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Primitive Quantum Gates for an SU(3) Discrete Subgroup: $\Sigma(36\times3)$

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arxiv 2405.05973 v4 pith:RKMPOZ5X submitted 2024-04-30 hep-lat quant-ph

Erik J. Gustafson , Yao Ji , Henry Lamm , Edison M. Murairi , Sebastian Osorio Perez , Shuchen Zhu This is my paper · ORCID
classification hep-latquant-ph
keywords gatequantumsigmatimes3groupprimitivesimulationsubgroup
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We construct the primitive gate set for the digital quantum simulation of the 108-element $\Sigma(36\times3)$ group. This is the first time a nonabelian 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 $\Sigma(36\times3)$ 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.

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Forward citations

Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Local Thermalization of SU(2) Lattice Gauge Fields on Quantum Computers

    hep-lat 2026-03 unverdicted novelty 7.0 of 10

    Quantum hardware simulation of SU(2) lattice gauge thermalization matches classical extrapolations up to 101 plaquettes after error mitigation, establishing feasibility for chaotic quantum field systems.

  2. Benchmarking trigonometric continuous-variable gate primitives with trapped ions

    quant-ph 2026-07 conditional novelty 6.0 of 10

    Cosine gates exp(-iθ cos(c x̂)) in one- and two-mode versions were implemented on trapped-ion motional modes and benchmarked against noise-inclusive simulations via Fock-space transition probabilities.

  3. Probing Hadron Scattering in Lattice Gauge Theories on Qudit Quantum Computers

    quant-ph 2025-07 conditional novelty 6.0 of 10

    Proposed qudit circuits simulate meson-antimeson scattering in a spin-1 U(1) lattice gauge theory and remain accurate under realistic dephasing and depolarization noise.

  4. Efficient Qudit Circuit for Quench Dynamics of $2+1$D Quantum Link Electrodynamics

    quant-ph 2025-07 conditional novelty 6.0 of 10

    A matter-integrated-out reformulation of 2+1D U(1) quantum link electrodynamics is translated into explicit qudit circuits, with Trotterized simulations matching exact dynamics on small lattices.

  5. String Breaking Dynamics and Glueball Formation in a $2+1$D Lattice Gauge Theory

    hep-lat 2025-07 accept novelty 6.0 of 10

    In a 2+1D Z2 lattice gauge theory, string breaking happens only at specific resonances set by field strength and matter mass, while long strings can dynamically form closed electric loops analogous to glueballs.

  6. Observation of hadron scattering in a lattice gauge theory on a quantum computer

    quant-ph 2025-05 conditional novelty 6.0 of 10

    The authors observe elastic and confined scattering, plus mass-quench-induced inelastic dynamics, in a 1+1D U(1) lattice gauge theory on IBM quantum hardware.

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