Equivalence Checking of Sequential Quantum Circuits

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 t...

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Veröffentlicht in:IEEE transactions on computer-aided design of integrated circuits and systems Jg. 41; H. 9; S. 3143 - 3156
Hauptverfasser: Wang, Qisheng, Li, Riling, Ying, Mingsheng
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.09.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algorithms
Automata
Circuits
Continuums
Equivalence
Equivalence checking
Finite state machines
Hilbert space
Integrated circuit modeling
Logic gates
mealy machines
Quantum circuit
quantum circuits
quantum computing
Quantum mechanics
Qubit
Qubits (quantum computing)
Sequential circuits
State machines
ISSN:0278-0070, 1937-4151
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Zusammenfassung: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 <inline-formula> <tex-math notation="LaTeX">\mathcal {O}(2^{3m+5l}(2^{3m}{\,+\,}2^{3l})) </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">m </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">l </tex-math></inline-formula> 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.
Bibliographie:ObjectType-Article-1
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ISSN:0278-0070
1937-4151
DOI:10.1109/TCAD.2021.3117506