-Xing organization: Information Security and National Computing Grid Laboratory, Southwest Jiaotong University, Department of Physics, University of Michigan – sequence: 3 givenname: E. surname: Zhang fullname: Zhang, E. organization: Department of Mathematics and Physics, Chongqing University of Science and Technology – sequence: 4 givenname: Hong-Ke surname: Wang fullname: Wang, Hong-Ke organization: Department of Mathematics and Physics, Chongqing University of Science and Technology – sequence: 5 givenname: Xiao-Feng surname: Wang fullname: Wang, Xiao-Feng organization: Department of Mathematics and Physics, Chongqing University of Science and Technology
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Snippet	Toffoli gates are natural elements for the circuit model based quantum computation. We investigate general resource requirements for arbitrary n -qubit Toffoli... Toffoli gates are natural elements for the circuit model based quantum computation. We investigate general resource requirements for arbitrary n-qubit Toffoli...
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SubjectTerms	Circuits Complexity Computation Decomposition Elementary Particles Gates Gates (circuits) Mathematical and Computational Physics Phase shift Physics Physics and Astronomy Quantum Field Theory Quantum Physics Qubits (quantum computing) Theoretical
Title	Decompositions of n-qubit Toffoli Gates with Linear Circuit Complexity
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