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PreprintCC BY 4.0arXiv

Resolving Spectral Gaps of the Frustrated Spin-1/2 J1-J2 Chain via Dual Spin-Sector Variational Quantum Eigensolver

  • Sk Saniur Rahaman
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Abstract

Finding excited states and resolving spectral gaps in frustrated quantum spin systems using Variational Quantum Eigensolvers is complicated by state-ordering inversions. In the frustrated spin-1/2 J1-J2 Heisenberg chain, standard single-sector variational quantum deflation collapses onto intermediate triplet excitation, preventing the isolation of excited singlets and the singlet-singlet gap. To resolve these gaps, a Dual Spin-Sector Variational Quantum Eigensolver framework is introduced for near-term quantum architectures. By partitioning the search across magnetization sectors Sz=0 and Sz=1, the lowest triplet is resolved as an unconstrained ground state in Sz=1 with zero deflation penalty. Leveraging exact global spin-rotation symmetry, this state is mapped analytically into Sz=0 without ancilla overhead, unlocking dual deflation via shallow compute-uncompute circuits. Tracking both singlet-triplet and singlet-singlet gaps across coupling ratios J2/J1 from $0$ to $1$ for chains up to $16$ qubits faithfully captures all critical phenomena: the continuous Berezinskii-Kosterlitz-Thouless transition, exact Majumdar-Ghosh dimer degeneracy, level-ordering inversion in the gapless liquid phase, and incommensurate spiral excitations. Circuit depth scaling up to twenty layers provides an overparameterization mechanism overcoming classical local minima in strongly frustrated regimes, reducing relative energy errors below 1% and elevating state fidelities above 97% on $16$ qubits. Projective measurement sampling demonstrates resilience against shot noise, providing a practical blueprint for exploring frustrated quantum magnetism on near-term quantum devices.

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Cite

BibTeXRIS
BibTeX
@misc{rahaman2026resolving,
  title = {{Resolving Spectral Gaps of the Frustrated Spin-1/2 $J_1$-$J_2$ Chain via Dual Spin-Sector Variational Quantum Eigensolver}},
  author = {Sk Saniur Rahaman},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10454},
  eprint = {2610.10454},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.10454},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Resolving Spectral Gaps of the Frustrated Spin-1/2 J_1-J_2 Chain via Dual Spin-Sector Variational Quantum Eigensolver
AU  - Sk Saniur Rahaman
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.10454
UR  - https://arxiv.org/abs/2610.10454
AB  - Finding excited states and resolving spectral gaps in frustrated quantum spin systems using Variational Quantum Eigensolvers is complicated by state-ordering inversions. In the frustrated spin-1/2 J_1-J_2 Heisenberg chain, standard single-sector variational quantum deflation collapses onto intermediate triplet excitation, preventing the isolation of excited singlets and the singlet-singlet gap. To resolve these gaps, a Dual Spin-Sector Variational Quantum Eigensolver framework is introduced for near-term quantum architectures. By partitioning the search across magnetization sectors S^z=0 and S^z=1, the lowest triplet is resolved as an unconstrained ground state in S^z=1 with zero deflation penalty. Leveraging exact global spin-rotation symmetry, this state is mapped analytically into S^z=0 without ancilla overhead, unlocking dual deflation via shallow compute-uncompute circuits. Tracking both singlet-triplet and singlet-singlet gaps across coupling ratios J_2/J_1 from $0$ to $1$ for chains up to $16$ qubits faithfully captures all critical phenomena: the continuous Berezinskii-Kosterlitz-Thouless transition, exact Majumdar-Ghosh dimer degeneracy, level-ordering inversion in the gapless liquid phase, and incommensurate spiral excitations. Circuit depth scaling up to twenty layers provides an overparameterization mechanism overcoming classical local minima in strongly frustrated regimes, reducing relative energy errors below 1% and elevating state fidelities above 97% on $16$ qubits. Projective measurement sampling demonstrates resilience against shot noise, providing a practical blueprint for exploring frustrated quantum magnetism on near-term quantum devices.
ER  -