Implementing a fast unbounded quantum fanout gate using power-law interactions
PHYSICAL REVIEW RESEARCH(2022)
摘要
The standard circuit model for quantum computation presumes the ability to directly perform gates between arbitrary pairs of qubits, which is unlikely to be practical for large-scale experiments. Power-law interactions with strength decaying as 1/r alpha in the distance r provide an experimentally realizable resource for information processing, whilst still retaining long-range connectivity. We leverage the power of these interactions to imple-ment a fast quantum fanout gate with an arbitrary number of targets. Our implementation allows the quantum Fourier transform (QFT) and Shor's algorithm to be performed on a D-dimensional lattice of qubits in time that scales (poly)logarithmically in the number of qubits, using interactions with alpha 2D. As a corollary, we show that power-law systems with alpha 2D are difficult to simulate classically even for short times, under a standard assumption that factoring is classically intractable. Complementarily, we develop a technique to give a general lower bound-linear in the size of the system-on the time required to implement the QFT and the fanout gate in systems that are constrained by a linear light cone. This allows us to prove an asymptotically tighter lower bound for long-range systems than was possible with previously available techniques.
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