Lossy Resonators Enable Direct Traveling State Generation

Researchers are directly generating traveling quantum states using microwave-frequency Josephson junctions and nonlinear resonators, sidestepping a key challenge in building quantum networks. Previous architectures relied on tunable couplers to transfer quantum information, but these components can introduce noise and timing issues that reduce fidelity. This new approach eliminates the need for couplers by directly releasing the quantum state into a transmission waveguide. The team describes a system where engineered nonlinear dissipation can shape the emitted waves, forming high-fidelity propagating quantum states in single wave-packet modes. This method, which utilizes constant linear loss to a transmission waveguide, offers a faster release of quantum information and represents a significant step toward the development of hardware-efficient quantum processors for long-distance communication.

Quantum States for Communication & Computing

Schrödinger cat states, binomial states, and Gottesman-Kitaev-Preskill grid states represent increasingly sophisticated approaches to building the foundations of a future quantum internet and scalable quantum computers. Researchers are actively investigating these complex quantum states as logical building blocks capable of error correction and long-distance communication. While photon or phonon-based systems have traditionally been explored for quantum transmission, limitations imposed by signal loss, decoherence, and dephasing have spurred investigation into encoding quantum information within more robust logical bases. Preparation of quantum information into the logical basis of Schrödinger cat states has been extensively explored in optical regimes, either by photon subtraction from squeezed states or by utilizing the interaction with single atoms, but alternative approaches are gaining traction. To address these challenges, a new method focuses on directly generating traveling non-Gaussian states through parametric driving of a nonlinear resonator coupled to a transmission waveguide.

In this approach, the release is faster, and the profile of the parametric drive determines the shape of the propagating wave packet, eliminating the need for tunable couplers. The work leverages Josephson junctions in the microwave regime to deterministically generate cat states within quantum resonator eigenmodes, offering a contrast to optical methods and demonstrating progress in manipulating these states at different frequencies. Unitary preparation of an n-legged cat state requires a nonlinear interaction proportional to a raised to the power of n times a raised to the power of n, but the researchers demonstrate that engineered nonlinear dissipation can achieve similar results. They utilize a “buffer mode” strongly coupled to a waveguide, effectively creating an engineered anticommutator loss term in the master equation that results in a nonlinearity of the second order.

Non-Gaussian State Generation via Parametric Driving

Previous works have explored architectures that include a tunable coupler to transfer the prepared stationary state to a waveguide. Such couplers may introduce unwanted nonlinear interactions, and the longer duration of the separate preparation and release processes reduces the output quantum-state fidelity due to dissipation.

Unitary preparation of an n-legged cat state requires a nonlinear interaction proportional to a raised to the power of n times a raised to the power of n. A procedure based on such interactions has been analyzed in the Kerr-parametric oscillator. As an alternative, one may obtain nonlinear effects from an engineered dissipative coupling, an n-photon decay to the environment. The use of dissipation to generate nonclassical states and achieve steady-state entanglement in stationary modes has been proposed and demonstrated in various quantum systems, and preparation of stationary bosonic states has been extensively studied both theoretically and experimentally. In this work, we demonstrate that an engineered nonlinear dissipation channel can affect a quantum bosonic system such that its linear emission into a waveguide forms high-fidelity propagating quantum states in single wave-packet modes. Our theory represents a significant step toward the development of hardware-efficient quantum processors for long-distance communication.

Researchers are developing a novel approach to generating quantum states for communication, sidestepping limitations inherent in traditional methods. This eliminates the need for couplers, which can introduce unwanted nonlinear interactions and reduce fidelity due to the timing of separate preparation and release processes. The core of their innovation lies in harnessing engineered nonlinear dissipation. While preparation of cat states has been extensively explored using photons or atoms, this work leverages the Kerr nonlinearity within Josephson junctions in the microwave regime. This contrasts with optical approaches and offers a distinct pathway for deterministic state generation. The system is described using a master equation, incorporating a Hamiltonian and Lindblad operator to model the interaction between the oscillator mode and the buffer mode. This allows for a faster release of the quantum state, minimizing dissipation-induced errors. The n-photon loss is achieved by engineering the interaction with the buffer mode, resulting in an effective nonlinearity in field amplitude operators.

Lindblad Master Equation & System Hamiltonian

These states demand precise control over quantum systems, and previous architectures relying on tunable couplers to transfer these states to waveguides presented significant challenges. To overcome these limitations, the team describes a theoretical framework governing the system’s evolution, utilizing the Lindblad master equation to describe the dynamics. This equation considers both the Hamiltonian, representing the system’s energy, and the Lindblad operator, which accounts for the effects of dissipation and decoherence.

Specifically, they considered a single oscillator mode, where the Lindblad master equation is expressed as ϱ dot equals negative i times the commutator of H and ϱ plus kappa times D of L applied to ϱ, where D of L applied to ϱ equals L times ϱ times L dagger minus one half of the anticommutator of L dagger and L, ϱ. Kappa is a dissipation rate, and the Hamiltonian H and Lindblad operator L are expressed in terms of the ladder operators a and a dagger. They demonstrate the direct generation of traveling non-Gaussian states. This approach allows for the creation of a non-Hermitian Hamiltonian, effectively inducing a nonlinearity proportional to the nth power of the field amplitude operator. The n-photon loss L is proportional to a raised to the power of n and can be accomplished by engineering the interaction with a second, so-called “buffer mode” through the interaction Hamiltonian H int equals g a b times the quantity a raised to the power of n times b dagger plus a dagger raised to the power of n times b.

Conventional methods of generating complex quantum states for communication and computation often rely on precise control of couplers to transfer information to waveguides, but these components can inadvertently introduce noise and require sequential preparation steps that diminish fidelity through dissipation. Researchers have now demonstrated an alternative approach, leveraging engineered nonlinear dissipation to directly generate traveling quantum states, bypassing the need for these potentially problematic couplers. This technique focuses on manipulating how a quantum system loses photons, specifically through interaction with a secondary “buffer mode”. The core of this innovation lies in engineering a specific type of photon loss, an n-photon loss, by coupling the primary quantum system to this buffer mode. The team describes the system using the equation mentioned above. This interaction effectively creates a nonlinear effect, mimicking higher-order nonlinearities typically requiring more complex and sensitive components. Crucially, this method doesn’t simply generate stationary states; it produces traveling quantum states directly emitted into a waveguide. The use of Josephson junctions in the microwave regime allows for deterministic generation of these cat states, a departure from traditional optical approaches.

This approach offers a compelling alternative to optical methods, potentially circumventing limitations inherent in photon-based systems. Previous architectures for transmitting these states relied heavily on tunable couplers to transfer stationary quantum states to waveguides, but these components introduce unwanted nonlinear interactions that degrade signal fidelity. The sequential nature of preparing and then releasing the quantum information inherently introduces timing challenges and increases susceptibility to dissipation. This approach centers on harnessing engineered nonlinear dissipation, a process where controlled dissipation actively shapes the emitted quantum state.