Quantum circuits with uniformly controlled one-qubit gates

Abstract

Uniformly controlled one-qubit gates are quantum gates which can be represented as direct sums of two-dimensional unitary operators acting on a single qubit. We present a quantum gate array which implements any n-qubit gate of this type using at most 2^{n-1} - 1 controlled-NOT gates, 2^{n-1} one-qubit gates and a single diagonal n-qubit gate. The circuit is based on the so-called quantum multiplexor, for which we provide a modified construction. We illustrate the versatility of these gates by applying them to the decomposition of a general n-qubit gate and a local state preparation procedure. Moreover, we study their implementation using only nearest-neighbor gates. We give upper bounds for the one-qubit and controlled-NOT gate counts for all the aforementioned applications. In all four cases, the proposed circuit topologies either improve on or achieve the previously reported upper bounds for the gate counts. Thus, they provide the most efficient method for general gate decompositions currently known.

8 pages, 10 figures. v2 has simpler notation and sharpens some results

References in corpus (14)

• Elementary gates for quantum computation
• Decoherence, einselection, and the quantum origins of the classical
• NMR Techniques for Quantum Control and Computation
• Information and Computation: Classical and Quantum Aspects
• Optimal Quantum Circuits for General Two-Qubit Gates
• Quantum Circuits for General Multiqubit Gates
• Minimal Universal Two-qubit Quantum Circuits
• A universal quantum circuit for two-qubit transformations with three CNOT gates
• Efficient decomposition of quantum gates
• Exact two-qubit universal quantum circuit
• Two-electron quantum dots as scalable qubits
• Programmable networks for quantum algorithms
• Optimal local preparation of an arbitrary mixed state of two qubits. Closed expression for the single copy case
• Tools for Quantum Algorithms

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