Primitive quantum gates for an 
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 discrete subgroup: Binary octahedral

Gustafson, Erik J.; Lamm, Henry; Lovelace, Felicity

doi:10.1103/physrevd.109.054503

Phys. Rev. D

2024

DOI: 10.1103/physrevd.109.054503

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Primitive quantum gates for an SU(2) discrete subgroup: Binary octahedral

Erik J. Gustafson,

Henry Lamm,

Felicity Lovelace

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2024

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Cited by 4 publications

References 159 publications

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Nearly optimal state preparation for quantum simulations of lattice gauge theories

Kane,

Gomes,

Kreshchuk

2024

Phys. Rev. A

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Nearly optimal state preparation for quantum simulations of lattice gauge theories

Kane,

Gomes,

Kreshchuk

2024

Phys. Rev. A

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Primitive quantum gates for an SU(3) discrete subgroup: Σ(36×3)

Gustafson,

Ji,

Lamm

et al. 2024

Phys. Rev. D

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We construct the primitive gate set for the digital quantum simulation of the 108-element Σ(36×3) group. This is the first time a non-Abelian crystal-like subgroup of SU(3) has been constructed for quantum simulation. The gauge link registers and necessary primitives—the inversion gate, the group multiplication gate, the trace gate, and the Σ(36×3) Fourier transform—are presented for both an eight-qubit encoding and a heterogeneous three-qutrit plus two-qubit register. For the latter, a specialized compiler was developed for decomposing arbitrary unitaries onto this architecture. Published by the American Physical Society 2024

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Quantum error thresholds for gauge-redundant digitizations of lattice field theories

Carena,

Lamm,

et al. 2024

Phys. Rev. D

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In the quantum simulation of lattice gauge theories, gauge symmetry can be either fixed or encoded as a redundancy of the Hilbert space. While gauge-fixing reduces the number of qubits, keeping the gauge redundancy can provide code space to mitigate and correct quantum errors by checking and restoring Gauss’s law. In this work, we consider the correctable errors for generic finite gauge groups and design the quantum circuits to detect and correct them. We calculate the error thresholds below which the gauge-redundant digitization with Gauss’s law error correction has better fidelity than the gauge-fixed digitization involving only gauge-invariant states. Our results provide guidance for fault-tolerant quantum simulations of lattice gauge theories. Published by the American Physical Society 2024

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Primitive quantum gates for an SU(2) discrete subgroup: Binary octahedral

Cited by 4 publications

References 159 publications

Nearly optimal state preparation for quantum simulations of lattice gauge theories

Nearly optimal state preparation for quantum simulations of lattice gauge theories

Primitive quantum gates for an SU(3) discrete subgroup: Σ(36×3)

Quantum error thresholds for gauge-redundant digitizations of lattice field theories

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