Channel capacity of small modular quantum networks in the ultrastrongly coupled regime

TL;DR

This work addresses robust, high-fidelity state transfer between quantum processing units connected by on-chip interconnects in the ultrastrong coupling regime, where the dynamical Casimir effect (DCE) can induce leakage. It compares two protocols, QB and CTAP, using a $d$-level IC model to quantify the single-letter quantum capacity $\mathcal{Q}_1$ and leakage phenomena, under resonant conditions and parity-conserving dynamics. The key finding is that CTAP delivers near-unit $\mathcal{Q}_1$ across a broad coupling range ($g$ up to about $0.6\,\omega_c$) and is robust to parameter fluctuations, while QB experiences more pronounced DCE leakage that worsens with larger $d$; nonlinearity in the IC can further suppress leakage. These results inform the design of modular quantum networks by highlighting CTAP as a practical, low-control-demand interconnect protocol in the ultrastrong regime, while also outlining open questions on memory effects, anharmonicity enhancements, and experimental realization.

Abstract

We investigate state-transfer in modular quantum computer architectures exploiting the ultrastrong coupling regime of interaction between quantum processing units and ICs. We show that protocols based on adiabatic coherent transport may achieve near-ideal single-letter quantum capacity and robustness against parametric fluctuations suppressing leakage induced by the dynamical Casimir effect.

Figures (2)

• Figure 1: Single-letter channel capacity $\mathcal{Q}_1$ vs $g$ for the QB (dashed lines) and for the CTAP (solid lines) protocols for IC with $d=2$ (blue), $d=3$ (red) and $d=4$ (green). If the IC is a harmonic oscillator $\mathcal{Q}_1$ for the QB vanishes at $g\approx 0.42$ (orange dot) article_benenti. CTAP is operated with Gaussian pulses with $gT =20$ and $\tau = 0.7\, T$ from the initial $t_i=-2 \sqrt{2}\,T$ to the final $t_f= 2 \sqrt{2}\,T$. Left-bottom inset: schematics of the system consisting of two qubits coupled to a $d$-level interconnect. Right inset: $\mathcal{Q}_1$ as function of $d$ for CTAP at $g=0.6$ for $gT=20$ (purple) and $gT=40$ (orange) saturating in both cases to a constant value for increasing $d$.
• Figure 2: Leakage from the target subsystem $\{\ket{0}_{Q_1} \otimes \ket{0}_{IC} \otimes \ket{\psi}_{Q_2} \}$ (solid lines) and from the subspace ${\@fontswitch\mathcal{N}}=0,1$ excitations (dashed lines and dot-dashed lines), for the QB (blue lines) and the CTAP (red lines) protocols. Parameters are the same as in the previous figure. The numerical error is $<5\cdot10^{-5}$. All the curves refer to an IC with $d > 8$ equispaced levels excepect the dot-dashed line referring to $d=4$. This suggests that anharmonicity of the IC may suppress DCE-induced errors in the CTAP protocol.