Hamiltonian Benchmark of a Solid-State Spin-Photon Interface for Computation

TL;DR

This work solves the full Hamiltonian dynamics of a solid-state spin-photon interface in a half-1D microcavity to benchmark three key photonic protocols: generation of photon-number superpositions, a photon-photon CZ gate, and Lindner-Rudolph cluster-state generation. Using a collision-model treatment for multi-mode fields and incorporating a static Overhauser field to model hyperfine-induced spin decoherence, the authors derive exact fidelities and identify fundamental limits across realistic parameter regimes. Photon-number state generation remains highly faithful under typical spin-noise levels (w/gamma pprox 0.01.1), while the CZ gate is exceptionally susceptible to spin decoherence, challenging optimization under practical constraints. By contrast, the LR protocol exhibits comparatively robust performance, suggesting its viability for fault-tolerant photonic quantum computation within current solid-state SPIs. The results establish a Hamiltonian-based benchmarking approach that directly informs error-mitigation strategies for scalable quantum information processing with SPIs.

Abstract

Light-matter interfaces are pivotal for quantum computation and communication. While typically analyzed using single-mode or open-quantum-system approximations, these models often neglect multi-mode field states and light-matter entanglement, hindering exact protocol modeling. Here, we solve the full Hamiltonian dynamics of a solid-state spin-photon interface for three key protocols: the generation of photon-number superpositions, a controlled photon-photon gate, and the production of photonic cluster states. By deriving exact fidelities, we identify fundamental performance limits. Our results reveal that while realistic imperfections severely limit photon-photon gates, they only slightly affect linear photonic clusters and are nearly harmless for photon-number state superpositions.

Figures (6)

• Figure 1: Spin-photon interface implemented with a charged quantum dot (QD) in a directional micro-cavity, schematics. a) The directional micro-cavity confines the field to propagate along half of the $z$ axis, i.e. input and output fields travel on the same side of the emitter. b) Structure of the energy levels of the charged QD: a degenerate 4-level system with optical selection rules, R and L stand for right- and left-circular polarization respectively.
• Figure 2: Fidelity of the superposition of 0- and 1-photon states varying the spin relaxation time $w^{-1}$ with respect to the trion's lifetime. The plotted function is given in Eq. \ref{['eq_final_photon_source']}. State of the art QD devices having $w/\gamma$ between $0.01$ and $0.1$ correspond to a nearly unitary fidelity (see the inset).
• Figure 3: Schematic representation of a CZ photonic gate. The states of both control and target photons are arbitrary superpositions of $0-$ and $1-$photon states. The electron spin is prepared in $\ket{\downarrow_y}$ and it interacts with the two photons via the spin-selective phase mapping, $\mathcal{H}$, given in Eq. \ref{['eq_phase_gate']}. After interacting with each photon, a $\pi/2$ rotation around the $x$ axis is performed on the electron spin. The spin-photon-photon state is given at this stage by Eq. \ref{['ideal_cz']}. The electron spin is then measured, projecting the evolution onto a CZ gate up to a single photon unitary (see text).
• Figure 4: Fidelity of the CZ photon-photon gate varying the photons' bandwidth $\Gamma$ for different values of the external magnetic field $\hbar\Omega_e/( g_{\text{tr}}\mu_B)= B^{\text{ext}}$, and of the spin relaxation time $w^{-1}$. The curves are obtained from the numerical integration of Eq. \ref{['eq_fidelity_gate_Bloch_average']} with Overhauser field distribution of width $w$ setting $\Omega_e=\bar{\Omega}_g$ (see the text).
• Figure 5: Schematic representation of the Lindner-Rudolph protocol. The electron spin is prepared in $\ket{\uparrow_y}$. Then a "unit step" is performed $N$ times to generate an entangled state of $N$ photons plus spin. The unit step consists of a classical excitation of the QD, followed by spontaneous emission, followed by a $\pi/2$ rotation of the electron spin around the $x$ axis. The joint state of the spin and the $N$ photons is given by Eq. \ref{['ideal_LR']}. After this the spin is measured and disentangled from the $N$ photons resulting in an $N$ photon cluster state.