Compiling Permutations for Superconducting QPUs

In this paper we consider the compilation of quantum state permutations into quantum gates for physical quantum computers. A sequence of generic single-target gates, which realize the input permutation, are extracted using a decomposition based reversible logic synthesis algorithm. We present a compilation algorithm that translates single-target gates into a quantum circuit composed of the elementary quantum gate sets that are supported by IBM's 5-qubit and 16-qubit, and Rigetti's 8-qubit and 19-qubit superconducting transmon QPUs. Compared to generic state-of-the-art compilation techniques, our technique improves gate volume and gate depth by up to 59% and 53%, respectively.

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Quantum computing

A quantum computer is a computer that exploits quantum mechanical phenomena. At small scales, physical matter exhibits properties of both particles and waves, and quantum computing leverages this behavior, specifically quantum superposition and entanglement, using specialized hardware that supports the preparation and manipulation of quantum states. Classical physics cannot explain the operation of these quantum devices, and a scalable quantum computer could perform some calculations exponentially faster than any modern "classical" computer.

Quantum logic gate

In quantum computing and specifically the quantum circuit model of computation, a quantum logic gate (or simply quantum gate) is a basic quantum circuit operating on a small number of qubits. They are the building blocks of quantum circuits, like classical logic gates are for conventional digital circuits. Unlike many classical logic gates, quantum logic gates are reversible. It is possible to perform classical computing using only reversible gates.

Quantum Fourier transform

In quantum computing, the quantum Fourier transform (QFT) is a linear transformation on quantum bits, and is the quantum analogue of the discrete Fourier transform. The quantum Fourier transform is a part of many quantum algorithms, notably Shor's algorithm for factoring and computing the discrete logarithm, the quantum phase estimation algorithm for estimating the eigenvalues of a unitary operator, and algorithms for the hidden subgroup problem. The quantum Fourier transform was discovered by Don Coppersmith.