Error correction optimisation in the presence of X/Z asymmetry

Abstract

By taking into account the physical nature of quantum errors it is possible to improve the efficiency of quantum error correction. Here we consider an optimisation to conventional quantum error correction which involves exploiting asymmetries in the rates of X and Z errors by reducing the rate of X correction. As an example, we apply this optimisation to the [[7,1,3]] code and make a comparison with conventional quantum error correction. After two levels of concatenated error correction we demonstrate a circuit depth reduction of at least 43% and reduction in failure rate of at least 67%. This improvement requires no additional resources and the required error asymmetry is likely to be present in most physical quantum computer architectures.

8 pages, 4 figures

References in corpus (4)

• Simulated Quantum Computation of Molecular Energies
• Subsystem fault tolerance with the Bacon-Shor code
• Effective fault-tolerant quantum computation with slow measurements
• A precise CNOT gate in the presence of large fabrication induced variations of the exchange interaction strength

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• Families of LDPC Codes Derived from Nonprimitive BCH Codes and Cyclotomic Cosets
• Quantum codes for asymmetric channels: ZZZY surface codes
• Nonbinary Quantum Cyclic and Subsystem Codes Over Asymmetrically-decohered Quantum Channels
• Error Correction for Reliable Quantum Computing
• High performance single-error-correcting quantum codes for amplitude damping
• Quantum stabilizer codes from Abelian and non-Abelian groups association schemes