Toward Entailment Checking: Explore Eigenmarking Search
Tatpong Katanyukul

TL;DR
This paper explores a quantum computing approach using eigenmarking with Grover's algorithm to improve entailment checking by distinguishing no-winner cases, potentially advancing logic reasoning methods.
Contribution
It introduces eigenmarking schemes that enhance Grover's algorithm for entailment checking, enabling better identification of no-winner scenarios in quantum logic reasoning.
Findings
Strong distinguishability achieved in all schemes
Best relative distinguishability of 19 and 53
Viable quantum mechanism for differentiating no-winner cases
Abstract
Logic entailment is essential to reasoning, but entailment checking has the worst-case complexity of an exponential of the variable size. With recent development, quantum computing when mature may allow an effective approach for various combinatorial problems, including entailment checking. Grover algorithm uses Grover operations, selective phase inversion and amplitude amplification to address a search over unstructured data with quadratic improvement from a classical method. Its original form is intended to a single-winner scenario: exactly one match is promised. Its extension to multiple-winner cases employs probabilistic control over a number of applications of Grover operations, while a no-winner case is handled by time-out. Our study explores various schemes of ``eigenmarking'' approach. Still relying on Grover operations, but the approach introduces…
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum Information and Cryptography · Quantum Mechanics and Applications
