TY - GEN

T1 - Quantum Advantage with Noisy Shallow Circuits in 3D

AU - Bravyi, Sergey

AU - Gosset, David

AU - Koenig, Robert

AU - Tomamichel, Marco

N1 - Publisher Copyright:
© 2019 IEEE.

PY - 2019/11

Y1 - 2019/11

N2 - Prior work has shown that there exists a relation problem which can be solved with certainty by a constant-depth quantum circuit composed of geometrically local gates in two dimensions, but cannot be solved with high probability by any classical constant depth circuit composed of bounded fan-in gates. Here we provide two extensions of this result. Firstly, we show that a separation in computational power persists even when the constant-depth quantum circuit is restricted to geometrically local gates in one dimension. The corresponding quantum algorithm is the simplest we know of which achieves a quantum advantage of this type. Our second, main result, is that a separation persists even if the shallow quantum circuit is corrupted by noise. We construct a relation problem which can be solved with near certainty using a noisy constant-depth quantum circuit composed of geometrically local gates in three dimensions, provided the noise rate is below a certain constant threshold value. On the other hand, the problem cannot be solved with high probability by a noise-free classical circuit of constant depth. A key component of the proof is a quantum error-correcting code which admits constant-depth logical Clifford gates and single-shot logical state preparation. We show that the surface code meets these criteria.

AB - Prior work has shown that there exists a relation problem which can be solved with certainty by a constant-depth quantum circuit composed of geometrically local gates in two dimensions, but cannot be solved with high probability by any classical constant depth circuit composed of bounded fan-in gates. Here we provide two extensions of this result. Firstly, we show that a separation in computational power persists even when the constant-depth quantum circuit is restricted to geometrically local gates in one dimension. The corresponding quantum algorithm is the simplest we know of which achieves a quantum advantage of this type. Our second, main result, is that a separation persists even if the shallow quantum circuit is corrupted by noise. We construct a relation problem which can be solved with near certainty using a noisy constant-depth quantum circuit composed of geometrically local gates in three dimensions, provided the noise rate is below a certain constant threshold value. On the other hand, the problem cannot be solved with high probability by a noise-free classical circuit of constant depth. A key component of the proof is a quantum error-correcting code which admits constant-depth logical Clifford gates and single-shot logical state preparation. We show that the surface code meets these criteria.

KW - quantum algorithms

KW - quantum error correction

UR - http://www.scopus.com/inward/record.url?scp=85078437263&partnerID=8YFLogxK

U2 - 10.1109/FOCS.2019.00064

DO - 10.1109/FOCS.2019.00064

M3 - Conference contribution

AN - SCOPUS:85078437263

T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

SP - 995

EP - 999

BT - Proceedings - 2019 IEEE 60th Annual Symposium on Foundations of Computer Science, FOCS 2019

PB - IEEE Computer Society

T2 - 60th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2019

Y2 - 9 November 2019 through 12 November 2019

ER -