Variational Quantum Transduction

TL;DR

This work introduces a variational quantum transduction (VQT) framework that employs variational tools from near-term quantum computing to systematically optimize protocol performance and provides a systematic path toward optimal quantum transduction.

Abstract

Quantum transducers are critical for quantum interconnect, enabling coherent signal transfer across disparate frequency domains. Beyond material and device advances, protocol design has become a powerful means to improve transduction. We introduce a variational quantum transduction (VQT) framework that employs variational tools from near-term quantum computing to systematically optimize protocol performance. As a variational quantum circuit framework, VQT is not plagued by known training issues such as barren plateau, because a small-scale problem is sufficient for substantial advantage and training only needs to be done once to configure a VQT system. Maximizing the quantum information rate within this framework yields protocols that surpass all known schemes in their respective classes. For non-adaptive protocols, VQT exceeds the performance envelopes of Gottesman-Kitaev-Preskill (GKP)-based and entanglement-assisted approaches. In the adaptive setting, VQT provides only a marginal improvement over Gaussian feedforward strategies, indicating that Gaussian adaptive transduction is already close to optimal. With increasingly universal quantum control, VQT provides a systematic path toward optimal quantum transduction.

Figures (6)

• Figure 1: (a) Variational transduction scheme. VQCs prepare the optical inputs $S$ and microwave inputs $(P,A)$ and apply a final decoding VQC after the transducer. (b) Schematic of a multi-layer ECD variational circuit. Each layer consists of qubit–qumode conditional-displacement operations (pink) and single-qubit rotations (blue), providing universal hybrid control.
• Figure 2: Coherent information achieved by various non-adaptive transduction protocols with energy constraints $n_S=n_P=2$. The fully variational entanglement-assisted scheme (VQT) yields the highest performance across all $\eta$. The single-mode variant (VQT without EA) follows a similar trend but with reduced values, highlighting the benefit of entanglement assistance. The GKP-QT model, using finite-energy GKP state for both for $S$ and $P$, matches VQT (with and without EA) at low $\eta$ and deviates at higher transmissivity. The TMS-EA protocol shows a threshold-like onset and approaches VQT at high $\eta$, but remains suboptimal overall.
• Figure 3: Wigner functions of the optimized input states for the VQT protocol at different transmissivities $\eta$. For small $\eta (\lesssim0.4)$ , the optimal signal state of $\rho_S$ and $\rho_P$ exhibit the characteristic lattice structure of a GKP-like state. As $\eta$ increases, both $\rho_S$ and $\rho_P$ gradually lose their non-Gaussian structure and approach Gaussian states.
• Figure 4: (a) Coherent information of adaptive transduction protocols as a function of transmissivity $\eta$. The variational schemes (VQT and VQT-without-EA) exhibit nearly identical performance, indicating that feedforward effectively removes the benefits of additional ancilla modes. The adaptive Gaussian protocol (AQT) closely tracks both variational results. (b) Wigner functions of the optimized input states for the VQT protocol. Across all transmissivities $\eta$, the optimal input to $S$ is a squeezed thermal state, while the optimal input to $P$ is a squeezed vacuum. Neither entanglement nor non-Gaussian features appear in the optimized inputs.
• Figure 5: Baseline transduction strategies. (a) Intraband entanglement–assisted protocol shi2024overcoming: a microwave probe $P$ and ancilla $A$ are entangled via a two-mode squeezer $S(G)$, interact with the optical signal $S$, and are processed by an antisqueezer $S(G')$. (b) GKP-assisted protocol Wang2025Passive: both $S$ and $P$ are prepared in GKP states prior to the transducer. (c) Adaptive quantum transduction protocol Zhang2018Quantum: the signal mode $S$ is prepared in a squeezed-thermal state and the probe mode $P$ in a squeezed-vacuum state prior to the transducer, followed by homodyne detection in $S$ and feedforward displacement in $P$ conditioned on the measurement outcome $\tilde{q}$.