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arXiv · 2304.01704

Efficient parallelization of quantum basis state shift

Ljubomir Budinski·Ossi Niemimäki·Roberto Zamora-Zamora·Valtteri Lahtinen
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Abstract

Basis state shift is central to many quantum algorithms, most notably the quantum walk. Efficient implementations are of major importance for achieving a quantum speedup for computational applications. We optimize the state shift algorithm by incorporating the shift in different directions in parallel. This provides a significant reduction in the depth of the quantum circuit in comparison to the currently known methods, giving a linear scaling in the number of gates versus working qubits in contrast to the quadratic scaling of the state-of-the-art method based on the quantum Fourier transform. For a one-dimensional array of size $2^n$ for $n > 4$, we derive the total number of $15n + 74$ two-qubit $CX$ gates in the parallel circuit, using a total of $2n-2$ qubits including an ancilla register for the decomposition of multi-controlled gates. We focus on the one-dimensional and periodic shift, but note that the method can be extended to more complex cases.

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Ljubomir Budinski, Ossi Niemimäki, Roberto Zamora-Zamora, Valtteri Lahtinen. 2023-04-04. Efficient parallelization of quantum basis state shift. https://doi.org/10.1088/2058-9565%2Facfab7

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