Spin Chain Quantum Communication on a Trapped-Ion Processor

Abstract: Efficient communication between distant qubits is one of the central challenges in scaling quantum processors. Although engineered spin chain protocols have been extensively investigated theoretically, their experimental realization has remained comparatively limited. Here, we experimentally realize engineered quantum communication protocols through digitally simulated spin Hamiltonian on IonQ's Forte 1/ Forte Enterprise 1 trapped-ion quantum processor. Combining exact numerical simulations with quantum hardware experiments, we benchmark uniform nearest-neighbour and engineered coupling profiles and demonstrate that engineered interactions significantly enhance the fidelity of quantum state transfer. We further show that exploiting the commutation structure of the spin Hamiltonian enables a parallel Trotter decomposition that more faithfully reproduces the target dynamics while substantially reducing the circuit depth and execution time compared to the conventional sequential implementations. Our results demonstrate that programmable quantum processors can effectively realize and efficiently implement quantum communication protocols, bringing Hamiltonian-based quantum communication closer to practical quantum technologies.

• The paper demonstrates that engineered coupling profiles produce superior fidelity and scalability compared to uniform nearest-neighbour interactions in spin chains.
• The study leverages a parallel Trotter decomposition to reduce circuit depth and enhance digital simulation of spin chain dynamics.
• Experimental results validate that optimal Trotter steps and Hamiltonian engineering significantly improve quantum communication on trapped-ion processors despite hardware limitations.

Spin Chain Quantum Communication on Trapped-Ion Processors: Digital Implementation and Benchmarking

Introduction

Quantum communication between remote qubits is essential for scalable quantum computing architectures. Traditional gate-based transfer protocols relying on sequences of SWAP gates are suboptimal due to the linear growth in circuit depth with increased transfer distance, which exacerbates error accumulation. This paper (2607.12999) experimentally realizes engineered quantum state transfer protocols using spin chain dynamics, digitally implemented on IonQ's Forte and Forte Enterprise trapped-ion quantum processors. Both uniform nearest-neighbour (NN) and engineered coupling profiles are investigated, demonstrating superior fidelity and scalability for quantum communication via Hamiltonian engineering, as well as circuit depth reduction through exploiting the commutation structure of the spin Hamiltonian.

Spin Chain Dynamics and Digital Simulation

Quantum state transfer is mediated by the Hamiltonian evolution of spin chains. The XY Hamiltonian,

$$H = \sum_{i=1}^N \sum_{j=i+1}^N J_{ij} (X_i X_j + Y_i Y_j),$$

facilitates excitation-conserving dynamics, suitable for both NN and engineered coupling scenarios. Uniform coupling yields simple spin transport but suffers from fidelity decay and transfer delay with increased chain length. In contrast, the Christandl et al. PST protocol,

$J_j = J_0 \sqrt{j(N-j)},$

produces an equally spaced energy spectrum, allowing perfect state transfer and suppressing dispersion irrespective of chain length.

The trapped-ion architecture natively supports efficient synthesis of $XX$ and $YY$ gates. Continuous time dynamics are approximated with first-order Lie-Trotter decomposition. Single-excitation state initialization and transfer fidelity measurements constitute the principal experimental readout.

Figure 1: Schematic illustration of quantum state transfer in an engineered spin chain, showing both the state propagation and gate-based digital Trotterization.

Convergence of Trotter Approximation

Simulation accuracy versus circuit depth tradeoff is empirically optimized. Increasing the number of Trotter steps improves the approximation to the exact spin chain dynamics, yet boosts gate count and unavoidable hardware-induced errors. The study identifies an optimal regime (30 Trotter steps), balancing simulation fidelity and hardware constraints.

Figure 2: Fidelity convergence of Trotterized gate-based evolution to exact NN dynamics as Trotter steps increase for $N=3$ and $N=5$.

Experimental Benchmarking: Uniform NN Chains

Experimental and numerical state-transfer fidelities for NN chains ($N=3$, $4$, $5$) are compared. For all system sizes, measured fidelities exceed the classical threshold of 2/3, establishing genuine quantum advantage. Increased chain length induces delayed fidelity peak and lower transfer success, consistent with theoretical predictions and implicating decoherence, gate errors, and readout noise as principal limiting factors.

