Scaling and logic in the color code on a superconducting quantum processor (2412.14256v1)

Abstract: Quantum error correction is essential for bridging the gap between the error rates of physical devices and the extremely low logical error rates required for quantum algorithms. Recent error-correction demonstrations on superconducting processors have focused primarily on the surface code, which offers a high error threshold but poses limitations for logical operations. In contrast, the color code enables much more efficient logic, although it requires more complex stabilizer measurements and decoding techniques. Measuring these stabilizers in planar architectures such as superconducting qubits is challenging, and so far, realizations of color codes have not addressed performance scaling with code size on any platform. Here, we present a comprehensive demonstration of the color code on a superconducting processor, achieving logical error suppression and performing logical operations. Scaling the code distance from three to five suppresses logical errors by a factor of $\Lambda_{3/5}$ = 1.56(4). Simulations indicate this performance is below the threshold of the color code, and furthermore that the color code may be more efficient than the surface code with modest device improvements. Using logical randomized benchmarking, we find that transversal Clifford gates add an error of only 0.0027(3), which is substantially less than the error of an idling error correction cycle. We inject magic states, a key resource for universal computation, achieving fidelities exceeding 99% with post-selection (retaining about 75% of the data). Finally, we successfully teleport logical states between distance-three color codes using lattice surgery, with teleported state fidelities between 86.5(1)% and 90.7(1)%. This work establishes the color code as a compelling research direction to realize fault-tolerant quantum computation on superconducting processors in the near future.

• The paper demonstrates efficient logical error suppression with a scaling factor of 1.56(4) using a color code on a superconducting quantum processor.
• The paper details a hexagonal lattice implementation that achieves a low transversal Clifford gate error rate of 0.0027(3) via logical randomized benchmarking.
• The paper reports over 99% fidelity in magic state injection and successful lattice surgery teleportation, highlighting its potential for scalable fault-tolerant quantum computing.

Scaling and Logic in the Color Code on a Superconducting Quantum Processor

Quantum error correction (QEC) serves as a cornerstone in the pursuit of practical quantum computing, mitigating the errors inherent in quantum systems that are yet to achieve the exceedingly low logical error rates necessary for robust quantum algorithm execution. Within this context, this paper shifts focus from the more prevalently demonstrated surface code towards the alternative color code, presented here in a superconducting quantum processor environment. The primary aim is to assess the viability of the color code as a mechanism for logical error suppression and efficient logical operations, which are essential for scalable, fault-tolerant quantum computing.

Color Code Implementation and Results

This paper reports significant strides in error correction using the color code, which, unlike the surface code, allows more efficient logical operations although requiring complex stabilizer measurements. The implementation was realized using a hexagonal lattice construction overlaid on a square grid typical of superconducting qubit systems, designed to facilitate nearest-neighbor interactions—a practical consideration that aligns well with current device architectures.

A comprehensive suite of experiments demonstrated the tangible benefits of employing color codes. Scaling the code distance from three to five yielded a logical error suppression factor of 1.56(4), indicating performance beneath the threshold for effective QEC in color codes. This result is paired with logical randomized benchmarking of transversal Clifford gates, revealing an impressively low error rate of 0.0027(3), substantially mitigating errors compared to an idle error correction cycle.

Moreover, the injection of magic states, a critical component for implementing non-Clifford gates in universal quantum computation, was achieved with high fidelity (over 99% with post-selection). This fidelity is crucial for the subsequent distillation processes required in fault-tolerant quantum operations. Finally, successful teleportation of logical states between code distances using lattice surgery was demonstrated, with fidelities ranging from 86.5(1) to 90.7(1).

Implications and Future Directions

These findings substantiate the color code as a promising candidate for efficient fault-tolerant quantum computation on superconducting devices. The transversal implementation of all single-qubit Clifford gates in a single error correction cycle and efficient lattice surgery suggest significant reductions in resource overhead compared to surface code implementations. The potential qubit efficiency advantage posited for color codes becomes a tangible possibility with prospective improvements in device error rates.

Future developments must aim to further reduce physical error rates and improve both decoding strategies and device sizes. Demonstrating logical gate error suppression with increasing code sizes will be pivotal in transitioning from experimental to practical implementations of fault-tolerant quantum computations. Additionally, detailed resource estimation studies would be invaluable in comparing the practical advantages color codes offer over their surface code counterparts in large-scale quantum algorithms.

Overall, this research marks an important step towards diversified quantum error correction strategies that go beyond traditional methodologies, potentially accelerating the development of scalable and efficient quantum computing architectures.