Autoparametric Resonance Extends Cat Qubit’s BitFlip Time, Bolstering Quantum Computing

Researchers have utilized auto-parametric resonance to extend the bitflip time of a cat qubit, a quantum bit in a superposition of two states, up to 0.3 seconds. This development is significant for quantum error correction, a key aspect of quantum computing. The study introduced an auto-parametric superconducting circuit that couples a mode containing the cat qubit to a lossy mode, preventing bitflip errors for up to 0.3 seconds. The research also introduced the autoparametric cat, a new nonlinear design with a stronger three-wave mixing interaction, offering a higher two-photon dissipation rate, crucial for preventing bitflip errors and ensuring fast qubit manipulation.

What is Autoparametric Resonance and How Does it Extend the BitFlip Time of a Cat Qubit?

Auto parametric resonance is a phenomenon that has been recently utilized to extend the bitflip time of a cat qubit up to 0.3 seconds. A cat qubit, named after Schrödinger’s famous thought experiment, is a quantum bit that exists in a superposition of two states. In this case, the logical states of the cat qubit are coherent states of a harmonic mode. This offers a promising route towards quantum error correction, a crucial aspect of quantum computing.

The bitflip time of a cat qubit can be exponentially increased with the photon number. This is achieved by using dissipation to our advantage, exchanging photon pairs of the harmonic mode with single photons of its environment. A large two-photon dissipation rate ensures fast qubit manipulation and short error-correction cycles, which are instrumental in correcting the remaining phase-flip errors in a repetition code of cat qubits.

The autoparametric superconducting circuit introduced in this study couples a mode containing the cat qubit to a lossy mode whose frequency is set at twice that of the cat mode. This passive coupling does not require a parametric pump and it reaches a rate with a strong two-photon dissipation. With such a strong two-photon dissipation, bitflip errors of the autoparametric cat qubit are prevented for a characteristic time up to 0.3 seconds with only a mild impact on phase-flip errors.

How Does Quantum Error Correction Work?

Quantum error correction is instrumental in building useful quantum processors. It is based on the gathering of many physical quantum systems in order to form protected logical qubits. The number of required physical systems can be daunting, but strategies involving harmonic oscillators instead of qubits promise to reduce that number by a large factor.

A prominent example is the cat qubit, whose computational states are coherent states of a harmonic oscillator such as a superconducting microwave cavity. These states can be stabilized through measurement-based feedback, Hamiltonian engineering, or reservoir engineering. The latter strategy prevents the state of that memory cavity from leaking out of the cat qubit subspace by engineering its coupling to the environment with the key feature that photon pairs are lost at a rate.

The bitflip time then increases exponentially with the photon number at the modest expense of a linear deterioration of the phase-flip rate. Reaching large values of the two-photon rate is critical in this strategy. First, to ensure exponential bitflip protection, it should overcome any parasitic processes affecting the memory such as dephasing, thermal excitation, the Kerr effect, frequency shifts due to a thermally populated ancilla qubit, or gate drives.

What is the Role of the Autoparametric Cat in Quantum Error Correction?

The auto parametric cat is a new nonlinear design that benefits from a stronger three-wave mixing interaction compared to the four-wave mixing interaction of previous schemes. It demonstrates rates as high as about 150 times larger than the main cause of phase-flip errors. As the photon number increases, an improvement of the bitflip time by more than a factor 25000 is observed, reaching 0.36 seconds while the phase-flip rate degrades by less than a factor of 6.

To achieve two-photon coupling between the memory and its environment, an intermediary mode with single-photon coupling to the environment acts as a buffer and a two-to-one photon exchange Hamiltonian is activated with a rate. In the limit where this rate is small enough compared to the buffer, the two-photon dissipation rate reads.

The remaining phase-flip errors could then be corrected using a repetition code made of a chain of cat qubits under the condition that the two-photon rate is larger than the single-photon loss rate. This condition is characteristic of autoparametric systems, so the buffer field passively performs a parametric driving of the memory.

How Does the Mixing Element of the Autoparametric Cat Work?

The mixing element of the autoparametric cat consists of two main Josephson junctions with energy symmetrically arranged within a superconducting loop that is threaded with an external magnetic flux. These two junctions in a parallel configuration have been engineered in the past by parametrically pumping a four-wave mixing non-linearity.

However, although the two-to-one photon exchange rate scales with the pump amplitude, increasingly larger pump powers are known to affect coherence times and activate higher nonlinear terms in the Hamiltonian. In practice, the limited range of rates that could be obtained with pumped nonlinearities prevents surpassing the self-Kerr rate or the dispersive coupling rate between the transmon and memory.

In this work, three-wave mixing is used instead, thus alleviating the need for a pump to mediate the two-photon interaction. The frequency matching condition then becomes twice the memory frequency equals the buffer frequency. Remarkably, the resulting exchange rate is much larger than what can be reached for four-wave mixing.

What are the Implications of this Research?

This research has significant implications for the field of quantum computing. By extending the bitflip time of a cat qubit up to 0.3 seconds, it provides a promising route towards quantum error correction. This is crucial for the development of useful quantum processors, as it allows for the formation of protected logical qubits.

The introduction of the autoparametric cat, a new nonlinear design, also offers a stronger three-wave mixing interaction compared to previous schemes. This results in a higher two-photon dissipation rate, which is instrumental in preventing bitflip errors and ensuring fast qubit manipulation and short error-correction cycles.

Furthermore, the use of three-wave mixing alleviates the need for a pump to mediate the two-photon interaction, which has been a limiting factor in previous designs. This opens up new possibilities for the engineering of quantum systems and could pave the way for more efficient and reliable quantum computing technologies.

What are the Future Directions for this Research?

The findings of this research open up several avenues for future exploration. One potential direction is to further investigate the properties and potential applications of the autoparametric cat. Given its strong three-wave mixing interaction and high two-photon dissipation rate, it could prove to be a valuable tool in the development of quantum computing technologies.

Another area of interest is the exploration of other strategies for quantum error correction. While the use of harmonic oscillators instead of qubits has shown promise in reducing the number of required physical systems, there may be other approaches that could offer similar or even greater efficiencies.

Finally, further research could also focus on improving the bitflip time of cat qubits. While this study has achieved a significant extension of the bitflip time up to 0.3 seconds, there may be ways to extend this even further, thereby enhancing the reliability and performance of quantum computing systems.