TL;DR
This paper introduces a symbolic reasoning method for quantum circuits using Coq, enabling scalable and automated analysis of quantum behavior without exponential matrix computations.
Contribution
It presents a novel symbolic approach to quantum circuit reasoning that improves scalability and automation compared to traditional matrix-based methods.
Findings
Symbolic reasoning scales better than explicit matrix computation.
The approach is effectively automated in Coq.
Demonstrated with typical quantum circuit examples.
Abstract
A quantum circuit is a computational unit that transforms an input quantum state to an output one. A natural way to reason about its behavior is to compute explicitly the unitary matrix implemented by it. However, when the number of qubits increases, the matrix dimension grows exponentially and the computation becomes intractable. In this paper, we propose a symbolic approach to reasoning about quantum circuits. It is based on a small set of laws involving some basic manipulations on vectors and matrices. This symbolic reasoning scales better than the explicit one and is well suited to be automated in Coq, as demonstrated with some typical examples.
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