Control Protocol for Dynamic Synthesis of Qubit and Qudit Gates Using Photonic Pulses and Magnetic Fields

TL;DR

This work addresses the challenge of designing high-fidelity quantum gates in a semiconductor microcavity by leveraging a trion–exciton–polariton platform controlled with external magnetic fields and photonic Gaussian pulses. The authors develop a finite-system Hamiltonian and an effective X/T polariton model to capture light–matter interactions, then map the dynamics to a four-level qudit and apply a Nelder–Mead optimization of a Gaussian-pulse train to synthesize gates. They report near-optimal fidelities for single-qubit gates ($F \approx 0.9999$) and a robust iSWAP gate on a four-level qudit ($F \approx 0.996$), with detailed analysis of how magnetic field modulates Coulomb matrix elements and binding energies (e.g., a singlet-triplet crossing at $B \approx 42$ T). The results demonstrate that magnetic-field control combined with tailored photonic pumping can realize precise quantum state manipulation in semiconductor cavities, offering a pathway for scalable photonic–electronic quantum information processing.

Abstract

We propose a theoretical control protocol designed for the dynamic synthesis of single qubit and four-level qudit quantum gates using external parameters, such as photonic Gaussian pulses and magnetic fields, in a microcavity quantum well system. Our approach takes advantage of tunable coherent light matter interactions that can be modulated by the magnetic field between the exciton and negative trion coupled to the lowest photonic mode. We demonstrate that it is possible to achieve precise manipulation of populations of encoded quantum states through the unitary evolution of the system. In particular, we illustrate our optimization method for generating a single qubit gate with a mean fidelity of 99.99 as well as the realization of an iSWAP gate in the four level qudit case with a fidelity of 99.6.

Figures (10)

• Figure 1: Illustration of the physical system: A single quantum well (QW) is immersed in a semiconductor microcavity formed by two distributed Bragg reflectors (DBR) and exposed to a perpendicular magnetic field. Within this material, trion and exciton resonances can emerge owing to the interaction between the charged carriers and the confined lowest photonic mode. For the interpretation of the colors in the figure(s), the reader is referred to the web version of this article.
• Figure 2: The flowchart illustrates the stages involved in the optimization algorithm for a quantum gate. For the interpretation of the colors in the figure(s), the reader is referred to the web version of this article.
• Figure 3: Panel (a) shows the form factor $F_\alpha(q)$ as a function of $q$ coordinates for different values of the $\alpha$ length ratio. The case of $\alpha = 0$ corresponds to the two-dimensional limit. Panel (b) shows the dependence of Coulomb matrix elements $\langle ii|V|ii\rangle$ on the external magnetic field. We considered the first three single-particle states at each level. Label $i$ refers to the corresponding Landau-level basis ordering. For the interpretation of the colors in the figure(s), the reader is referred to the web version of this article.
• Figure 4: Lowest-energy states of the negative trion in a GaAs QW as a function of the magnetic field. The main panel shows the triplet $E_T$, singlet $E_S$, and exciton plus free electron energies $E_{X+e^{-}}$. The inset shows the numerical calculations for the binding energies $E_b^{S}$ (blue circle line) and $E_b^{T}$ (red circle line) of the negative trion states relative to the exciton ground state and the free electrons as a function of the magnetic field. Extrapolation of the numerical results for the binding energies $E_b^{S}$ and $E_b^{T}$ are shown as blue and red dashed lines, respectively. A crossing between these two energies is predicted at $B\approx42T$. For the interpretation of the colors in the figure(s), the reader is referred to the web version of this article.
• Figure 5: Numerical results for the quantum average infidelity using the optimization technique for creating single-qubit quantum gates for excitons (depicted by the blue circle line) and trions (represented by the red circle line). For the interpretation of the colors in the figure(s), the reader is referred to the web version of this article.