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This study presents a practical framework for simulating higher-spin quantum systems on standard qubit hardware by using symmetry-preserving encodings to suppress unphysical states and improve trainability. The research demonstrates that while binary encoding saves qubits, preserving spin symmetries yields significantly higher fidelities and faster convergence for complex many-body problems like Heisenberg chains. These findings offer a clear path forward for leveraging existing quantum processors to tackle intrinsically multi-level physical models without requiring new hardware architectures.
Variational simulation of higher-spin systems on qubit-based quantum simulators
arXiv:2405.05051v4 Announce Type: replace Abstract: Qubit-based quantum simulators naturally target two-level systems, whereas many quantum many-body problems are intrinsically $d$ level. Encodings from qudits to qubits then enlarge the Hilbert space and can introduce unphysical states that interfere with variational optimization. We formulate a variational framework for encoded $d$-level models that suppresses these illegitimate states with penalty terms and benchmark it for spin-1 and spin-3/2 bilinear-biquadratic Heisenberg chains. We compare binary encoding, which minimizes the qubit overhead, with symmetry encoding, which preserves the relevant spin symmetries and enables symmetry-conserving ans\"atze. Although binary encoding is more qubit efficient, its hardware-efficient ansatz is harder to train and less effective at exploiting conserved quantities. In contrast, symmetry encoding requires more qubits but reaches substantially higher fidelities, converges faster, and exhibits better trainability than the binary hardware-efficient ansatz. These results identify symmetry-preserving encodings as a practical route to simulating higher-spin models on existing qubit platforms.
Abstract:Qubit-based quantum simulators naturally target two-level systems, whereas many quantum many-body problems are intrinsically $d$ level. Encodings from qudits to qubits then enlarge the Hilbert space and can introduce unphysical states that interfere with variational optimization. We formulate a variational framework for encoded $d$-level models that suppresses these illegitimate states with penalty terms and benchmark it for spin-1 and spin-3/2 bilinear-biquadratic Heisenberg chains. We compare binary encoding, which minimizes the qubit overhead, with symmetry encoding, which preserves the relevant spin symmetries and enables symmetry-conserving ansätze. Although binary encoding is more qubit efficient, its hardware-efficient ansatz is harder to train and less effective at exploiting conserved quantities. In contrast, symmetry encoding requires more qubits but reaches substantially higher fidelities, converges faster, and exhibits better trainability than the binary hardware-efficient ansatz. These results identify symmetry-preserving encodings as a practical route to simulating higher-spin models on existing qubit platforms.
arXiv:2405.05051 [quant-ph]
(or arXiv:2405.05051v4 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2405.05051 Focus to learn more arXiv-issued DOI via DataCite
Phys. Rev. Research 8, 033119 (2026)
https://doi.org/10.1103/lfc9-cjqd Focus to learn more DOI(s) linking to related resources
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