High-Fidelity Quantum State Transfer in Multimode Resonators via Tunable Pulses

Abstract

Quantum state transfer between distant nodes is essential for distributed quantum information processing. Existing protocols are typically optimized for specific coupling regimes, such as adiabatic dark-state transfer in the single-mode limit and pitch-and-catch schemes in the multimode regime, leaving the crossover between them without a simple and unified control strategy. Here we identify a minimal two-parameter control framework that enables high-fidelity quantum state transfer across this single-mode-to-multimode crossover in a multimode quantum channel. Using a pulse-shaped pitch-and-catch protocol controlled only by the pulse ramp rate and the emission-absorption delay, we achieve transfer fidelities exceeding 99.9%, extending pitch-and-catch protocols toward the single-mode limit without requiring dark-state protection or complex pulse design. We further demonstrate robustness against dissipation, disorder, detuning, and imperfect initialization under experimentally realistic conditions. These results provide a simple and broadly applicable framework for state transfer in multimode quantum channels, with relevance to circuit-QED and hybrid quantum-acoustic systems.

Figures (5)

• Figure 1: State-transfer schematics. (a) Two qubits (labelled as $Q_A$ and $Q_B$) are coupled to a common multimode resonator acting as a quantum channel. Remote state transfer is implemented by dynamically tuning the qubit-channel coupling via tunable couplers (labelled $G_1$ and $G_2$). (b) In the single-mode limit, the system supports a dark eigenstate with negligible population in the resonator. A STIRAP-like adiabatic sequence transfers the state from $Q_A$ to $Q_B$ while avoiding excitation of the channel. (c) In the multi-mode limit, the dark-state condition breaks down. State transfer is achieved using the pitch-and-catch protocol: $Q_A$ emits a shaped photon/phonon wavepacket into the multimode resonator (pitch), and $Q_B$ time-reverses the process to reabsorb it (catch).
• Figure 2: Pulse shaping suppresses multimode dispersion and enables high capture efficiency. We consider an intermediate coupling ratio ($g/\nu_{\mathrm{fsr}} = 0.5$) and examine single-qubit round-trip dynamics by setting $g_B = 0$, so that only $Q_A$ interacts with the multimode channel. Top (bottom) panels show constant coupling (sech-shaped pulses), including qubit population and mode-resolved dynamics. (a) With constant coupling, the excitation emitted by $Q_A$ is only weakly reabsorbed, resulting in incomplete and progressively weaker revivals over successive round trips. (b) The corresponding modal population shows strong multimode dispersion and clear asymmetry between emission and capture, leading to wavepacket delocalization and poor reabsorption. (c) With shaped coupling $g_A(t)$, $Q_A$ fully reabsorbs the returning wavepacket, yielding near-unit return probability. (d) The shaped pulse suppresses multimode dispersion and enforces time-reversal symmetry between emission and capture, enabling complete reabsorption of the wavepacket.
• Figure 3: State transfer at arbitrary interaction strength. We optimize the pitch-and-catch protocol to transfer a single excitation from $Q_A$ to $Q_B$ in the crossover regime ($g/\nu_{\mathrm{fsr}}\in[0.2,0.8]$) by tuning two control parameters: the ramp speed $\kappa$ and the delay $\tau_d$ between the emission and absorption ramps. (a,b) Infidelity $1-F$ as a function of $(\kappa,\tau_d)$ for $g/\nu_{\mathrm{fsr}}=0.2$ and $g/\nu_{\mathrm{fsr}}=0.8$, respectively. Red markers indicate the optimal points that maximize the transfer fidelity $F$, with the insets showing the corresponding ramp functions. (c,d) Optimal parameters extracted from two-dimensional scans across multiple coupling ratios. The optimal ramp speed $\kappa$, optimal delay $\tau_d$, and total cycle duration $\tau_{\rm cycle}$ are plotted as functions of $g/\nu_{\mathrm{fsr}}$, together with exponential and logarithmic fits (solid lines). (e) Time-domain dynamics under optimal conditions for representative values of $g/\nu_{\mathrm{fsr}}$. Solid curves show the transfer infidelity $1-P_B(t)$, while dashed curves show $1-P_A(t)$, the inverse of the residual population on $Q_A$.
• Figure 4: Robustness of state transfer against dissipation, disorder, and frequency mismatch. Transfer infidelity $1-F$ for different coupling ratios $g/\nu_{\mathrm{fsr}}$ in the presence of realistic imperfections. (a) Infidelity versus qubit decay rate $\gamma$. (b) Infidelity versus resonator decay rate $\kappa_c$. (c) Infidelity versus mode-frequency disorder, with Gaussian fluctuations of standard deviation $\sigma=\delta\nu_{\mathrm{fsr}}/3$ (data averaged over 100 realizations). (d) Infidelity versus qubit frequency mismatch $\Delta\omega$. In the low-loss, low-disorder, and small-detuning limits, the curves saturate at the intrinsic unitary infidelity obtained from Fig. 3, which exceeds 99.9% and is higher in the single-mode limit. Across all imperfections, the protocol remains most robust in the multi-mode limit due to the shorter transfer time and larger hybridization bandwidth.
• Figure 5: Robustness to imperfect initial states. (a) Transfer infidelity as a function of the preparation error probability $\epsilon_f$, where qubit A is initialized in the mixed state $(1-\epsilon_f)\ket{e}\bra{e}+\epsilon_f\ket{f}\bra{f}$. Solid and dashed lines correspond to $\alpha/\nu_{\mathrm{fsr}}=1$ and $10$, respectively. (b) Transfer infidelity in the presence of a residual single photon in the channel with probability $\epsilon_p$, averaged uniformly over all channel modes. In both panels the control pulses are optimized for the ideal two-level, vacuum-channel case. The linear increase at large error probability reflects the first-order sensitivity to nonideal initial conditions, while the saturation at small error probability is set by the intrinsic two-level infidelity.