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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Bibliographic Details
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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Summary: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.
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ISSN:0020-7748
1572-9575
DOI:10.1007/s10773-017-3389-4