Abstract We propose a scalable quantum circuit architecture for enforcing logical consistency in systems susceptible to contradiction. The model introduces a modular structure in which each contradiction qubit is paired with a corresponding resolution qubit, and a global consistency flag qubit monitors coherence across the system. Logical constraints are embedded directly into the unitary evolution of the circuit using standard quantum gates (CNOT and Toffoli), ensuring that paradox-inducing states are structurally excluded rather than externally filtered. We formally prove that the set of logically coherent configurations corresponds to the fixed-point subspace of the circuit’s unitary operator and demonstrate that the approach generalizes to arbitrary N-qubit systems. As a concrete illustration, we implement a minimal 3-qubit system that models contradiction detection, resolution, and global logical coherence in the context of natural language ambiguity resolution. In this example, unresolved linguistic ambiguity is flagged as a logical inconsistency, while successful disambiguation preserves coherence. Simulations on both ideal quantum circuits and IBM’s quantum hardware validate that only consistent states remain invariant under the computation, while contradictory configurations are actively suppressed.
Abstract We propose a scalable quantum circuit architecture for enforcing logical consistency in systems susceptible to contradiction. The model introduces a modular structure in which each contradiction qubit is paired with a corresponding resolution qubit, and a global consistency flag qubit monitors coherence across the system. Logical constraints are embedded directly into the unitary evolution of the circuit using standard quantum gates (CNOT and Toffoli), ensuring that paradox-inducing states are structurally excluded rather than externally filtered. We formally prove that the set of logically coherent configurations corresponds to the fixed-point subspace of the circuit’s unitary operator and demonstrate that the approach generalizes to arbitrary N-qubit systems. As a concrete illustration, we implement a minimal 3-qubit system that models contradiction detection, resolution, and global logical coherence in the context of natural language ambiguity resolution. In this example, unresolved linguistic ambiguity is flagged as a logical inconsistency, while successful disambiguation preserves coherence. Simulations on both ideal quantum circuits and IBM’s quantum hardware validate that only consistent states remain invariant under the computation, while contradictory configurations are actively suppressed.
Logical paradoxes and inconsistent information pose deep challenges in epistemology and the philosophy of logic. Classical systems typically handle contradictions only through external checks or by altering the logical framework, as in Tarski's hierarchy or paraconsistent logics. We propose a novel approach: a quantum circuit architecture that intrinsically enforces logical consistency during its unitary evolution. By encoding self-referential or contradictory propositions into a quantum state, the circuit uses interference effects to suppress inconsistent outcomes while preserving coherent ones. We demonstrate this with the Liar Paradox ("This statement is false"), showing that the quantum model naturally stabilizes truth values that would be paradoxical classically. The framework builds on orthomodular quantum logic treating logical propositions as subspace projectors and connects to belief revision and cognitive modeling by providing a physical mechanism for coherence restoration in epistemic states. This work bridges formal logic and quantum computation, suggesting that consistency can be embedded as a structural property of reasoning systems rather than imposed externally.
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.
Abstract Implementing quantum algorithms on realistic devices requires translating high-level global operations into sequences of hardware-native logic gates, a process known as quantum compiling. Physical limitations, such as constraints in connectivity and gate alphabets, often result in unacceptable implementation costs. To enable successful near-term applications, it is crucial to optimize compilation by exploiting the capabilities of existing hardware. Here we implement a resource-efficient construction for a quantum version of AND logic that can reduce the compilation overhead, enabling the execution of key quantum circuits. On a high-scalability superconducting quantum processor, we demonstrate low-depth synthesis of high-fidelity generalized Toffoli gates with up to 8 qubits and Grover’s search algorithm in a search space of up to 64 entries. Our experimental demonstration illustrates a scalable and widely applicable approach to implementing quantum algorithms, bringing more meaningful quantum applications on noisy devices within reach.
The realization of large-scale quantum computers requires not only quantum error correction but also fault-tolerant (FT) operations to handle errors that propagate into harmful errors. Recently, flag-based protocols have been introduced that use ancillary qubits to flag harmful errors. However, there is no clear recipe for finding a FT quantum circuit with flag-based protocols, especially when we consider hardware constraints, such as the qubit connectivity and available gate set. This work presents a novel approach to automatically discover compact and hardware-adapted FT quantum circuits to make significant progress towards scalable FT quantum computing. We employ reinforcement learning (RL) as an enabling tool, leveraging a fast, parallelized stabilizer quantum circuit simulator and a nontrivial reward function specifically adapted to the problem. We show that, in the task of FT logical state preparation, RL discovers not only circuits with fewer gates and ancillary qubits than published results but also novel circuits without and with hardware constraints of up to distance-5 codes with 25 physical qubits, and they can be implemented directly in experiments. Furthermore, RL allows for straightforward exploration of different qubit connectivities and the use of transfer learning to accelerate the discovery. More generally, our work sets the framework towards the use of RL or other machine learning techniques for FT quantum circuit discovery with hardware constraints to make real progress towards the realization of large-scale quantum computers, addressing tasks beyond state preparation, including magic state preparation, logical gate synthesis, and syndrome measurement.
The simulation of non-Abelian anyon braiding is a critical step towards fault-tolerant quantum computation. We introduce a framework for this task based on a one-dimensional Quasicrystal Inflation Code (QIC). The code is defined by a local Hamiltonian whose ground state manifold enforces Fibonacci tiling constraints and possesses the correct Fibonacci degeneracy. We derive the corresponding braid operators and demonstrate that, while they are formally non-local, they possess an exact, local 3-qubit structure. This allows us to distill their action into a single, physically realizable 8×8 gate, which we term the Bgate. We prove through comparative compilation for systems with different numbers of qubits that constructing circuits by composing these local gates is dramatically more scalable than compiling the equivalent global unitary, showing a greater than tenfold reduction in circuit depth. To validate the framework, we successfully executed a braiding algorithm for the Jones polynomial, a topological invariant of knots, on an IBM Quantum processor, quantifying the signal degradation due to hardware noise. Finally, we numerically confirm for systems up to 17 qubits that our construction rigorously satisfies the required Temperley-Lieb and braid group relations while preserving the code subspace. This work establishes a validated and physically grounded pathway for the scalable simulation of anyonic braiding on programmable quantum systems.
This paper investigates the potential of modular logic to revolutionize parallel quantum computing, addressing the challenges of scalability and fault tolerance. We propose a novel system leveraging formal language and reasoning to design and orchestrate quantum computations, promoting independent and verifiable execution of computational modules within a quantum circuit. The core mechanism centers around a language that explicitly defines the logical relationships between modules, enabling automated circuit design and optimization. This approach seeks to overcome the limitations of traditional quantum programming by enhancing expressiveness, simplifying verification, and facilitating a more robust and scalable approach to quantum computation. The paper details the proposed system, its reasoning framework, and preliminary results demonstrating improvements in circuit design and verification.