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arXiv:2606.28552

Enhancing Initial-State Sensitivity through Time-Dependent Hamiltonian Readout in Ising Spin Chains

Hoang Van Do

quant-phSubmitted Jun 26, 2026• Announced Jun 30, 2026• 0 citations• Revised Jun 30, 2026 (v2)
v1 · Jun 26, 2026v2 · Jun 30, 2026v3 · Jul 1, 2026
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Abstract

Local observables can lose sensitivity to an initial state during strongly interacting many-body evolution even though the global dynamics remain unitary. We show that this sensitivity can be enhanced through a time-dependent Hamiltonian readout. Two orthogonal product states are first evolved under a slanted-field Ising Hamiltonian, where their distinction becomes strongly suppressed as observed through several local observables, including subsystem magnetizations and correlation functions, and are then quenched to the transverse-field Ising model at a tunable time. Exact simulations of chains up to $N=12$ show that the optimized time-averaged separation after the switch exceeds the residual slanted-field baseline for every observable and system size tested. In the strongest channels, the standardized readout separation remains robust over the accessible size range, with no clear systematic suppression at larger $N$. The enhancement recurs in widely separated late-time windows and persists qualitatively for open boundaries. These results establish Hamiltonian switching as an observable-selective mechanism for enhancing initial-state sensitivity without time reversal or implying recovery of the full reduced state.

Comments
15 pages, 11 figures; includes appendices

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Local observables can lose sensitivity to an initial state during strongly interacting many-body evolution even though the global dynamics remain unitary. We show that this sensitivity can be enhanced through a time-dependent Hamiltonian readout. Two orthogonal product states are first evolved under a slanted-field Ising Hamiltonian, where their distinction becomes strongly suppressed as observed through several local observables, including subsystem magnetizations and correlation functions, and are then quenched to the transverse-field Ising model at a tunable time. Exact simulations of chains up to N=12N=12N=12 show that the optimized time-averaged separation after the switch exceeds the residual slanted-field baseline for every observable and system size tested. In the strongest channels, the standardized readout separation remains robust over the accessible size range, with no clear systematic suppression at larger NNN. The enhancement recurs in widely separated late-time windows and persists qualitatively for open boundaries. These results establish Hamiltonian switching as an observable-selective mechanism for enhancing initial-state sensitivity without time reversal or implying recovery of the full reduced state.
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Abstract Hamiltonian simulation is one of the main proposed applications of near-term quantum computers, but its practical value depends on whether real hardware can preserve intended Hamiltonian dynamics once sampling limits, gate noise, decoherence, and circuit depth are taken into account. This study investigates whether the IBM quantum backend \texttt{ibm\_marrakesh} can reproduce the many-body dynamics shown by ideal simulation, using a 15-qubit one-dimensional tilted-field Ising chain as the benchmark system. The system was initialized with all qubits spin-up except for a localized spin-down excitation at the central qubit, q8q_8q8​, and evolved using a second-order Trotterized circuit with timestep Δt=0.1\Delta t=0.1Δt=0.1. The reference case, hz=0h_z=0hz​=0, was compared with the tilted-field case, hz=hx=0.35625h_z=h_x=0.35625hz​=hx​=0.35625, across three interaction regimes: J=0.90hxJ=0.90h_xJ=0.90hx​, J=hxJ=h_xJ=hx​, and J=1.40hxJ=1.40h_xJ=1.40hx​. Local magnetization, total magnetization, and connected spin correlations were used to track magnetization memory and finite-speed correlation spreading from the central excitation. The ideal simulation shows clear local and total magnetization evolution, as well as connected-correlation spreading outward from q8q_8q8​, giving a baseline for the intended Hamiltonian dynamics. The IBM hardware results reproduce the broad early-time magnetization trend but show compressed local-magnetization values, reduced separation between qubits, and weaker long-range connected-correlation structure. These differences indicate that the open-access quantum hardware preserves some early-time features of the intended dynamics, while longer-time correlation spreading is increasingly obscured by finite sampling, two-qubit gate errors, readout error, decoherence, and circuit depth. Overall, the study uses this spin-chain system as a direct benchmark for testing how much physically meaningful many-body behavior can still be extracted from noisy open-access quantum hardware.
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