Subsystem bivariate bicycle codes achieve high-rate BB logical qubits with local four-qubit gauge checks, yielding examples such as [[108,12,6]] that outperform surface-code alternatives.
Subsystem surface codes with three-qubit check operators
4 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We propose a simplified version of the Kitaev's surface code in which error correction requires only three-qubit parity measurements for Pauli operators XXX and ZZZ. The new code belongs to the class of subsystem stabilizer codes. It inherits many favorable properties of the standard surface code such as encoding of multiple logical qubits on a planar lattice with punctured holes, efficient decoding by either minimum-weight matching or renormalization group methods, and high error threshold. The new subsystem surface code (SSC) gives rise to an exactly solvable Hamiltonian with 3-qubit interactions, topologically ordered ground state, and a constant energy gap. We construct a local unitary transformation mapping the SSC Hamiltonian to the one of the ordinary surface code thus showing that the two Hamiltonians belong to the same topological class. We describe error correction protocols for the SSC and determine its error thresholds under several natural error models. In particular, we show that the SSC has error threshold approximately 0.6% for the standard circuit-based error model studied in the literature. We also consider a model in which three-qubit parity operators can be measured directly. We show that the SSC has error threshold approximately 0.97% in this setting.
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quant-ph 4representative citing papers
Constructs free-fermion subsystem codes with a 2D topological example, graph-based solvability algorithm, and gap analysis via skew energy and median eigenvalues.
Magic state cultivation prepares high-fidelity T states with an order of magnitude fewer qubit-rounds than prior distillation methods by gradually growing them within a surface code under depolarizing noise.
Plaquette compiles realistic quantum hardware noise models into multiple sampler representations, showing that Pauli-twirled approximations can misestimate logical error rates by an order of magnitude compared to leakage-aware and near-Clifford methods.
citing papers explorer
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Topological subsystem bivariate bicycle codes with four-qubit check operators
Subsystem bivariate bicycle codes achieve high-rate BB logical qubits with local four-qubit gauge checks, yielding examples such as [[108,12,6]] that outperform surface-code alternatives.
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Free-Fermion Subsystem Codes
Constructs free-fermion subsystem codes with a 2D topological example, graph-based solvability algorithm, and gap analysis via skew energy and median eigenvalues.
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Magic state cultivation: growing T states as cheap as CNOT gates
Magic state cultivation prepares high-fidelity T states with an order of magnitude fewer qubit-rounds than prior distillation methods by gradually growing them within a surface code under depolarizing noise.
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Plaquette: A hardware-aware design platform for fault-tolerant quantum computers
Plaquette compiles realistic quantum hardware noise models into multiple sampler representations, showing that Pauli-twirled approximations can misestimate logical error rates by an order of magnitude compared to leakage-aware and near-Clifford methods.