Abstract
We demonstrate that the unbounded fan-out gate is very powerful. Constant-depth polynomial-size quantum circuits with bounded fan-in and unbounded fan-out over a fixed basis (denoted by QNCso0f) can approximate with polynomially small error the following gates: parity, mod[q], And, Or, majority, threshold[t], exact[q], and counting. Classically, we need logarithmic depth even if we can use unbounded fan-in gates. If we allow arbitrary one-qubit gates instead of a fixed basis, then these circuits can also be made exact in log-star depth. Sorting, arithmetical operations, phase estimation, and the quantum Fourier transform can also be approximated in constant depth.
Supported by the Alberta Ingenuity Fund and the Pacific Institute for the Mathematical Sciences.
Work conducted in part while at Vrije Universiteit, Amsterdam. Partially supported by EU fifth framework project QAIP, IST-1999-11234 and RESQ, IST-2001-37559.
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Høyer, P., Špalek, R. (2003). Quantum Circuits with Unbounded Fan-out. In: Alt, H., Habib, M. (eds) STACS 2003. STACS 2003. Lecture Notes in Computer Science, vol 2607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36494-3_22
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DOI: https://doi.org/10.1007/3-540-36494-3_22
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