Environment-Assisted Generation of Non-Gaussian Wavepacket Quantum States

TL;DR

The paper addresses the challenge of generating traveling non-Gaussian quantum states for quantum networks using superconducting circuits. It introduces a hardware-efficient scheme that combines engineered nonlinear dissipation with a linear loss channel to emit non-Gaussian states as traveling wave packets in a single mode, via a cascaded interaction between a state generation source and a buffer mode. Key results include high-fidelity 2-cat and 4-cat states in single-mode outputs (fidelities around 0.95) and extensions to propagating grid states and pair-cat states with similar performance, demonstrating robust, mode-selective emission. The approach eliminates the need for tunable couplers, enables rapid state release, and holds promise for scalable, fault-tolerant quantum communication and distributed quantum computing with superconducting platforms.

Abstract

Generating non-Gaussian states and converting them into traveling wavepackets is crucial yet challenging for scalable, fault-tolerant quantum computing. We present a hardware-efficient approach that simultaneously achieves both tasks by combining an engineered nonlinear dissipation with a linear transmission loss from a superconducting circuit to a waveguide. This combination of dissipative channels leverages low-order interactions to induce a high-order nonlinearity, enabling deterministic emission of a wide range of non-Gaussian, error-correctable states, such as Schrödinger cat states, GKP states, and pair-cat states. We identify experimental superconducting circuit platforms and realistic parameter regimes for our proposal.

Figures (4)

• Figure 1: Combination of engineered non-linear dissipation and linear dissipation for the preparation of traveling cat-state wave packets. The cat state is generated in the output field of the $a$-mode, state generation source (SGS) (orange box). The buffer $b$-mode (blue box) is coupled to the SGS through the $n$-to-$1$-photon interaction $H_{\mathrm{int}}$. Both modes undergo strong linear transmission, $\Gamma$ and $\gamma$, into two separate waveguides. The total output field consists of a cat state $\ket{\psi}_{\mathrm{cat}}$ in the left waveguide and a coherent state $\ket{\alpha}_b$ in the right waveguide. The entire system is initialized in the vacuum state, and the time-dependent drive $H_{\mathrm{drive}}$ shapes the output fields.
• Figure 2: The fidelity of the output field 2-legged and 4-legged cat states is shown together with the corresponding achievable amplitude parameters $\alpha_{\text{out}}$. The relative values of the coupling and dissipation rate, $\gamma/g_{ab}$, are indicated by the number on several filled circles in each panel. The colorbar indicates the ratio between linear $\Gamma$ and nonlinear dissipation $\kappa_n$. The left and right insets show the Wigner function of the highest and lowest fidelity 2-legged and 4-legged cat states (here, and in all figures, the Wigner functions are rotated to align with the real and imaginary axes).
• Figure 3: Panels (a) and (b) show the population of the SGS and the buffer mode (solid curves) on the left y-axis, and the total drive amplitude $(\Omega_d+\Omega_{ca})/\Gamma$ (dashed curve) on the right y-axis, corresponding to 2-cat and 4-cat generation, respectively. The inset plots in (a) and (b) illustrate the Wigner functions corresponding to propagating 2-cat and 4-cat qubit states obtained by the simulation parameters $\kappa_n/\Gamma = 6.9,2.0$ and rotating drive strength $\epsilon/\Omega= 5\%,8\%$, respectively; see the text for more details.
• Figure 4: Panel (a) and (b) show the Wigner distribution of the propagating grid state obtained by the first and second iteration of the breeding protocol on the generated 4-cat state with fidelity 95% with $|\alpha|^2 \approx$2.1, respectively. The effective squeezing parameters $\Delta_x = 3.6\, \mathrm{dB}$ and $\Delta_p = 1.1\, \mathrm{dB}$ along the $x$- and $p$-axes, respectively, are evaluated for the panel (b).