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International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials)

Speeding up quantum state transfer in a three-qubit chain

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

Published Sep 1, 2025• 0 citations
Publisher

Abstract

Efficient state transfer in quantum systems is crucial for advancing quantum communication. In this work, we apply the quantum brachistochrone method to find a time-optimal state transfer in a fully connected array of three qubits. By leveraging multi-path interference through both nearest-neighbor and direct couplings, we demonstrate that multi-path evolution reduces transfer time compared to the single-path protocols.

DOI
10.1109/metamaterials65622.2025.11174207

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Efficient state transfer in quantum systems is crucial for advancing quantum communication. In this work, we apply the quantum brachistochrone method to find a time-optimal state transfer in a fully connected array of three qubits. By leveraging multi-path interference through both nearest-neighbor and direct couplings, we demonstrate that multi-path evolution reduces transfer time compared to the single-path protocols.
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.
Abstract The speed limit of quantum state transfer (QST) in a system of interacting particles is not only important for quantum information processing, but also directly linked to Lieb–Robinson-type bounds that are crucial for understanding various aspects of quantum many-body physics. For strongly long-range interacting systems such as a fully-connected quantum computer, such a speed limit is still unknown. Here we develop a new quantum brachistochrone method that can incorporate inequality constraints on the Hamiltonian. This method allows us to prove an exactly tight bound on the speed of QST on a subclass of Hamiltonians experimentally realizable by a fully-connected quantum computer.
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.
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.
Abstract We analytically investigate the role of entanglement in time-optimal state evolution as an application of the quantum brachistochrone, a general method for obtaining the optimal time-dependent Hamiltonian for reaching a target quantum state. As a model, we treat two qubits indirectly coupled through an intermediate qubit that is directly controllable, which represents a typical situation in quantum information processing. We find the time-optimal unitary evolution law and quantify residual entanglement by the two-tangle between the indirectly coupled qubits, for all possible sets of initial pure quantum states of a tripartite system. The integrals of the motion of the brachistochrone are determined by fixing the minimal time at which the residual entanglement is maximized. Entanglement plays a role for W and Greenberger–Horne–Zeilinger ( GHz ) initial quantum states, and for the bi-separable initial state in which the indirectly coupled qubits have a nonzero value of the 2-tangle.