Exponential suppression of bit-flips in a qubit encoded in an oscillator

Abstract: A quantum system interacts with its environment, if ever so slightly, no matter how much care is put into isolating it. As a consequence, quantum bits (qubits) undergo errors, putting dauntingly difficult constraints on the hardware suitable for quantum computation. New strategies are emerging to circumvent this problem by encoding a qubit non-locally across the phase space of a physical system. Since most sources of decoherence are due to local fluctuations, the foundational promise is to exponentially suppress errors by increasing a measure of this non-locality. Prominent examples are topological qubits which delocalize quantum information over real space and where spatial extent measures non-locality. In this work, we encode a qubit in the field quadrature space of a superconducting resonator endowed with a special mechanism that dissipates photons in pairs. This process pins down two computational states to separate locations in phase space. As we increase this separation, we measure an exponential decrease of the bit-flip rate while only linearly increasing the phase-flip rate. Since bit-flips are continuously and autonomously corrected at the single qubit level, only phase-flips are left to be corrected via a one-dimensional quantum error correction code. This exponential scaling demonstrates that resonators with non-linear dissipation are promising building blocks for universal fault-tolerant quantum computation with drastically reduced hardware overhead.

Exponential Suppression of Bit-Flips in a Qubit Encoded in an Oscillator

The paper explores a novel approach to encoding qubits within superconducting resonators to achieve exponential suppression of bit-flip errors while managing phase-flip rates effectively. In quantum computing, protecting qubits from decoherence is crucial for reliable computation, and this research contributes to the development of fault-tolerant quantum systems by innovatively utilizing field quadrature spaces within these resonators.

Key Contributions

The authors propose a method where qubits are encoded in the field quadrature space of a superconducting resonator, using a mechanism that dissipates photons in pairs. This approach effectively isolates computational states in separate locations in phase space, enhancing their stability and reducing the bit-flip rate exponentially as the separation in the phase space increases. This exponential reduction is achieved while maintaining a linear increase in phase-flip rates, which is a notable achievement in quantum error correction (QEC).

Mechanisms and Implementation

The research leverages a dissipative mechanism known as two-photon dissipation, which stabilizes qubit states without compromising their ability to form quantum superpositions. This mechanism plays a pivotal role in pinning computational states and correcting bit-flip errors continuously and autonomously at the single-qubit level. By doing so, it reduces the QEC overhead required for phase-flip corrections, aligning with one-dimensional QEC codes for managing phase-flip errors.

The paper introduces a novel non-linear dipole element, the Asymmetrically Threaded SQUID (ATS), which allows for a pristine non-linear coupling between the resonator and its environment. This innovation resolves various issues seen in previous implementations, such as induced relaxation and dynamic instabilities, while mitigating quasiparticle generation.

Results and Implications

The empirical results showcased in this research reveal a 300-fold improvement in bit-flip time from the intrinsic lifetime of the resonator, reaching up to milliseconds. Such significant enhancements suggest the potential for developing scalable, fault-tolerant quantum computation architectures with considerably reduced hardware overhead.

One notable aspect is the observed exponential scaling of the bit-flip time with the cat size, which persists up to certain resonator photon numbers. Beyond this point, the bit-flip time saturates due to residual errors that are not correctable by the two-photon dissipation mechanism. However, this saturation point still represents a marked extension of qubit longevity in comparison to previous methodologies.

Future Outlook

Advancements proposed in this paper highlight important directions for future quantum computing developments. Reducing the transmon-induced fluctuations that lead to saturation, combined with the integration of high-quality cavities, could prolong the bit-flip time to seconds or beyond, allowing for more focus on handling phase-flips. The potential to perform universal quantum gates within this two-dimensional phase space using conditional rotations presents a promising opportunity to eliminate the need for magic state distillation, further reducing quantum computing overhead.

In conclusion, the research presented offers a significant step towards realizing universal, fault-tolerant quantum computation with an innovative encoding strategy that effectively balances operational complexity with increased qubit stability and reduced error rates. The techniques introduced here could reshape the infrastructure and methodologies employed in scalable quantum computing design.