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Equivalence Checking of Sequential Quantum Circuits.

Authors :
Wang, Qisheng
Li, Riling
Ying, Mingsheng
Source :
IEEE Transactions on Computer-Aided Design of Integrated Circuits & Systems. Sep2022, Vol. 41 Issue 9, p3143-3156. 14p.
Publication Year :
2022

Abstract

We define a formal framework for equivalence checking of sequential quantum circuits. The model we adopt is a quantum state machine, which is a natural quantum generalization of Mealy machines. A major difficulty in checking quantum circuits (but not present in checking classical circuits) is that the state spaces of quantum circuits are continuums. This difficulty is resolved by our main theorem showing that equivalence checking of two quantum Mealy machines can be done with input sequences that are taken from some chosen basis (which are finite) and have a length quadratic in the dimensions of the state Hilbert spaces of the machines. Based on this theoretical result, we develop an (and to the best of our knowledge, the first) algorithm for checking equivalence of sequential quantum circuits with running time $\mathcal {O}(2^{3m+5l}(2^{3m}{\,+\,}2^{3l}))$ , where $m$ and $l$ denote the numbers of input and internal qubits, respectively. The complexity of our algorithm is comparable with that of the known algorithms for checking classical sequential circuits in the sense that both are exponential in the number of (qu)bits. Several case studies and experiments are presented. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
02780070
Volume :
41
Issue :
9
Database :
Academic Search Index
Journal :
IEEE Transactions on Computer-Aided Design of Integrated Circuits & Systems
Publication Type :
Academic Journal
Accession number :
158649738
Full Text :
https://doi.org/10.1109/TCAD.2021.3117506