Computational advantage from quantum superposition of multiple temporal orders of photonic gates

• URL: http://arxiv.org/abs/2002.07817v3
• Date: Tue, 9 Feb 2021 11:30:38 GMT
• Title: Computational advantage from quantum superposition of multiple temporal orders of photonic gates
• Authors: M\'arcio M. Taddei, Jaime Cari\~ne, Daniel Mart\'inez, Tania Garc\'ia, Nayda Guerrero, Alastair A. Abbott, Mateus Ara\'ujo, Cyril Branciard, Esteban S. G\'omez, Stephen P. Walborn, Leandro Aolita and Gustavo Lima
• Abstract summary: A control quantum system can coherently determine the order in which a target quantum system undergoes $N$ gate operations. We 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Models for quantum computation with circuit connections subject to the quantum superposition principle have been recently proposed. There, 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 speed-up with target-system dimension as small as 2 regardless of $N$. We use state-of-the-art multi-core 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.

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