Quantum-inspired permanent identities
The permanent is pivotal to both complexity theory and combinatorics. In quantum computing, the permanent appears in the expression of output amplitudes of linear optical computations, such as in the Boson Sampling model. Taking advantage of this connection, we give quantum-inspired proofs of many e...
Saved in:
| Published in: | Quantum (Vienna, Austria) Vol. 6; p. 877 |
|---|---|
| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
19-12-2022
|
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | The permanent is pivotal to both complexity theory and combinatorics. In quantum computing, the permanent appears in the expression of output amplitudes of linear optical computations, such as in the Boson Sampling model. Taking advantage of this connection, we give quantum-inspired proofs of many existing as well as new remarkable permanent identities. Most notably, we give a quantum-inspired proof of the MacMahon master theorem as well as proofs for new generalizations of this theorem. Previous proofs of this theorem used completely different ideas. Beyond their purely combinatorial applications, our results demonstrate the classical hardness of exact and approximate sampling of linear optical quantum computations with input cat states. |
|---|---|
| ISSN: | 2521-327X 2521-327X |
| DOI: | 10.22331/q-2022-12-19-877 |