Quantum circuit verification is a critical yet notoriously challenging task in quantum computing. Full simulation of quantum circuits scales exponentially with the number of qubits and circuit depth, rendering it impractical for even moderately sized circuits. This paper proposes a novel approach to automated theorem proving for quantum circuit verification leveraging abstract interpretation. Our core idea is to approximate the behavior of quantum circuits using abstract interpretations, significantly reducing the computational complexity of the verification process. We outline a framework where abstract domains are constructed to represent the key properties of quantum circuits, such as qubit state fidelities and gate operations. The framework then employs logical reasoning and inference rules based on these abstract representations to automatically determine the correctness of a circuit against a given specification. We demonstrate the feasibility of this approach and discuss its potential to dramatically improve the efficiency and scalability of quantum circuit verification. The key benefit lies in shifting the verification burden from exact simulation to a more tractable abstract analysis.
Formal verification of quantum circuits is a crucial step towards building reliable quantum computers. However, the exponential scaling of quantum states makes traditional formal verification methods impractical for anything beyond small circuits. This paper proposes a novel approach leveraging self-referential quantum circuits for verification. The core idea is to create a verification circuit that recursively simulates and verifies the behavior of the original circuit. This self-referential process allows for a more efficient exploration of the state space, mitigating the exponential growth problem. We define the key components of this system, including the self-referential circuit architecture and the underlying mathematical framework. The paper outlines the potential for this approach to overcome limitations of existing techniques and represents a significant advancement in the field of quantum verification. The primary mathematical challenge addressed is the efficient simulation of quantum circuits within a self-referential structure.