⚛️ quantum physics

Environment-Assisted Generation of Non-Gaussian Wavepacket Quantum States

This paper proposes a hardware-efficient method using engineered nonlinear dissipation and linear transmission loss in superconducting circuits to deterministically generate and emit a wide range of non-Gaussian, error-correctable quantum wavepacket states, such as Schrödinger cat and GKP states, for scalable fault-tolerant quantum computing.

Original authors: Maryam Khanahmadi, Klaus Mølmer

Published 2026-07-29

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Maryam Khanahmadi, Klaus Mølmer

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a world where information doesn't just sit on a hard drive but travels like a messenger bird, flying from one computer to another at the speed of light. This is the dream of a "quantum internet," where computers talk to each other using the weird, magical rules of quantum physics. To make this work, we need to send quantum information in the form of flying waves of energy, called wavepackets. But here's the catch: these waves are incredibly fragile. If they get bumped or lose a little energy, the message gets scrambled. To fix this, scientists have been trying to pack the information into special, robust shapes called "non-Gaussian states." Think of these not as simple, smooth hills, but as complex, multi-peaked mountains that can survive a little turbulence. The big challenge has been how to create these complex shapes and then immediately launch them into the air without them falling apart during the launch.

In this paper, Maryam Khanahmadi and Klaus Mølmer propose a clever new way to build and launch these quantum wavepackets simultaneously. Instead of building a stationary mountain and then trying to push it off a cliff (which often causes it to crumble), they designed a system that shapes the mountain while it is already flowing out of a pipe. They use a superconducting circuit—a tiny, super-cold electrical loop—to create a special kind of "engineered loss." Imagine a leaky bucket that, instead of just letting water drip out randomly, is designed so that the water only escapes in perfect, synchronized groups. By combining this specific type of leak with a carefully timed push, they show in their simulations that they can deterministically generate and release high-quality quantum states, including "Schrödinger cat states" (which are like being in two places at once) and "GKP states" (which are like a grid of tiny, stable islands). Their method suggests that we can create these complex, error-resistant states and send them flying down a wire with high fidelity, all in one smooth motion, without needing complicated, slow-moving parts to switch the state from "stored" to "traveling."

The Problem with the Old Way

For a long time, scientists tried to make these special quantum states by first building them inside a box (a stationary resonator) and then opening a door to let them fly out. The problem with this "build-then-release" approach is that the door mechanism itself can be messy. It might introduce unwanted interactions, or the process might take too long, causing the delicate quantum state to lose its shape due to friction and heat before it even leaves the box. It's like trying to bake a perfect cake and then immediately trying to slide it onto a moving truck without smashing it; the longer you fumble with the transfer, the more likely the cake is to fall apart.

The New "Leaky Bucket" Trick

The authors propose a different strategy: why build the cake inside the box at all? Instead, they suggest shaping the cake as it flows out. They use a superconducting circuit that has two main parts: a "Source" (where the magic happens) and a "Buffer" (a helper mode).

The Source is connected to a transmission line (the wire where the quantum message travels) and is designed to have a very specific kind of "leak." In normal physics, leaks are bad; they just let energy escape randomly. But here, the scientists "engineer" the leak so that it forces the system to lose energy in a very specific, non-random way. They pair the Source with a Buffer mode that is connected to a second wire. The Buffer is designed to be a "super-leaky" sponge that drains away almost instantly.

Here is the magic analogy: Imagine the Source is a dance floor, and the Buffer is a very fast, enthusiastic exit door. The scientists set up a rule where the dancers (photons) can only leave the dance floor if they leave in groups of two or four at a time. Because the Buffer is so fast and so eager to take them, it acts like a filter. It forces the Source to organize its energy into these specific groups (2-photon or 4-photon losses) as it flows out. This "engineered dissipation" creates a high-order nonlinearity—a complex rule that makes the system behave in a sophisticated way—using only simple, low-order interactions.

What They Found

Through detailed computer simulations, the authors found that this setup works remarkably well.

The Shape: They successfully generated "cat states" with 2 legs (two distinct shapes) and 4 legs (four distinct shapes) in the traveling wave. These are the complex, non-Gaussian shapes needed for robust quantum computing.
The Fidelity: In their simulations, the quality of the flying wavepacket was very high, reaching fidelities of 95.3% for the 2-legged cat state and 94.5% for the 4-legged cat state. This means the flying wave looked almost exactly like the perfect mathematical shape they wanted.
The Speed: Because they generate and release the state at the same time, the process is fast. They calculated generation times of approximately 2 µs for the 2-legged state and 9.3 µs for the 4-legged state.
The Buffer's Role: Crucially, they found that the Buffer mode didn't get tangled up with the main message. Instead, the Buffer just emitted a simple, clean "coherent state" (a standard, boring wave) that was completely separate from the complex cat state. This meant the flying message remained pure and uncorrupted.

Why This Matters

This approach is a significant step toward building a scalable quantum internet. By removing the need for slow, complex switches to move the state from storage to flight, the system becomes more efficient and less prone to errors. The authors suggest that this method could be implemented using existing superconducting circuit technology, specifically using Josephson junctions (tiny electronic components that act like non-linear springs) and magnetic flux drives to tune the interactions.

