A quantum state transfer protocol with Ising Hamiltonians

TL;DR

This work tackles the problem of robust quantum state transfer (QST) in analog quantum devices with Ising-like hardware. It introduces domain-wall encoding to map a Heisenberg-like transport problem onto a ZZ-dominated Ising dynamics, enabling a two-step transfer protocol that includes a transport phase and a disentangling reset. Numerically, the authors demonstrate high fidelities (up to about $0.99$) for 1–3 qubits and analyze the dominant $|J|^{-2}$ error scaling arising from the domain-wall approximation, showing how parameter rescaling can mitigate this at the cost of longer runtimes. The protocol is positioned as a practical route for QST on platforms such as superconducting flux qubits and as a stepping stone toward experimental demonstrations and potential quantum repeater schemes.

Abstract

Quantum state transfer is a fundamental requirement for scalable quantum computation, where fast and reliable communication between distant spins is essential. In this work, we present a protocol for quantum state transfer in linear spin chains tailored to superconducting flux qubits. Starting from a perfect state transfer scheme via a Heisenberg Hamiltonian with inhomogeneous couplings, we adapt it for architectures implementing the transverse-field Ising model by encoding the information in domain walls. The resulting linear Ising chain makes quantum transport experiments accessible to many platforms for analog quantum simulation. We test the protocol for 1-, 2-, and 3- spin states, obtaining high transfer fidelities of up to 0.99 and study the accuracy dependence on the domain wall approximation. These results are the first step in paving the way for an experimental implementation of the protocol.

Figures (7)

• Figure 1: Schematic representation of the initial state (a) that evolves under $H_G$ Eq. \ref{['eq:hamiltonian_standard']} into the final state (b) of the transport process of $\ket{\psi} = \alpha\ket{1} + \beta\ket{0}$ along an example chain of 5 spins.
• Figure 2: Figures (a, b) describe a spin transport using the standard spin-chain system Eq. \ref{['eq:hamiltonian_standard']}. (a) Fidelity between the state at time $t$ and the final expected state $\ket{0...01}$, for $N=13$, and initial state $\ket{10...0}$. It reaches the maximum of 1 after a finite time $\tau$. (b) Evolution of z-component of each spin. The $-1$ value corresponds to the spin in the $\ket{1}$ state, and the $+1$ to the state $\ket{0}$. We can observe the swap of the initial and final spins after time $\tau$. Figures (c, d) describe the same transport, but using the domain wall encoding and the two-step protocol. (c) Fidelity between the state at time $t$ and the final expected state $\ket{0...01}$, for $N=13$, $J=0.5$ GHz, $\lambda = 22.72$ MHz, and initial state $\ket{10...0}$. (d) Evolution of z-component of each spin of the domain-wall system. We can observe the intial domain wall travelling to the other end of the chain after time $\tau$. However, there is now another domain wall traversing the chain from time $\tau$ to $2\tau$, due to the required reset of the chain.
• Figure 3: Domain wall representation of the initial state $\ket{100000}$ (a) and final state $\ket{000001}$ (b) evolving under the Hamiltonian from Eq. \ref{['eq:Hamiltonian_domain_wall_1']}. Initially, the domain wall is located between the first physical spin and the virtual, fixed spin. After the evolution, it has moved to the last physical and the virtual fixed spin at the other end of the chain.
• Figure 4: (a) Domain wall representation of the state from Eq. \ref{['eq:Hamiltonian_domain_wall_2']} under the domain wall Hamiltonian with only one virtual spin and no transverse field in the first physical spin; (b) Change of Hamiltonian after the transport has been comlpeted, where the virtual spin is switched to the first spin and the transverse field is removed from the last spin. The relative phase between the states is also included; (c) End result of the transport after the Hamiltonian switch, including the relative phase between the states $\ket{1}$ and $\ket{0}$. The physical spins are numbered 1-5, while the the fixed virtual spins are colored black.
• Figure 5: Example of an initial chain for the transfer of the logical state $\ket{001}$. The blue sections left and right are Alice and Bob's registers respectively, and the red section is the length of the wire. The different stages of the protocol are shown with the changes in the virtual spins and the results of time evolution. The gray spin at the right represents a field that is turned off, but is still used to determine the value of the last logical spin we measure ($\ket{0}$ if the last physical spin is down and $\ket{1}$ if it is up).