Year: 2025
Type: preprint
Abstract: Simon's problem admits an exponential quantum speedup, but current quantum devices support only qubits. This work introduces a general construction for simulating qudit versions of Simon's algorithm on qubit hardware by defining virtual qudits implemented through controlled permutations and qudit phase operations. We build a dimension lifted oracle that encodes the hidden shift in dimension d and show how to realize its action using only qubit gates. We mathematically verify that the lifted circuit reproduces the correct measurement statistics, analyze the depth overhead tradeoffs as a function of d, and provide numerical simulations in QuTiP for example values. Our approach demonstrates how higher-dimensional structures can be embedded into qubit devices and provides a general method for extending qudit algorithms to current hardware.
Source: arXiv (Cornell University)
Authors: Semre, Abed, Frankel, Steven
Institution: Technion – Israel Institute of Technology
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7110848884
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