Fault-tolerant Preparation of Stabilizer States for Quantum CSS Codes by Classical Error-Correcting Codes

Abstract

Stabilizer states are extensively studied in quantum information theory for their structures based on the Pauli group. Calderbank-Shor-Steane (CSS) stabilizer states are of particular importance in their application to fault-tolerant quantum computation (FTQC). However, how to fault-tolerantly prepare arbitrary CSS stabilizer states for general CSS stabilizer codes is still unknown, and their preparation can be highly costly in computational resources. In this paper, we show how to prepare a large class of CSS stabilizer states useful for FTQC. We propose distillation protocols using syndrome encoding by classical codes or quantum CSS codes. Along the same lines, we show that classical coding techniques can reduce the ancilla consumption in Steane syndrome extraction by using additional transversal controlled-NOT gates and classical computing power. In the scenario of a fixed ancilla consumption rate, we can increase the frequency of quantum error correction and effectively lower the error rate.

The paper has been extensively revised to explain the distillation protocol by classical codes. 13 pages, 6 figures

References in corpus (12)

• Surface codes: Towards practical large-scale quantum computation
• Detecting arbitrary quantum errors via stabilizer measurements on a sublattice of the surface code
• Restrictions on Transversal Encoded Quantum Gate Sets
• Magic state distillation with low overhead
• Novel constructions for the fault-tolerant Toffoli gate
• Subsystem fault tolerance with the Bacon-Shor code
• Fault-tolerant conversion between the Steane and Reed-Muller quantum codes
• Multilevel distillation of magic states for quantum computing
• Entanglement purification protocols for all graph states
• Entanglement-Assisted Quantum Error-Correcting Codes with Imperfect Ebits
• Distilling one-qubit magic states into Toffoli states
• Ability of stabilizer quantum error correction to protect itself from its own imperfection

Cited by in corpus (6)

• Time-Efficient Constant-Space-Overhead Fault-Tolerant Quantum Computation
• Efficient Preparation of Large Block Code Ancilla States for Fault-tolerant Quantum Computation
• Constant depth fault-tolerant Clifford circuits for multi-qubit large block codes
• Reducing Quantum Error Correction Overhead with Versatile Flag-Sharing Syndrome Extraction Circuits
• Error correctable efficient quantum homomorphic encryption using Calderbank-Shor-Steane codes
• Improved performance of the Bacon-Shor code with Steane's syndrome extraction method