Error rates and resource overheads of encoded three-qubit gates

Abstract

A non-Clifford gate is required for universal quantum computation, and, typically, this is the most error-prone and resource intensive logical operation on an error-correcting code. Small, single-qubit rotations are popular choices for this non-Clifford gate, but certain three-qubit gates, such as Toffoli or controlled-controlled-Z (CCZ), are equivalent options that are also more suited for implementing some quantum algorithms, for instance those with coherent classical subroutines. Here, we calculate error rates and resource overheads for implementing logical CCZ with pieceable fault-tolerance, a non-transversal method for implementing logical gates. We provide a comparison with a non-local magic-state scheme on a concatenated code and a local magic-state scheme on the surface code. We find the pieceable fault-tolerance scheme particularly advantaged over magic states on concatenated codes and in certain regimes over magic states on the surface code. Our results suggest that pieceable fault-tolerance is a promising candidate for fault-tolerance in a near-future quantum computer.

6 pages + 7 pages of Appendices, 9 figures

References in corpus (11)

• Surface codes: Towards practical large-scale quantum computation
• Restrictions on Transversal Encoded Quantum Gate Sets
• Quantum computing with nearest neighbor interactions and error rates over 1%
• Magic state distillation with low overhead
• Novel constructions for the fault-tolerant Toffoli gate
• Fault-tolerant conversion between the Steane and Reed-Muller quantum codes
• Improved magic states distillation for quantum universality
• Multilevel distillation of magic states for quantum computing
• Optimal and Efficient Decoding of Concatenated Quantum Block Codes
• Distilling one-qubit magic states into Toffoli states
• Correctable noise of Quantum Error Correcting Codes under adaptive concatenation