Universal quantum circuit for two-qubit transformations with three controlled-NOT gates
By Guifré Vidal, Christopher M. Dawson. 2003
250 citations recorded by the source corpus.
We consider quantum circuits made of controlled-NOT (CNOT) gates and single-qubit unitary gates and look for constructions that minimize the use of CNOT gates. We show, by means of an explicit quantum circuit, that three CNOT gates are necessary and sufficient in order to implement an arbitrary unitary transformation of two qubits. We also identify the subset of two-qubit gates that can be performed with only two CNOT gates and provide a simple characterization for them.
View Paper: https://www.semanticscholar.org/paper/340445b277ac3b518689432c2eccf6c0fe6da160
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
- Seyon Sivarajah
- David J. Wineland
- D. Hanneke
- Silas Dilkes
- Brian Coyle
- Alexander Cowtan
- Dietrich Leibfried
- Will Simmons
Citations in the corpus
- Large-scale silicon quantum photonics implementing arbitrary two-qubit processing (2018, unknown): “[4] Guifre Vidal and Christopher M Dawson.”
- t|ket⟩: a retargetable compiler for NISQ devices (2020, methodology): “Any two-qubit unitary can be synthesised using at most three CX gates and 15 parametrised single-qubit gates (from any choice of Rx, Ry, and Rz), given by the KAK decomposition [68, 69].”
- Realization of a programmable two-qubit quantum processor (2009, methodology): “Some wellchosen operations can be performed with two or fewer applications of two-qubit gates, but these form an infinitesimal subset in the space of two-qubit operations[13].”
- Geometric (2019, background): “Thus, there were eight global patterns formed by local dot motion, with four patterns exhibiting a right-tilted contour ( No. 1 –”
- Robust data encodings for quantum classifiers (2020, background): “This decomposition can realize any two qubit unitary [83] up to global phase with the addition of a single qubit rotation on the bottom qubit at the end of the circuit.”