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Photonics & Electromagnetics Research Symposium - Fall (PIERS-Fall)

Time-Optimal Quantum State Transfer in Long Qubit Chains

Kseniia S. Chernova, Andrei A. Stepanenko, Maxim A. Gorlach

Published Nov 1, 2025• 0 citations
Publisher

Abstract

Recent progress in quantum technologies enables the fabrication of large-scale qubit arrays, but their optimal control remains challenging. In our work, we present a protocol for perfect quantum state transfer in a nearest-neighbor coupled chain of qubits, achieving maximal fidelity and minimal transfer time simultaneously. We apply the quantum brachistochrone method and obtain a protocol for the transfer of Fock and Bell states. Our solution reaches the fundamental quantum speed limit in the lattices with time-varying couplings.

DOI
10.23919/piers-fall62445.2025.11394133

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Recent progress in quantum technologies enables the fabrication of large-scale qubit arrays, but their optimal control remains challenging. In our work, we present a protocol for perfect quantum state transfer in a nearest-neighbor coupled chain of qubits, achieving maximal fidelity and minimal transfer time simultaneously. We apply the quantum brachistochrone method and obtain a protocol for the transfer of Fock and Bell states. Our solution reaches the fundamental quantum speed limit in the lattices with time-varying couplings.
Recent technological advances have allowed the fabrication of large arrays of coupled qubits, serving as prototypes for quantum processors. However, the optimal control of such systems remains notoriously challenging, limiting the potential of large-scale quantum systems. Here, we investigate a model problem of quantum state transfer in a large nearest-neighbor-coupled qubit array. We derive an optimal control strategy that simultaneously achieves maximal fidelity and minimal transfer time, reaching the quantum speed limit in a lattice with time-varying couplings.
We present an approach to compute time-optimal control of a quantum system which combines quantum brachistochrone and Lax pair techniques and enables efficient investigation of large-scale quantum systems. We illustrate our method by finding the quantum speed limit for a single-particle excitation in a nearest-neighbor-coupled qubit lattice with switchable couplings and fixed sum of their squares. We obtain the solution for a finite system with up to 10 000 qubits and for the effectively infinite lattice closed into ring. As another application of our method, we derive the quantum speed limit for a lattice with time-independent couplings.
Quantum information processing requires faithful on-chip transfer of quantum states, but the couplings in solid-state systems are usually preset and not tunable, and thus in general cannot meet the special configurations needed for perfect quantum state transfer. The authors demonstrate such a perfect transfer in a chain of four superconducting qubits with nearest-neighbor coupling through $i\phantom{\rule{0}{0ex}}n$ $s\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}u$ parametric modulation, in a single step, with high fidelity (99.2%) in a short time (84 ns), thus overcoming the fixed-coupling problem. Their scheme for flexible tunability of multiqubit coupling can be easily extended to larger systems.
We investigate the fidelity of the quantum state transfer (QST) of two qubits by means of an arbitrary spin-12\frac{1}{2}21​ network, on a lattice of any dimensionality. Under the assumptions that the network Hamiltonian preserves the magnetization and that a fully polarized initial state is taken for the lattice, we obtain a general formula for the average fidelity of the two qubits QST, linking it to the one- and two-particle transfer amplitudes of the spin excitations among the sites of the lattice. We then apply this formalism to a 1D spin chain with XXXXXX-Heisenberg type nearest-neighbour interactions adopting a protocol that is a generalization of the single qubit one proposed in Paganelli et al. [Phys. Rev. A 87, 062309 (2013)]. We find that a high-quality two qubit QST can be achieved provided one can control the local fields at sites near the sender and receiver. Under such conditions, we obtain an almost perfect transfer in a time that scales either linearly or, depending on the spin number, quadratically with the length of the chain.