Figure 3: Experimental state-transfer fidelity as a function of time for NN spin chains with $N=3,4,5$, highlighting the fidelity decay and transfer delay with chain length.

Engineered Coupling for Perfect State Transfer

Engineered PST coupling profiles substantially outperform uniform NN couplings in fidelity, especially as chain length increases. The digital-implemented engineered chain experimentally achieves higher fidelity transfer, validating the theoretical suppression of dispersion and establishing Hamiltonian engineering as a crucial component for robust quantum communication.

Figure 4: Comparative fidelity profiles for NN vs. engineered PST coupling in a four-qubit chain, showing clear superiority of PST engineering.

Efficient Digital Implementation via Parallel Trotter Decomposition

The spin-1/2 XY Hamiltonian exhibits a commutation structure where interaction terms on non-overlapping qubit pairs commute. Exploiting this, parallel even-odd Trotterization partitions interactions into two commuting groups, permitting simultaneous entangling gates, thereby reducing circuit depth from $J_j = J_0 \sqrt{j(N-j)},$0 to $J_j = J_0 \sqrt{j(N-j)},$1 per Trotter step. Experimental results confirm improved fidelity and faster transfer times under parallel decomposition relative to sequential Trotterization.

Figure 5: Sequential versus parallel Trotterization for engineered PST chain ($J_j = J_0 \sqrt{j(N-j)},$2), with parallel circuits exhibiting earlier fidelity maxima and lower depth.

Spin Chain Transport Mechanism and Population Dynamics

By tracking the populations of all single-excitation basis states during the transfer process, the experiment directly observes coherent propagation through intermediate qubits, underscoring many-body transport mechanisms intrinsic to spin chain dynamics.

Figure 6: Time evolution of single-excitation basis states for $J_j = J_0 \sqrt{j(N-j)},$3 NN chain, displaying coherent population migration from leftmost to rightmost qubit.

Hardware Limitations: Leakage Errors and System Size

Dominant experimental error is excitation-number leakage, a direct consequence of imperfect gate fidelity and execution noise. Leakage probability grows with both system size and circuit runtime, as demonstrated with $J_j = J_0 \sqrt{j(N-j)},$4, $J_j = J_0 \sqrt{j(N-j)},$5, $J_j = J_0 \sqrt{j(N-j)},$6, highlighting constraints for future scalability. Cross-generation comparisons reveal hardware performance dependence, underscoring nontrivial calibration and noise profiles.

Figure 7: Leakage probability as a function of evolution time for spin chains of varying length, demonstrating error scaling and processor-dependent fidelity.

Coherent State Transfer of Quantum Superpositions

Transport of quantum superposition states (e.g., $J_j = J_0 \sqrt{j(N-j)},$7) via engineered spin chains is demonstrated, confirming preservation of quantum coherence during transfer. Experimental attenuation in the transfer peak relative to simulation is attributed to transient hardware performance, rather than protocol limitations.

Figure 8: Time evolution of superposition state transfer signal $J_j = J_0 \sqrt{j(N-j)},$8, demonstrating coherent transport and fidelity limitations due to hardware fluctuations.

Implications and Future Directions

Experimental realization of Hamiltonian-engineered quantum communication protocols on trapped-ion processors establishes a viable route for scalable quantum computation architectures. Practical implications include reduced communication overhead, enhanced remote gate operations, and efficient entanglement distribution. Theoretically, exploiting commutation structure for digital simulation optimizes circuit resources, reinforcing the importance of algorithmic-hardware codevelopment. Future research directions include expanded coupling profiles, larger chain sizes, complex network geometries, and generalization to multipartite entanglement transfer and distributed quantum operations.

Conclusion

The study rigorously benchmarks quantum communication protocols via spin chain dynamics on programmable trapped-ion platforms. Engineered Hamiltonian evolutions and parallelized digital simulation yield substantial improvements in fidelity and circuit efficiency. These findings specify clear architectural and algorithmic strategies for quantum processor scale-up and communication optimization, with direct implications for large-scale quantum computing and distributed quantum information processing.