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Comparison of encoding schemes for quantum computing of $S > 1/2$ spin chains
Quantum Physics · Submitted 26 Feb 2025
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The Dicke mapping, in which the spin states are encoded as superpositions of multi-qubit states, is found to be the most efficient because of the small number of terms in the qubit Hamiltonian.
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The abstract, sentence by sentence
We compare four different encoding schemes for the quantum computing of spin chains with a spin quantum number $S>1/2$: a compact mapping, a direct (or one-hot) mapping, a Dicke mapping, and a qudit mapping. The three different qubit encoding schemes are assessed by conducting Hamiltonian simulation for $1/2 \le S \le 5/2$ using a trapped-ion quantum computer. The qudit mapping is tested by running simulations with a simple noise model. The Dicke mapping, in which the spin states are encoded as superpositions of multi-qubit states, is found to be the most efficient because of the small number of terms in the qubit Hamiltonian. We also investigate the $S$-dependence of the time step length $\Delta\tau$ in the Suzuki-Trotter approximation and find that, in order to obtain the same accuracy for all $S$, $\Delta\tau$ should be inversely proportional to $S$.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We compare four different encoding schemes for the quantum computing of spin chains with a spin quantum number $S>1/2$: a compact mapping, a direct (or one-hot) mapping, a Dicke mapping, and a qudit mapping. | contribution 0.97 | 0.83 | 0.04 | asserted 0.84 |
| s1 | The three different qubit encoding schemes are assessed by conducting Hamiltonian simulation for $1/2 \le S \le 5/2$ using a trapped-ion quantum computer. | method 0.98 | 0.94 | 0.04 | asserted 0.99 |
| s2 | The qudit mapping is tested by running simulations with a simple noise model. | method 0.99 | 0.93 | 0.02 | asserted 0.89 |
| s3 | The Dicke mapping, in which the spin states are encoded as superpositions of multi-qubit states, is found to be the most efficient because of the small number of terms in the qubit Hamiltonian. | result 0.99 | 0.95 | 0.77 | asserted 1.00 |
| s4 | We also investigate the $S$-dependence of the time step length $\Delta\tau$ in the Suzuki-Trotter approximation and find that, in order to obtain the same accuracy for all $S$, $\Delta\tau$ should be inversely proportional to $S$. | result 0.99 | 0.96 | 0.13 | asserted 1.00 |
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Original abstract
We compare four different encoding schemes for the quantum computing of spin chains with a spin quantum number $S>1/2$: a compact mapping, a direct (or one-hot) mapping, a Dicke mapping, and a qudit mapping. The three different qubit encoding schemes are assessed by conducting Hamiltonian simulation for $1/2 \le S \le 5/2$ using a trapped-ion quantum computer. The qudit mapping is tested by running simulations with a simple noise model. The Dicke mapping, in which the spin states are encoded as superpositions of multi-qubit states, is found to be the most efficient because of the small number of terms in the qubit Hamiltonian. We also investigate the $S$-dependence of the time step length $\Delta\tau$ in the Suzuki-Trotter approximation and find that, in order to obtain the same accuracy for all $S$, $\Delta\tau$ should be inversely proportional to $S$.
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Spin chains having $=1$ with four [ref] and five [ref] sites were simulated using trapped ions of $^171$Yb$^+$ [ref] and $^40$Ca$^+$ [ref] .
Constructing the spin-1 Haldane phase on a qudit quantum processor · Introduction · 0.86
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