Computational Advantage from the Quantum Superposition of Multiple Temporal Orders of Photonic Gates

Overview & Synopsis

Models for quantum computation with circuit connections subject to the quantum superposition principle have recently been proposed. In them, a control quantum system can coherently determine the order in which a target quantum system undergoes $N$ gate operations. This process, known as the quantum $N$-switch, is a resource for several information-processing tasks. In particular, it provides a computational advantage---over fixed-gate-order quantum circuits—for phase-estimation problems involving $N$ unknown unitary gates. However, the corresponding algorithm requires an experimentally unfeasible target-system dimension (super)exponential in $N$. Here, we introduce a promise problem for which the quantum $N$-switch gives an equivalent computational speedup with target-system dimension as small as 2 regardless of $N$. We use state-of-the-art multicore optical-fiber technology to experimentally demonstrate the quantum $N$-switch with $N=4$ gates acting on a photonic-polarization qubit. This is the first observation of a quantum superposition of more than $N=2$ temporal orders, demonstrating its usefulness for efficient phase estimation.