Abstract
Topological error correction codes are promising candidates to protect quantum computations from the deteriorating effects of noise. While some codes provide high noise thresholds suitable for robust quantum memories, others allow straightforward gate implementation needed for data processing. To exploit the particular advantages of different topological codes for fault-tolerant quantum computation, it is necessary to be able to switch between them. Here we propose a practical solution, subsystem lattice surgery, which requires only two-body nearest-neighbor interactions in a fixed layout in addition to the indispensable error correction. This method can be used for the fault-tolerant transfer of quantum information between arbitrary topological subsystem codes in two dimensions and beyond. In particular, it can be employed to create a simple interface, a quantum bus, between noise resilient surface code memories and flexible color code processors.
Highlights
Topological error correction codes are promising candidates to protect quantum computations from the deteriorating effects of noise
We qubits with Hilbert space cHon1⁄4sidÀeCr 2aÁsny. stTehme comprised group of of n Pauli operators Pn on H is generated under multiplication by n independent Pauli operators and the imaginary unit i
We have introduced the method of subsystem lattice surgery (SLS) as a generalization of lattice surgery[13,14] to any pair of 2D topological codes, exploiting their similarities[20]
Summary
Topological error correction codes are promising candidates to protect quantum computations from the deteriorating effects of noise. We propose a practical solution, subsystem lattice surgery, which requires only two-body nearest-neighbor interactions in a fixed layout in addition to the indispensable error correction This method can be used for the fault-tolerant transfer of quantum information between arbitrary topological subsystem codes in two dimensions and beyond. Our flexible algorithm for code switching is based on a formalization of lattice surgery[13,14] in terms of operator quantum error correction[15] and measurementbased quantum computation[16]. This introduces the notion of subsystem lattice surgery (SLS), a procedure that can be understood as initializing and gauge fixing a single subsystem code. The method proposed here has the prospect of connecting different components of a future quantum computer in an elegant, practical, and simple fashion
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