Low-Cost Noise Reduction for Clifford Circuits.

Area of Science:

• Quantum computing
• Quantum information science
• Error mitigation and correction

Background:

• Quantum computations are susceptible to noise, leading to errors.
• Existing methods like quantum error correction (QEC) and error mitigation have significant overheads.
• Clifford circuits are fundamental building blocks in quantum algorithms.

Purpose of the Study:

• To propose a novel scheme, Clifford noise reduction (CliNR), for reducing logical error rates in Clifford circuits.
• To achieve lower overhead compared to traditional quantum error correction.
• To avoid the exponential sampling overhead associated with error mitigation techniques.

Main Methods:

• CliNR implements Clifford circuits by decomposing them into subcircuits.
• Gate teleportation is utilized to perform these subcircuits.
• Random stabilizer measurements are employed to detect errors in resource states used for gate teleportation.
• This approach is a teleported version of the coherent parity-check scheme with offline fault-detection.

Main Results:

• CliNR achieves a vanishing logical error rate for specific families of n-qubit Clifford circuits where ns*p^2 approaches 0 (ns=o(1/p^2)).
• This performance surpasses the limitations of direct implementation (s=o(1/p)).
• The scheme requires minimal resources: 3n+1 qubits, 2s+o(s) gates, and has zero rejection rate.
• Numerical simulations confirm error rate reduction in relevant noise regimes.

Conclusions:

• CliNR presents a practical and efficient method for reducing logical errors in quantum computations.
• Its low overhead makes it a viable alternative to quantum error correction for near-term quantum devices.
• The scheme demonstrates scalability and effectiveness in mitigating noise within Clifford circuits.