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Scientific Reports

On the quantum circuit implementation of modus ponens

Songsong Dai

Published Jun 20, 2024• 3 citations
Publisher

Abstract

The process of inference reflects the structure of propositions with assigned truth values, either true or false. Modus ponens is a fundamental form of inference that involves affirming the antecedent to affirm the consequent. Inspired by the quantum computer, the superposition of true and false is used for the parallel processing. In this work, we propose a quantum version of modus ponens. Additionally, we introduce two generations of quantum modus ponens: quantum modus ponens inference chain and multidimensional quantum modus ponens. Finally, a simple implementation of quantum modus ponens on the OriginQ quantum computing cloud platform is demonstrated.

DOI
10.1038/s41598-024-65224-9

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The process of inference reflects the structure of propositions with assigned truth values, either true or false. Modus ponens is a fundamental form of inference that involves affirming the antecedent to affirm the consequent. Inspired by the quantum computer, the superposition of true and false is used for the parallel processing. In this work, we propose a quantum version of modus ponens. Additionally, we introduce two generations of quantum modus ponens: quantum modus ponens inference chain and multidimensional quantum modus ponens. Finally, a simple implementation of quantum modus ponens on the OriginQ quantum computing cloud platform is demonstrated.
Classical logic does not apply in quantum theory. However one would like to be able to reason according to some standard rules for quantum systems as well (whether they are an electron or the universe itself). We examine what exactly is needed in order to be able to construct deductive arguments and in particular to maintain the "Modus Ponens" which is the basic deductive rule of inference. It turns out that this requirement restricts the possible theories and in the context of the coevent interpretation it results uniquely to the "multiplicative-scheme".
Abstract Logic is an algebraic structure that defines a set of abstract rules which govern an area of interest. The abstraction property of the rules makes them reusable tools to model different problems and to reason with them. The proliferation of quantum theory brought attention to quantum logic which is a lattice of projectors and it is of importance to quantum computing. Unfortunately, basic tools like implication are not sufficiently studied in that logic, which prevents us from exploiting the power of quantum mechanics in reasoning. This note investigates the implication issue in quantum logic and defines a quantum implication operator for compatible events as well as for incompatible events. The suggested operator depends both on the angle between the vector sub-spaces of the involved events and the angles between the system state and the vector sub-spaces. It differentiates between three cases depending on the angle between the events’ sub-spaces. The article further shows through an example that some classical reasoning rules such as Modus Ponens and Modus Tollens hold given the suggested implication.
Quantum computers can be a revolutionary tool to implement inference engines for fuzzy rule-based systems. In fact, the use of quantum mechanical principles can enable parallel execution of fuzzy rules and allow them to be used efficiently in complex contexts such as distributed and big data environments. This article introduces the very first quantum-based fuzzy inference engine that is capable of providing exponential acceleration in fuzzy rule execution compared to its classical counterpart, and allows a quantum computer to be programmed by fuzzy linguistic rules. The proposed inference engine was implemented using a quantum algorithm design scheme based on the oracle notion. This scheme allows the modeling of a fuzzy rule-based system as a Boolean function, the oracle, which is able to reconstruct the relationships between the antecedent and consequent parts of fuzzy rules, and can be efficiently computed on a quantum computer. The suitability of the proposed quantum algorithm for use as a fuzzy inference engine was tested in a typical benchmark scenario, such as that provided by inverted pendulum control.
Notwithstanding interest and excitement building around quantum computing in the last decades, a concise statement saying where this computing can truly help is still missing. As it is shown in the present paper, equal cost of computation for truth and falsity of experimental quantum propositions (required in order to infer a conclusion from a premise) cannot be achieved with classical computing. On the other hand, this equality might be realized with quantum parallel computing provided that the efficiency of such computing can be greater than 1.
This report introduces a novel class of reasoning architectures, termed Quantum Circuit Reasoning Models (QCRM), which extend the concept of Variational Quantum Circuits (VQC) from energy minimization and classification tasks to structured logical inference and reasoning. We posit that fundamental quantum mechanical operations, superposition, entanglement, interference, and measurement, naturally map to essential reasoning primitives such as hypothesis branching, constraint propagation, consistency enforcement, and decision making. The resulting framework combines quantum-inspired computation with differentiable optimization, enabling reasoning to emerge as a process of amplitude evolution and interference-driven selection of self-consistent states. We develop the mathematical foundation of QCRM, define its parameterized circuit architecture, and show how logical rules can be encoded as unitary transformations over proposition-qubit states. We further formalize a training objective grounded in classical gradient descent over circuit parameters and discuss simulation-based implementations on classical hardware. Finally, we propose the Quantum Reasoning Layer (QRL) as a differentiable hybrid component for composable reasoning models applicable to scientific, biomedical, and chemical inference domains.
In this research, we present a quantum circuit design and implementation for a parallel universal linear bounded automata. This circuit is able to accelerate the inference of algorithmic structures in data for discovering causal generative models. The computation model is practically restricted in time and space resources. A classical exhaustive enumeration of all possible programs on the automata is shown for a couple of example cases. The precise quantum circuit design that allows executing a superposition of programs, along with a superposition of inputs as in the standard quantum Turing machine formulation, is presented. This is the first time, a superposition of classical automata is implemented on the circuit model of quantum computation, having the corresponding mechanistic parts of a classical Turing machine. The superposition of programs allows our model to be used for experimenting with the space of program-output behaviors in algorithmic information theory. Our implementations on OpenQL and Qiskit quantum programming language is copy-left and is publicly available on GitHub.