# Theoretical Physics

**13 March 2012**

**Time:**15:00 to 16:00

**Location:**E C Stoner SR 8.62

Clare Horsman (Tokyo, Japan)

Surface code quantum computing by lattice surgery

Surface codes have the highest fault-tolerant threshold of any current error correction code, and require only a fixed 2D nearest neighbour structure, making them an obvious choice for large scale designs in experimentally realistic systems. The planar version surface code uses the fewest physical qubits for a given logical error tolerance, making it the implementation of choice for small-scale achievable experiments for error correction codes. However, planar codes have previously been restricted to using transversal gates for qubit interactions, destroying the inherent 2D nearest-neighbour nature of the code. In this talk I will introduce a scheme for coupling planar qubits without transversal operations, using a technique we call "lattice surgery". This involves splitting and merging code surfaces, enabling state distribution and controlled operations to be performed without braiding. The qubit requirement for planar implementations can be further reduced by rotating the lattice used, leaving diagonal rather than straight logical operators. I will demonstrate how an encoded CNOT between two distance 3 logical states is possible with 53 physical qubits, half of that required in any other know construction in 2D.

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