Abstract
Playing with causal orders leads to quadratic speed-up: An efficient algorithm is introduced and implemented in a scalable fiber-optic based experiment that achieves, for the first time, a quantum 4-switch gate.
Highlights
Quantum mechanics allows for processes where two or more events take place in a quantum superposition of different temporal orders
From a more practical perspective, advanced quantum computational models without definite gate orders have sparked a great deal of fundamental interest, as they do not fit into the usual paradigm of circuits with fixed gate connections [6,7,10,11,12,13]
We present an algorithm to solve it efficiently, illustrating a quantum computational advantage associated to the coherent quantum control of the order in which a sequence of N unitary operations is applied
Summary
Quantum mechanics allows for processes where two or more events take place in a quantum superposition of different temporal orders. SN allows one to solve a promise problem [12,14] on the permutations of N unknown unitary gates with quadratically fewer queries in N than all known circuits with fixed gate order. The algorithm to solve this problem exploits the quantum N -switch—consuming N queries to the gates—to deterministically find the column This represents a speedup quadratic in N in query complexity (i.e., number of queries) with respect to all known algorithms exploiting circuits with fixed gate orders The algorithm is an interesting computational primitive on its own and a practical tool to benchmark experimental realizations of SN , because the quantum N -switch is the only known process for which the algorithm succeeds with unit probability for all gates satisfying the promise while only consuming N gate queries. Our results represent the first demonstration of the quantum N -switch gate for N larger than 2, as well as of its efficiency for phase-estimation problems involving multiple unknown gates
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