Quantum states for error correction are described by their stabilizer, a commuting group of tensor products of Pauli matrices, enabling analysis of a rich class of quantum effects short of full quantum computation.
A Theory of Fault-Tolerant Quantum Computation
4 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
In order to use quantum error-correcting codes to actually improve the performance of a quantum computer, it is necessary to be able to perform operations fault-tolerantly on encoded states. I present a general theory of fault-tolerant operations based on symmetries of the code stabilizer. This allows a straightforward determination of which operations can be performed fault-tolerantly on a given code. I demonstrate that fault-tolerant universal computation is possible for any stabilizer code. I discuss a number of examples in more detail, including the five-qubit code.
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quant-ph 4representative citing papers
A 256-atom neutral ytterbium processor demonstrates fault-tolerant entanglement of 24 logical qubits and runs Bernstein-Vazirani on 28 logical qubits with better-than-physical error rates using erasure conversion.
Generalizes stat-mech mapping from toric code memories to transversal Clifford circuits, mapping tCNOT to random Ashkin-Teller and 4-body Ising models and estimating reduced thresholds of p=0.080 and p>=0.028.
Quotienting the Cayley graph of the Clifford group by a quantum state's stabilizer subgroup produces a graph of the state's Clifford orbit.
citing papers explorer
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The Heisenberg Representation of Quantum Computers
Quantum states for error correction are described by their stabilizer, a commuting group of tensor products of Pauli matrices, enabling analysis of a rich class of quantum effects short of full quantum computation.
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Fault-tolerant quantum computation with a neutral atom processor
A 256-atom neutral ytterbium processor demonstrates fault-tolerant entanglement of 24 logical qubits and runs Bernstein-Vazirani on 28 logical qubits with better-than-physical error rates using erasure conversion.
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Rigorous estimation of error thresholds of transversal Clifford logical circuits
Generalizes stat-mech mapping from toric code memories to transversal Clifford circuits, mapping tCNOT to random Ashkin-Teller and 4-body Ising models and estimating reduced thresholds of p=0.080 and p>=0.028.
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Clifford Orbits from Cayley Graph Quotients
Quotienting the Cayley graph of the Clifford group by a quantum state's stabilizer subgroup produces a graph of the state's Clifford orbit.