Arithmetic Circuits for Multilevel Qudits Based on Quantum Fourier Transform

Abstract

We present some basic integer arithmetic quantum circuits, such as adders and multipliers-accumulators of various forms, as well as diagonal operators, which operate on multilevel qudits. The integers to be processed are represented in an alternative basis after they have been Fourier transformed. Several arithmetic circuits operating on Fourier transformed integers have appeared in the literature for two level qubits. Here we extend these techniques on multilevel qudits, as they may offer some advantages relative to qubits implementations. The arithmetic circuits presented can be used as basic building blocks for higher level algorithms such as quantum phase estimation, quantum simulation, quantum optimization etc., but they can also be used in the implementation of a quantum fractional Fourier transform as it is shown in a companion work presented separately.

arXiv comment34 pages, 18 figures

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• Generalized Toffoli gate decomposition using ququints: Towards realizing Grover's algorithm with qudits
• Towards multiqudit quantum processor based on a ${}^{171}$Yb${}^{+}$ ion string: Realizing basic quantum algorithms
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• Qutrit Circuits and Algebraic Relations: A Pathway to Efficient Spin-1 Hamiltonian Simulation
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• Everything You Always Wanted to Know About Quantum Circuits
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• QFT based quantum arithmetic logic unit on IBM quantum computer
• A Complete and Natural Rule Set for Multi-Qutrit Clifford Circuits
• Transpiling quantum assembly language circuits to a qudit form
• Resilient superconducting-element design with genetic algorithms
• Tradeoff between noise and banding in a quantum adder with qudits
• Efficient circuit compression by multiqudit entangling gates in linear optical quantum computation