Doubled Color Codes

Abstract

We show how to perform a fault-tolerant universal quantum computation in 2D architectures using only transversal unitary operators and local syndrome measurements. Our approach is based on a doubled version of the 2D color code. It enables a transversal implementation of all logical gates in the Clifford+T basis using the gauge fixing method proposed recently by Paetznick and Reichardt. The gauge fixing requires six-qubit parity measurements for Pauli operators supported on faces of the honeycomb lattice with two qubits per site. Doubled color codes are promising candidates for the experimental demonstration of logical gates since they do not require state distillation. Secondly, we propose a Maximum Likelihood algorithm for the error correction and gauge fixing tasks that enables a numerical simulation of logical circuits in the Clifford+T basis. The algorithm can be used in the online regime such that a new error syndrome is revealed at each time step. We estimate the average number of logical gates that can be implemented reliably for the smallest doubled color code and a toy noise model that includes depolarizing memory errors and syndrome measurement errors.

53 pages, 10 figures

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Cited by in corpus (9)

• Magic State Distillation: Not as Costly as You Think
• A fault-tolerant non-Clifford gate for the surface code in two dimensions
• Analysing correlated noise on the surface code using adaptive decoding algorithms
• Thresholds for universal concatenated quantum codes
• Stacked codes: universal fault-tolerant quantum computation in a two-dimensional layout
• Magic State Distillation from Entangled States
• Resilience to time-correlated noise in quantum computation
• Instantaneous braids and Dehn twists in topologically ordered states
• Achieving fault tolerance on capped color codes with few ancillas