Fast Universal Control of an Oscillator with Weak Dispersive Coupling to a Qubit

Abstract: A controlled evolution generated by nonlinear interactions is required to perform full manipulation of a quantum system, and such control is only coherent when the rate of nonlinearity is large compared to the rate of decoherence. As a result, engineered quantum systems typically rely on a bare nonlinearity much stronger than all decoherence rates, and this hierarchy is usually assumed to be necessary. In this work, we challenge this assumption by demonstrating the universal control of a quantum system where the relevant rate of bare nonlinear interaction is comparable to the fastest rate of decoherence. We do this by introducing a novel noise-resilient protocol for the universal quantum control of a nearly-harmonic oscillator that takes advantage of an in-situ enhanced nonlinearity instead of harnessing a bare nonlinearity. Our experiment consists of a high quality-factor microwave cavity with weak-dispersive coupling to a much lower quality superconducting qubit. By using strong drives to temporarily excite the oscillator, we realize an amplified three-wave-mixing interaction, achieving typical operation speeds over an order of magnitude faster than expected from the bare dispersive coupling. Our demonstrations include preparation of a single-photon state with $98\pm 1(\%)$ fidelity and preparation of squeezed vacuum with a squeezing level of $11.1$ dB, the largest intracavity squeezing reported in the microwave regime. Finally, we also demonstrate fast measurement-free preparation of logical states for the binomial and Gottesman-Kitaev-Preskill (GKP) quantum error-correcting codes.

Fast Universal Control of an Oscillator with Weak Dispersive Coupling to a Qubit

The manuscript titled "Fast Universal Control of an Oscillator with Weak Dispersive Coupling to a Qubit" presents a significant advancement in the field of quantum control by challenging the conventional assumption that coherent control of a quantum system necessitates a large rate of bare nonlinearity relative to the rate of decoherence. The authors introduce a novel protocol for universal control of a nearly-harmonic oscillator, one that leverages in-situ enhanced nonlinearity achieved through strong drives. This leads to control operation speeds exceeding the expectation from bare dispersive coupling by more than an order of magnitude.

The research focuses on a microwave cavity with weak dispersive coupling to a superconducting qubit. The authors demonstrate the preparation of a single-photon state with fidelity of (\mathbf{98\pm 1(\%)}) and squeezing of 11.1 dB, marking the highest intracavity squeezing reported in the microwave regime thus far. Further, they achieve fast, measurement-free preparation of logical states for quantum error-correcting codes such as the binomial and Gottesman-Kitaev-Preskill (GKP) codes.

In an environment where the rate of undriven nonlinear interaction is typically large compared to decoherence, the authors show that this hierarchy is not a requisite for high-fidelity operations. They demonstrate that engineered nonlinear interaction strength, augmented via strong drives to temporarily displace the oscillator, plays a key role in coherent control. The conductor for universal control here is the Echoed Conditional Displacement (ECD) gate, an entangling gate that leverages the effective interaction strength between the oscillator and qubit, denoted as (g_\text{eff} = \chi \alpha_0).

The manuscript employs a comprehensive methodology with numerous experiments to substantiate the counterintuitive claim that a large native nonlinear interaction strength is not indispensable. The experiments are performed using a superconducting microwave cavity and a transmon qubit, operating in a regime where decoherence would lead to low control fidelity. The authors enhance interaction by implementing a three-wave-mixing interaction, which transitions rapidly surpassing the limitations from the bare dispersive shift.

This work opens broad implications for quantum information science, especially in scenarios where enhancing nonlinearity is challenging or introduces adverse effects. The ability to perform high-fidelity universal control without relying heavily on intrinsic nonlinearity allows for the design of modular quantum architectures, minimizing undesired cross-talk and decoherence, crucial during idling periods.

Future directions as suggested by this research include exploring similar control schemes in other quantum systems with weak nonlinearity, such as Kerr oscillators or diverse bosonic systems. These methods could apply to architectures coupling various modes to a single qubit, or systems where a strong dispersive coupling is tough to achieve. It prompts a rethink in the approach to quantum control, setting the stage for broader, faster, and scalable quantum computing infrastructures.