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arXiv:2607.08840

Fermion-mediated Casimir effect on mesoscopic rings implementing non-Clifford SWAP$^α$ gates

Liang Du, Qing-Dong Jiang, Yijia Wu

Published Jul 9, 2026• 0 citations
arXivHTMLPDF

Abstract

The Casimir effect is typically governed by intrinsic material properties and lacks in situ tunability. We show that, in mesoscopic rings, both the magnitude and sign of the fermion-mediated Casimir interaction can be controlled via the Aharonov-Bohm effect. The resulting interplay between the Aharonov-Bohm phase and the Casimir interaction provides a route to engineer long-range interactions. In particular, this mechanism enables the implementation of non-Clifford SWAP$^α$ gates between spatially separated spin qubits, thereby reducing the overhead for universal quantum computation and quantum error correction in spin-qubit architectures.

DOI
10.48550/arxiv.2607.08840

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Fermion-mediated Casimir effect on mesoscopic rings implementing non-Clifford SWAPα^αα gates
The Casimir effect is typically governed by intrinsic material properties and lacks in situ tunability. We show that, in mesoscopic rings, both the magnitude and sign of the fermion-mediated Casimir interaction can be controlled via the Aharonov-Bohm effect. The resulting interplay between the Aharonov-Bohm phase and the Casimir interaction provides a route to engineer long-range interactions. In particular, this mechanism enables the implementation of non-Clifford SWAPα^αα gates between spatially separated spin qubits, thereby reducing the overhead for universal quantum computation and quantum error correction in spin-qubit architectures.
We analyze the posibility of employing the mesoscopic-nanoscopic ring of a normal metal in a doubly degenerate persistent current state with a third auxihilary level and in the presence of the Aharonov-Bohm flux equal to the half of the normal flux quantum ℏc/e\hbar c/eℏc/e as a qubit. The auxiliary level can be effectively used for all fundamental quantum logic gate (qu-gate) operations which includes the initialization, phase rotation, bit flip and the Hadamard transformation as well as the double-qubit controlled operations (conditional bit flip). We suggest a tentative realization of the mechanism as either the mesoscopic structure of three quantum dots coherently coupled by mesoscopic tunnelling in crossed magnetic and electric fields, or as a nanoscopic structure of triple anionic vacancy (similar to F3F_3F3​ centers in alkali halides) with one trapped electron in one spin projection state.
In a typical quantum circuit, nonlocal quantum gates are applied to nonproximal qubits. If the underlying physical interactions are short-range (e.g., exchange interactions between spins), intermediate swap operations must be introduced, thus increasing the circuit depth. Here we develop a class of ``mediated'' gates for spin qubits, which act on nonproximal spins via intermediate ancilla qubits. At the end of the operation, the ancillae return to their initial states. We show how these mediated gates can be used (1) to generate arbitrary quantum states and (2) to construct arbitrary quantum gates. We provide some explicit examples of circuits that generate common states [e.g., Bell, Greenberger-Horne-Zeilinger (GHZ), WWW, and cluster states] and gates (e.g., swap\sqrt{swap}swap​, swap, cnotcnotcnot, and Toffoli gates). We show that the depths of these circuits are often shorter than those of conventional swapswapswap-based circuits. We also provide an explicit experimental proposal for implementing a mediated gate in a triple-quantum-dot system.
Gauge theories arise in physical systems displaying space-time local symmetries. They provide a powerful description of important realms of physics ranging from fundamental interactions to statistical mechanics, condensed matter, and, more recently, quantum computation. As such, a remarkably deep understanding has been achieved in the field. With the advent of quantum technology, lower energy analogs, capable of capturing important features of the original quantum field theories through quantum simulation, have been intensively studied. Here, we propose a specific scheme implementing an quantum simulation of lattice gauge theories constrained to mesoscopic spatial scales. To this end, we study the dynamics of mesons residing in a ring-shaped lattice of mesoscopic size pierced by an effective magnetic field. In particular, we find a type of Aharonov-Bohm effect that goes beyond the particlelike effect, reflecting the features of the confining gauge potential. The coherence properties of the meson are quantified by the persistent current and by specific features of the correlation functions. When the magnetic field is quenched, Aharonov-Bohm oscillations and correlations start a specific matter-wave current dynamics. Published by the American Physical Society 2024
Silicon quantum dot spin qubits have become a promising platform for scalable quantum computing because of their small size and compatibility with industrial semiconductor manufacturing processes. Although Si/SiGe heterostructures are commonly used to host spin qubits due to their high mobility and low percolation density, the SiGe spacer creates a gap between the qubits and control electrodes, which limits the ability to tune exchange coupling. As a result, residual coupling leads to unwanted single-qubit phase shifts, making multi-qubit control more difficult. In this work, we explore swapping the roles of overlapping nanogates to overcome this issue. By reconfiguring the gate voltages, we demonstrate in situ role switching while maintaining multi-qubit control. Additionally, this method significantly improves the tunability of exchange coupling by several orders of magnitude over the traditional approach. This strategy reduces unintended single-qubit phase shifts and minimizes the complexity of multi-qubit control, supporting scalable growth with minimal experimental overhead.
We theoretically propose a set of universal quantum gates acting on a hybrid qubit formed by coupling a quantum-dot spin qubit and Majorana fermion qubit. First, we consider a quantum dot that is tunnel coupled to two topological superconductors. The effective spin-Majorana exchange facilitates a hybrid cnot gate for which either qubit can be the control or target. The second setup is a modular scalable network of topological superconductors and quantum dots. As a result of the exchange interaction between adjacent spin qubits, a cnot gate is implemented that acts on neighboring Majorana qubits and eliminates the necessity of interqubit braiding. In both setups, the spin-Majorana exchange interaction allows for a phase gate, acting on either the spin or the Majorana qubit, and for a swap or hybrid swap gate which is sufficient for universal quantum computation without projective measurements.