Average-case quantum advantage with shallow circuits
FL Gall - arXiv preprint arXiv:1810.12792, 2018 - arxiv.org
arXiv preprint arXiv:1810.12792, 2018•arxiv.org
Recently Bravyi, Gosset and K\" onig (Science 2018) proved an unconditional separation
between the computational powers of small-depth quantum and classical circuits for a
relation. In this paper we show a similar separation in the average-case setting that gives
stronger evidence of the superiority of small-depth quantum computation: we construct a
computational task that can be solved on all inputs by a quantum circuit of constant depth
with bounded-fanin gates (a" shallow" quantum circuit) and show that any classical circuit …
between the computational powers of small-depth quantum and classical circuits for a
relation. In this paper we show a similar separation in the average-case setting that gives
stronger evidence of the superiority of small-depth quantum computation: we construct a
computational task that can be solved on all inputs by a quantum circuit of constant depth
with bounded-fanin gates (a" shallow" quantum circuit) and show that any classical circuit …
Recently Bravyi, Gosset and K\"onig (Science 2018) proved an unconditional separation between the computational powers of small-depth quantum and classical circuits for a relation. In this paper we show a similar separation in the average-case setting that gives stronger evidence of the superiority of small-depth quantum computation: we construct a computational task that can be solved on all inputs by a quantum circuit of constant depth with bounded-fanin gates (a "shallow" quantum circuit) and show that any classical circuit with bounded-fanin gates solving this problem on a non-negligible fraction of the inputs must have logarithmic depth. Our results are obtained by introducing a technique to create quantum states exhibiting global quantum correlations from any graph, via a construction that we call the \emph{extended graph}. Similar results have been very recently (and independently) obtained by Coudron, Stark and Vidick (arXiv:1810.04233), and Bene Watts, Kothari, Schaeffer and Tal (STOC 2019).
arxiv.org