Error Mitigation for Universal Gates on Encoded Qubits.

Area of Science:

• Quantum computing
• Quantum error correction
• Fault-tolerant quantum computation

Background:

• The Eastin-Knill theorem prohibits universal transversal gates in quantum error-correcting codes.
• Calderbank-Shor-Steane codes achieve universality with transversal Clifford gates and one non-Clifford gate (e.g., T gate).
• Current fault-tolerant T gate implementations, like magic state distillation, incur significant hardware overhead, hindering near-term applications.

Purpose of the Study:

• To propose a novel method for implementing universal quantum computation on near-term, small-scale quantum devices.
• To overcome the hardware overhead associated with traditional fault-tolerant T gates.
• To leverage both error correction and error mitigation techniques synergistically.

Main Methods:

• Implementing encoded Clifford gates using transversal operations within quantum error-correcting codes.
• Employing the quasiprobability method for error mitigation of noisy encoded T gates.
• Combining error correction for Clifford gates and error mitigation for T gates in a hybrid approach.

Main Results:

• Demonstrated the feasibility of implementing encoded Clifford+T circuits without magic state distillation.
• Showcased a method where the number of T gates scales inversely with the physical noise rate.
• Proposed circuits that may challenge the capabilities of current classical simulation algorithms.

Conclusions:

• The developed approach offers a practical pathway to universal quantum computation on near-term quantum hardware.
• This hybrid strategy significantly reduces the hardware requirements compared to traditional fault-tolerant methods.
• The proposed circuits represent a promising direction for advancing quantum algorithm implementation in the NISQ era.