Performance Analysis of a Repetition Cat Code Architecture: Computing 256-bit Elliptic Curve Logarithm in 9 Hours...

Area of Science:

• Quantum computing
• Quantum information science
• Quantum error correction

Background:

• Cat qubits offer tunable noise bias for quantum computation.
• Repetition codes can protect against phase errors in cat qubits.
• Large-scale quantum computer architectures require performance analysis.

Purpose of the Study:

• To quantify the cost of repetition codes for cat qubits.
• To provide guidance for large-scale cat qubit architectures.
• To analyze the performance of a 2D grid architecture using Shor's algorithm.

Main Methods:

• Performance analysis of a 2D grid cat qubit architecture.
• Implementation of 2-qubit gates via lattice surgery.
• Off-line fault-tolerant preparation of magic states using projective measurements and gate teleportations.
• Routing qubits for all-to-all connectivity.

Main Results:

• A 256-bit elliptic curve logarithm was computed in 9 hours.
• The computation required 126,133 cat qubits with an average of 19 photons per state.
• Assumed a single- to two-photon loss ratio of 10^-5 and a cycle time of 500 ns.

Conclusions:

• The proposed 2D grid architecture with cat qubits is feasible for Shor's algorithm.
• The performance analysis provides a reusable framework for evaluating quantum computing architectures.
• This work guides the selection of architectures for future quantum computing platforms.