Abstract
Locality plays a fundamental role in quantum computation but also severely restricts our ability to store and process quantum information. We argue that this restriction may be unwarranted and re-examine quantum error correcting codes. We proceed to introduce new defects on the surface code called wormholes. These novel defects entangle two spatially separated sectors of the lattice. When anyonic excitations enter the mouth of a wormhole, they emerge through the other mouth. Wormholes thus serve to connect two spatially separated sectors of a flat, $2$D lattice. We show that these defects are capable of encoding logical qubits and can be used to perform all gates in the Clifford group.
Highlights
Locality plays a central role in condensed matter and quantum information science
From the perspective of quantum computation, this means that the code space is robust to local errors as perturbations must collude over a large distance to induce a logical error
The toric code [2] is a quantum error correcting code defined on a square lattice with periodic boundary conditions
Summary
Locality plays a central role in condensed matter and quantum information science. This is exemplified by Kitaev’s toric code [1], its variants [2], and the color code [3]. Modeling qubits as pointlike objects may not apply to physical implementations which use extended objects such as resonators to store quantum information [14] In such an architecture, the geometry of qubit couplings may not be suitably represented by a two-dimensional grid. In a companion paper [23], we outline how to generalize the techniques presented here to perform gates on a certain class of LDPC codes called hypergraph product codes [22,24] Engineering such connections may be infeasible with current technology, hypergraph product codes have the potential to reduce the overhead associated with constructing quantum circuits in the long term [25,26]. This mirrors the Bekenstein entropy [29] which scales proportionally to the area of a black hole
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