Quantum advantage with shallow circuits
Abstract
Quantum effects can enhance information-processing capabilities and speed up the solution of certain computational problems. Whether a quantum advantage can be rigorously proven in some setting or demonstrated experimentally using near-term devices is the subject of active debate. We show that parallel quantum algorithms running in a constant time period are strictly more powerful than their classical counterparts; they are provably better at solving certain linear algebra problems associated with binary quadratic forms. Our work gives an unconditional proof of a computational quantum advantage and simultaneously pinpoints its origin: It is a consequence of quantum nonlocality. The proposed quantum algorithm is a suitable candidate for near-future experimental realizations, as it requires only constant-depth quantum circuits with nearest-neighbor gates on a two-dimensional grid of qubits (quantum bits).
- Publication:
-
Science
- Pub Date:
- October 2018
- DOI:
- 10.1126/science.aar3106
- arXiv:
- arXiv:1704.00690
- Bibcode:
- 2018Sci...362..308B
- Keywords:
-
- COMP/MATH; PHYSICS;
- Quantum Physics;
- Computer Science - Computational Complexity
- E-Print:
- Science Vol. 362, Issue 6412, pp. 308-311 (2018)