Name
Abstract | ||
|---|---|---|
In this work, we present a method of decomposition of arbitrary unitary matrix $$U\\in \\mathbf {U}(2^k)$$UźU(2k) into a product of single-qubit negator and controlled-$$\\sqrt{\\text{ NOT }}$$NOT gates. Since the product results with negator matrix, which can be treated as complex analogue of bistochastic matrix, our method can be seen as complex analogue of Sinkhorn---Knopp algorithm, where diagonal matrices are replaced by adding and removing an one-qubit ancilla. The decomposition can be found constructively, and resulting circuit consists of $$O(4^k)$$O(4k) entangling gates, which is proved to be optimal. An example of such transformation is presented. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1007/s11128-016-1448-z | Quantum Information Processing |
Keywords | Field | DocType |
Matrix decomposition,Negator matrix,Scaling matrix | Quantum,Quantum mechanics,Constructive,Matrix (mathematics),Matrix decomposition,Unitary matrix,Pure mathematics,Symmetric matrix,Diagonal matrix,Scaling,Physics | Journal |
Volume | Issue | ISSN |
15 | 12 | 1570-0755 |
Citations | PageRank | References |
0 | 0.34 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Adam Glos | 1 | 0 | 0.68 |
| Przemyslaw Sadowski | 2 | 4 | 1.99 |