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

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.

6 pages, 8 figures + appendices. v2: expanded the discussion section

References in corpus (14)

• Suppressing quantum errors by scaling a surface code logical qubit
• Logical quantum processor based on reconfigurable atom arrays
• Topological Quantum Distillation
• Restrictions on Transversal Encoded Quantum Gate Sets
• A Race Track Trapped-Ion Quantum Processor
• Demonstration of fault-tolerant universal quantum gate operations
• Topological Computation without Braiding
• Fault-tolerant conversion between the Steane and Reed-Muller quantum codes
• Logical-qubit operations in an error-detecting surface code
• Encoding a magic state with beyond break-even fidelity
• The cost of universality: A comparative study of the overhead of state distillation and code switching with color codes
• Fault-Tolerant Code Switching Protocols for Near-Term Quantum Processors
• Code switching revisited: Low-overhead magic state preparation using color codes
• Code conversion with the quantum Golay code for a universal transversal gate set

Cited by in corpus (5)

• Efficient simulation of logical magic state preparation protocols
• Magic tricycles: Efficient magic state generation with finite block-length quantum LDPC codes
• Towards self-correcting quantum codes for neutral atom arrays
• Catalytic $z$-rotations in constant $T$-depth
• Clifford Transformations for Fermionic Quantum Systems: From Paulis to Majoranas to Fermions