Journal
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
Volume 56, Issue 7, Pages 2350-2361Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10773-017-3389-4
Keywords
Toffoli gate; Quantum circuit; Clifford gates; circuit complexity
Categories
Funding
- Science and Technology Research Project of Chongqing Education Commission [KJ1713339]
- Sichuan Youth Science and Technique Foundation [2017JQ0048]
- National Natural Science Foundation of China [61303039]
- CSC Scholarship
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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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