Abstract
One class of quantum error-correcting codes---hypergraph product codes---may offer fault tolerance with low hardware overhead. A new proposal shows how to perform universal quantum gates with these codes.
Highlights
Quantum computers have the capacity to change the landscape of computing
We have provided a general framework to implement Clifford gates on hypergraph product codes
This framework is based on code deformation and generalizes defectbased encoding from topological codes
Summary
Quantum computers have the capacity to change the landscape of computing. Recent advances demonstrate that we are capable of constructing quantum devices that cannot be simulated by their classical counterparts [1]. The hypergraph product code construction yields quantum codes with distance scaling as the square root of the block size Up to constants, this result is the same functional dependence between the distance and the block size as the surface code (but it applies to all the logical qubits). This result is the same functional dependence between the distance and the block size as the surface code (but it applies to all the logical qubits) These codes achieve similar error suppression as topological codes but do so at a constant encoding rate. This result, in turn, implies that, in certain special instances, we can efficiently verify when a certain operation is possible This approach can be contrasted to Gottesman’s work, which entails partitioning logical qubits into blocks of LDPC codes. We conclude with a summary and list some of the many open questions that need to be addressed
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