While these results are currently based on simulations and theoretical modeling, the proposed hardware is realistic and uses parameters that are achievable with current technology. The paper argues that this "engineered dissipation" technique could be a key ingredient for creating the error-correctable, flying quantum states necessary for long-distance quantum communication and large-scale quantum computing. It turns the problem of "leakage" from a bug into a feature, using the environment itself to help sculpt the perfect quantum wave.

Technical Summary: Environment-Assisted Generation of Non-Gaussian Wavepacket Quantum States

Problem Statement
The generation of non-Gaussian states and their conversion into traveling wavepackets is a critical bottleneck for scalable, fault-tolerant quantum computing and quantum internet architectures. While encoding quantum information in error-correctable logical bases (such as Schrödinger cat states, binomial states, and Gottesman-Kitaev-Preskill (GKP) grid states) can mitigate transmission losses and decoherence, current methods face significant challenges. Previous approaches often rely on separate preparation and release stages using tunable couplers, which introduce unwanted nonlinear interactions and reduce fidelity due to dissipation during the longer release duration. Furthermore, unitary preparation of $n$ -legged cat states typically requires high-order nonlinear interactions ( $a^{\dagger n}a^n$ ), which are difficult to implement directly.

Methodology
The authors propose a hardware-efficient approach that simultaneously generates and releases non-Gaussian states into a traveling waveguide. The core mechanism combines engineered nonlinear dissipation with linear transmission loss within a superconducting circuit platform.

The system consists of two coupled modes:

State Generation Source (SGS): A primary resonator mode ( $\hat{a}$ ) coupled to a transmission waveguide with a linear loss rate $\Gamma$ .
Buffer Mode: A secondary resonator mode ( $\hat{b}$ ) coupled to a separate waveguide with a strong linear loss rate $\gamma$ ( $\gamma \gg g_{ab}$ ).

The SGS and buffer mode interact via an engineered $n$ -photon exchange interaction described by the Hamiltonian $\hat{H}_{int} = g_{ab}(\hat{a}^n \hat{b}^\dagger + \hat{a}^{\dagger n} \hat{b})$ . The SGS is driven by a time-dependent parametric drive $\Omega_d(t)$ . The dynamics are governed by a Lindblad master equation incorporating both the engineered interaction and the linear dissipation channels.

By adiabatically eliminating the fast-decaying buffer mode, the system effectively realizes a master equation with an engineered anti-commutator loss term. This results in an effective non-Hermitian evolution proportional to $i\hat{a}^{\dagger n}\hat{a}^n$ , inducing a $(2n)$ -th order nonlinearity in the field amplitude operators. Crucially, this high-order nonlinearity is achieved using only $(n+1)$ -st order interaction terms in the physical coupling between the SGS and the buffer.

To generate specific logical qubit states (e.g., $|C^\pm_n\rangle$ ), the authors employ a linear or parametric drive $V = \epsilon p(t)(\hat{a}^n + \hat{a}^{\dagger n})$ alongside the primary drive. This drive rotates the state within the protected cat qubit space while the dissipative channel suppresses components outside this space.

Key Contributions and Results

Deterministic Emission: The paper demonstrates that this combined dissipative approach allows for the deterministic emission of high-fidelity, single-mode traveling wavepackets containing non-Gaussian states, specifically 2-legged and 4-legged Schrödinger cat states.
Fidelity and Efficiency: Numerical simulations for realistic superconducting circuit parameters show that the output field populates a single wavepacket mode with fidelities exceeding 95% for cat sizes relevant to quantum communication and computing.
Decoupling of Output: The simulation confirms that the buffer mode output is a pure coherent state ( $|\alpha\rangle$ ) decoupled from the propagating cat state. This ensures that the entanglement between the cat state and the buffer does not degrade the fidelity of the traveling wavepacket.
Experimental Feasibility: The authors identify the Asymmetrically Threaded SQUID (ATS) as a suitable experimental platform. By tuning magnetic flux drives on the ATS, they show how to suppress dominant self-Kerr and cross-Kerr interactions to isolate the required odd-order nonlinearities for the $n$ -photon drive and interaction.
Generation Times: The proposed method allows for rapid generation, with estimated total generation times of approximately $2\,\mu\text{s}$ for 2-legged cat states and $9.3\,\mu\text{s}$ for 4-legged cat states, significantly faster than methods requiring separate storage and release phases.

Significance
The authors claim this work represents a significant step toward the development of hardware-efficient quantum processors for long-distance communication. By integrating state preparation and release into a single process, the method eliminates the need for tunable couplers and reduces the impact of dissipation on state fidelity. The approach leverages low-order interactions to induce high-order nonlinearities, making it compatible with existing superconducting circuit technologies. Additionally, the authors note that the theory extends to the generation of other states, such as pair-cat states and propagating GKP grid states, and that the simultaneous generation and release inherently mitigates noise compared to stationary state preparation methods. The paper suggests that these propagating non-Gaussian states could also serve as sensitive probes for metrology.

The Problem with the Old Way

The New "Leaky Bucket" Trick

What They Found

Why This Matters

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