Experimental demonstration of high-fidelity logical magic states from code switching (2506.14169v1)

Abstract: Preparation of high-fidelity logical magic states has remained as a necessary but daunting step towards building a large-scale fault-tolerant quantum computer. One approach is to fault-tolerantly prepare a magic state in one code and then switch to another, a method known as code switching. We experimentally demonstrate this protocol on an ion-trap quantum processor, yielding a logical magic state encoded in an error-correcting code with state-of-the-art logical fidelity. Our experiment is based on the first demonstration of code-switching between color codes, from the fifteen-qubit quantum Reed-Muller code to the seven-qubit Steane code. We prepare an encoded magic state in the Steane code with $82.58\%$ probability, with an infidelity of at most $5.1(2.7) \times 10^{-4}$. The reported infidelity is lower than the leading infidelity of the physical operations utilized in the protocol by a factor of at least $2.7$, indicating the quantum processor is below the pseudo-threshold. Furthermore, we create two copies of the magic state in the same quantum processor and perform a logical Bell basis measurement for a sample-efficient certification of the encoded magic state. The high-fidelity magic state can be combined with the already-demonstrated fault-tolerant Clifford gates, state preparation, and measurement of the 2D color code, completing a universal set of fault-tolerant computational primitives with logical error rates equal or better than the physical two-qubit error rate.

• The paper experimentally demonstrates high-fidelity logical magic state creation via code switching between a 15-qubit Reed-Muller code and a 7-qubit Steane code.
• The paper employs a one-bit teleportation gadget and logical Bell basis measurements to certify state fidelity, achieving an infidelity as low as 5.1(2.7)×10⁻⁴.
• The paper’s findings reduce resource overhead in fault-tolerant quantum protocols and support transversal T gate implementations for universal quantum computation.

Experimental Demonstration of High-Fidelity Logical Magic States from Code Switching

This paper presents an experimental achievement in the field of quantum computing: the generation of high-fidelity logical magic states using code switching on an ion-trap quantum processor. The experiment focuses on demonstrating code-switching between the fifteen-qubit quantum Reed-Muller (qRM) code and the seven-qubit Steane code, two instances of error-correcting color codes, yielding a step towards universal fault-tolerant quantum computation.

Key Findings and Numerical Results

The experimental protocol efficiently prepares a logical magic state with a fidelity of $99.949\%$ and with an infidelity of at most $5.1(2.7) \times 10^{-4}$—a result achieved with only 28 qubits (22 data qubits and 6 ancilla qubits). Notably, this infidelity is lower than the reported leading physical operation errors in the quantum architecture, specifically the SPAM errors, which stand at $1.38(12)\times 10^{-3}$. The experiment demonstrates the quantum processor operates below the pseudo-threshold for the encoded magic states. This indicates that with continued improvements at the physical layer, further improvements in logical fidelity are achievable.

The experimental approach uses a one-bit teleportation gadget between the qRM and Steane code, enabled by a logical $\overline{\text{CNOT}$ gate defined across the two codes. Logical Bell basis measurements are conducted on the magic states, improving the efficiency of the fidelity certification process. The results from these multi-copy experiments ascertain a rigorous fidelity bound of the logical magic state, integrated with an innovative sample-efficient certification method leveraging logical state tomography.

Theoretical Implications

The implications of this research are significant in terms of reducing the resource overhead in fault-tolerant quantum computation protocols. Magic state distillation has historically constituted a substantial resource requirement in fault-tolerant quantum systems. The techniques demonstrated, including code-switching and verified pre-selection, show promise in mitigating some of these resource demands.

Furthermore, using code switching between color codes presents practicality for the implementation of transversal $T$ gates, contributing to a complete set of fault-tolerant logical gates. These findings could streamline quantum algorithms demanding high volumes of logical operations with small error rates, such as Shor’s algorithm, or complex simulations of quantum chemistry models like FeMoco.

Future Developments and Applications

The experimental methodology provides a template for potentially scaling to higher-distance color codes to achieve even lower infidelities for logical operations beyond the $T$ gate. Such advancements will drive the implementation of quantum algorithms with feasible quantum error rates, thus shortening the timeline to practical, large-scale quantum computing applications.

This experiment sets a benchmark for high-fidelity magic state preparation, crucial for universal fault-tolerant quantum computation, and may accelerate progress in solving the open challenges of quantum computing, particularly in implementing non-Clifford gates. The application and improvement in quantum architecture as discussed in this paper offer futuristic insights into quantum computing's impact on computational chemistry and complex quantum simulations.