Abstract
We present a planar surface-code-based scheme for fault-tolerant quantum computation which eliminates the time overhead of single-qubit Clifford gates, and implements long-range multi-target CNOT gates with a time overhead that scales only logarithmically with the control-target separation. This is done by replacing hardware operations for single-qubit Clifford gates with a classical tracking protocol. Inter-qubit communication is added via a modified lattice surgery protocol that employs twist defects of the surface code. The long-range multi-target CNOT gates facilitate magic state distillation, which renders our scheme fault-tolerant and universal.
Highlights
The performance of quantum computers is limited by the coherence times of the underlying physical qubits
We have demonstrated that edge tracking can be used to eliminate the time overhead of logical single-qubit Clifford gates in surface codes, as should be expected considering the Gottesman-Knill theorem
Compared to color code qubits, the surface code qubits used in our scheme require more physical qubits (∼ d2) for each logical qubit with code distance d, but – with the exception of twist defects – only require the measurement of weight-four stabilizers
Summary
The performance of quantum computers is limited by the coherence times of the underlying physical qubits. While the transversal Clifford gates of color codes provide them with fast logical H and S gates, defect-based proposals for surface codes [14] implement the H gate via a multi-step measurement protocol, and the S gate via a distilled ancilla qubit. Our scheme provides long-range multi-target CNOT gates – i.e., CNOTs with one control and arbitrarily many targets – between any set of edge-tracked surface code qubits These gates are useful for magic state distillation [20], which completes the universal gate set by fault-tolerantly implementing the T gate (or π/8 gate). Our scheme eliminates the need for hardware operations for single-qubit Clifford gates, and conceptually simplifies the twist-defect-based approach to surface-code quantum computing. We discuss our scheme in the context of possible hardware implementations and in comparison to alternative topological codes
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