On the quantum circuit implementation of fuzzy reasoning

Songsong Dai

Cesarino Bertini, Roberto Leporini

Vicente Moret‐Bonillo, Eduardo Mosqueira-Rey, Samuel Magaz-Romero

In this paper we present our proposal for a fuzzy logic model based on Quantum Computing. After analyzing how logical connectives are constructed and applied in fuzzy logic, we research how Quantum Computing can provide a new model to manage fuzzy variables, mainly using superposition of states for the implementation of fuzzy information. A comparison between our proposal and several classical connectives is carried out, including negation, conjunction and disjunction. We prove that quantum fuzzy connectives present a proper behavior, manifesting the peculiarities of the quantum paradigm, which is beneficial for the representation of uncertain knowledge. We conclude on how this work establishes a model that can be further expanded for the development of quantum fuzzy reasoning.

Graciela Domenech, Hector Freytes

Arushi Raghuvanshi, Marek A. Perkowski

In this paper, we propose the concepts that apply quantum circuits to model Fuzzy Sets, thereby creating a new method to model behaviors for a humanoid robot. It is similar to the standard fuzzy sets from two points of view -1) of measured probabilities of state |1〉, and 2) that of the normalized measurement in a quantum ensemble computer. However, one can also look at the internal quantum states created by the operators of the new model. This extends fuzzy sets from [0, 1] interval to some other domain, similar to complex fuzzy logic, but also brings superposed, entangled and parallel quantum behaviors. The standard fuzzy logic aspect (external) of the new model maps the numbers in interval [0,1] to points on one meridian of the Bloch Sphere and after measurement, the results map back to numbers from interval [0,1]. However, the other, more important, aspect of this model (internal) is the operation on arbitrary quantum states, and the realization of additional states via phase measurements. We discuss and illustrate how this model can be used to represent a hidden state of reasoning agents or an emotional state of a humanoid robot.

Halima Giovanna Ahmad, Roberto Schiattarella, P. Mastrovito +10 more

Abstract Quantum utility is severely limited in superconducting quantum hardware until now by the modest number of qubits and the relatively high level of control and readout errors, due to the intentional coupling with the external environment required for manipulation and readout of the qubit states. Practical applications in the Noisy Intermediate Scale Quantum (NISQ) era rely on Quantum Error Mitigation (QEM) techniques, which are able to improve the accuracy of the expectation values of quantum observables by implementing classical post‐processing analysis from an ensemble of repeated noisy quantum circuit runs. In this work, a recent QEM technique that uses Fuzzy C‐Means (FCM) clustering to specifically identify measurement error patterns is focused. For the first time, a proof‐of‐principle validation of the technique on a two‐qubit register, obtained as a subset of a real NISQ five‐qubit superconducting quantum processor based on transmon qubits is reported. It is demonstrated that the FCM‐based QEM technique allows for reasonable improvement of the expectation values of single‐ and two‐qubit gates‐based quantum circuits, without necessarily invoking state‐of‐the‐art coherence, gate, and readout fidelities.