In a quantum computer, creating superpositions of quantum bits (qubits) in
different states can lead to a speed-up over classical computers [1], but
quantum mechanics also allows for the superposition of quantum circuits [2]. In
fact, it has recently been theoretically predicted that superimposing quantum
circuits, each with a different gate order, could provide quantum computers
with an even further computational advantage [3-5]. Here, we experimentally
demonstrate this enhancement by applying two quantum gates in a superposition
of both possible orders to determine whether the two gates commute or
anti-commute. We are able to make this determination with only a single use (or
query) of each gate, while all quantum circuits with a fixed order of gates
would require at least two uses of one of the gates [3]. Remarkably, when the
problem is scaled to N gates, creating a superposition of quantum circuits is
likely to provide an exponential advantage over classical algorithms, and a
linear advantage over quantum algorithms with fixed gate order [4]. The new
resource that we exploit in our experiment can be interpreted as a
"superposition of causal orders". We demonstrate such a superposition could
allow some quantum algorithms to be implemented with an efficiency that is
unlikely to be achieved on a quantum computer with a fixed gate order.Comment: 10 pages, 7 figures, 2 table