Key Findings
The research team has constructed quantum codes with 48 and 90 physical qubits that support fully addressable transversal T gates, which are essential for fault-tolerant quantum computation. By employing a cyclic encoding scheme that operates outside the conventional binary CSS framework, the researchers achieved a performance improvement by a factor of approximately 2.86. Furthermore, they established a universal upper bound for codes supporting fully addressable transversal single-qubit phase gates that is only 1.28 times greater than the lower bound achieved by their exponential-time construction.
Technical Details
The construction offers two distinct approaches based on computational demands:
- Polynomial-time construction: An algebraic-geometric construction that yields a rate of 2.57% and a corresponding relative distance. This deterministic method uses evaluation matrices generated in polynomial time.
- Exponential-time construction: A method using a counting argument over encoding matrices and quadratic phases that elevates the rate and distance guarantee to approximately 7.34%. This approach utilizes sampling and exact rejection tests to verify performance and detect Pauli errors up to a defined weight.
The 8-to-10 inner encoding preserves logical phase action using registers represented by h qubits, relying on the invertibility of matrix B for an injective map. For the 48-qubit code, the researchers also describe an ancilla-free encoder.
Background and Context
The work addresses the challenge of controlling quantum phase in error-corrected systems. The deterministic construction establishes a lower bound of 52/(675h) for both rate and relative distance. The analysis of Garcia-Stichtenoth towers over F_(256) was used to yield AG code families with positive asymptotic rate and relative minimum distance, where degrees satisfy 2g_i-2 < a_(0,i) < a_(1,i) < n_i for sufficiently large ‘i’.
Significance and Outlook
This approach allows for the separation of logical phase control from the design of code rate and distance. By enhancing fully addressable transversal phase gates at each fixed level h ≥ 3 of the Clifford hierarchy, the method effectively doubles the certified physical-qubit distance with a 25% increase in blocklength while maintaining the number of logical qubits.
Source: https://quantumzeitgeist.com/singapore-qubit-code-supports-48-qubit/
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