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arXiv:2601.20237

Fast state transfer via loop weights

Gabor Lippner, Yujia Shi

quant-phmath.COSubmitted Jan 28, 2026• Announced Jan 29, 2026• 0 citations
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Abstract

We prove that almost-linear-time high-fidelity state transfer is achievable in a quantum spin chain using loop weights at the second and second-to-last nodes. We provide specific parameter values, and using a careful analysis of the eigenvectors we make precise quantitative estimates of the transfer time and strength.

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We quantify the effect of weighted loops at the source and target nodes of a graph on the strength of quantum state transfer between these vertices. We give lower bounds on loop weights that guarantee strong transfer fidelity that works for any graph where this protocol is feasible. By considering local spectral symmetry, we show that the required weight size depends only on the maximum degree of the graph and, in some less favorable cases, the distance between vertices. Additionally, we explore the duration for which transfer strength remains above a specified threshold.
Quantum state transfer along a one-dimensional spin chain has become a fundamental ingredient for quantum communication between distant nodes in a quantum network. We study the average fidelity of quantum state transfer (QST) along an XYXYXY spin chain by adjusting the basis identification between the first spin and the last spin. In a proper choice of the basis identification, we find that the QST fidelity depends only on the average parity of the initial state linearly. We propose a simple scheme to adjust the basis identification to optimize the average fidelity such that it depends linearly on the absolute value of the average parity. In the case where the absolute value of the average parity is 1 we prove that the fidelity takes the maximum at any time over arbitrary initial state and basis identification.
We present several protocols for reliable quantum state transfer through an XY spin chain. Among these is a simple two-spin encoding that achieves a remarkably high-fidelity transfer for an arbitrary quantum state. The fidelity of the transfer also decreases slowly with increasing chain length. Furthermore, the reliability can be increased by taking advantage of a local memory and/or confirming transfer using a second spin chain. The simplicity and high fidelity of the encoding makes this a candidate for near-future experiments including a test of the quantum speed limit.
This dissertation investigates continuous-time quantum walks and asymptotic state transfer in weighted graphs, with a particular focus on the impact of starting and target node weights on transfer fidelity and readout time. Through analysis of the eigenvectors and eigenvalues of the Hamiltonian, we derive quantitative results applicable to generalized graph structures. Our findings focus on the relationship between a graph's maximum degree and the minimum weights required to achieve specific transfer fidelities. This research advances the understanding of quantum state transfer in spin networks, with potential applications in quantum communication and computing.--Author's abstract
Based on the Lyapunov control, we present a scheme to realize state transfer with high fidelity by only modulating the boundary spins in a quantum spin-1/2 chain. Recall that the conventional transmission protocols aim at nonstationary state (or information) transfer from the first spin to the end spin at a fixed time. The present scheme possesses the following advantages. First, the scheme does not require precise manipulations of the control time. Second, it is robust against uncertainties in the initial states and fluctuations in the control fields. Third, the controls are exerted only on the boundary sites of the chain. It works for variable spin-1/2 chains with different periodic structures and has good scalability. The feasibility to replace the control fields by square pules is explored, which simplifies the realization in experiments.
In a one-dimensional Heisenberg chain, we show that there are no sets of coupling strengths such that the evolution perfectly transfers a quantum state between the two ends of the chain without the addition of magnetic fields. In lieu of perfect transfer, we consider a range of options for achieving high quality transfer, whether in finite time, or via "pretty good" transfer where one waits long times in the hope of getting arbitrarily close to perfect transfer. In attempting to engineer arbitrarily accurate transfer, we explore a new paradigm that facilitates time estimates for achieving any target accuracy εεε for the transfer.