Partitioning qubits in hypergraph product codes to implement logical
gates
- URL: http://arxiv.org/abs/2204.10812v3
- Date: Tue, 17 Oct 2023 12:47:50 GMT
- Title: Partitioning qubits in hypergraph product codes to implement logical
gates
- Authors: Armanda O. Quintavalle, Paul Webster, Michael Vasmer
- Abstract summary: Transversal gates are the simplest type of fault-tolerant logical gates.
We show that gates can be used as the basis for universal quantum computing on LDPC codes.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The promise of high-rate low-density parity check (LDPC) codes to
substantially reduce the overhead of fault-tolerant quantum computation depends
on constructing efficient, fault-tolerant implementations of logical gates on
such codes. Transversal gates are the simplest type of fault-tolerant gate, but
the potential of transversal gates on LDPC codes has hitherto been largely
neglected. We investigate the transversal gates that can be implemented in
hypergraph product codes, a class of LDPC codes. Our analysis is aided by the
construction of a symplectic canonical basis for the logical operators of
hypergraph product codes, a result that may be of independent interest. We show
that in these codes transversal gates can implement Hadamard (up to logical
SWAP gates) and control-Z on all logical qubits. Moreover, we show that
sequences of transversal operations, interleaved with error correction, allow
implementation of entangling gates between arbitrary pairs of logical qubits in
the same code block. We thereby demonstrate that transversal gates can be used
as the basis for universal quantum computing on LDPC codes, when supplemented
with state injection.
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