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New Journal of Physics

Inverse engineering for robust state transport along a spin chain via low-energy subspaces

Yunlan Ji, Ze Wu, Ran Liu, Yuchen Li, Fangzhou Jin, Hui Zhou, Xinhua Peng

Published Jan 1, 2024• 6 citations
Publisher

Abstract

Abstract Quantum state transfer (QST) plays a central role in the field of quantum computation and communication, but its quality will be deteriorated by the ubiquitous variations and noise in quantum systems. Here we propose robust and nonadiabatic protocols for transmitting quantum state across a strongly coupled spin chain, especially in the presence of unwanted disorders in the couplings. To this end, we approximately map the low-energy subspaces of the odd-size Heisenberg chain to a two-level system, and derive the sensitivity of the final fidelity with respect to systematic deviations or time-varying fluctuations. Subsequently, leveraging the flexibility of the inverse-engineering technique, we optimize the state-transfer robustness concerning these perturbations individually. The resulting schemes allow for more stable QST than the original accelerated schemes and only require manipulating the two boundary couplings instead of the whole system, which open up the possibility of fast and robust information transfer in spin-based quantum systems.

DOI
10.1088/1367-2630/ad19fd

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Abstract Quantum state transfer (QST) plays a central role in the field of quantum computation and communication, but its quality will be deteriorated by the ubiquitous variations and noise in quantum systems. Here we propose robust and nonadiabatic protocols for transmitting quantum state across a strongly coupled spin chain, especially in the presence of unwanted disorders in the couplings. To this end, we approximately map the low-energy subspaces of the odd-size Heisenberg chain to a two-level system, and derive the sensitivity of the final fidelity with respect to systematic deviations or time-varying fluctuations. Subsequently, leveraging the flexibility of the inverse-engineering technique, we optimize the state-transfer robustness concerning these perturbations individually. The resulting schemes allow for more stable QST than the original accelerated schemes and only require manipulating the two boundary couplings instead of the whole system, which open up the possibility of fast and robust information transfer in spin-based quantum systems.
We present a couple of counterdiabatic (CD) schemes for a rapid and high-fidelity transfer of quantum state across a one-dimensional spin chain, between two weakly coupled external qubits at each end. Employing the effective low-energy Hamiltonian of the system, we first construct the optimal CD terms based on the variational principle and then put forward two experimentally feasible shortcuts, which only need to manipulate couplings between the external qubits and chain. Compared to traditional adiabatic protocol, the resulting schemes allow a drastic increase in state-transfer fidelity in a short time. Furthermore, numerical simulation demonstrates that our speed-up protocols hold robustness against the imperfections of control fields and evolution time. The proposed schemes may be applicable to fast quantum-information transport in various spin-based physical systems.
We study quantum-state transfer (QST) through a strongly coupled antiferromagnetic spin chain (acting as a spin bus), between weakly coupled external qubits. By treating the weak coupling as a perturbation, we find that QST is enabled specifically by the second-order terms in the perturbative expansion. We show that QST is robust against disorder in the couplings, either within the bus or to the external qubits. We find that the protocol works when the qubits are attached to any node on an even-size bus or to the antiferromagnetic nodes on an odd-size bus. The optimal time for QST is found to depend nonmonotonically on qubit separation.
Quantum state transfer in the presence of static disorder and noise is one of the main challenges in building quantum computers. We compare the quantum state transfer properties for two classes of qubit chains under the influence of static disorder. In fully engineered chains all nearest-neighbor couplings are tuned in such a way that a single-qubit state can be transferred perfectly between the ends of the chain, while in chains with modified boundaries only the two couplings between the transmitting and receiving qubits and the remainder of the chain can be optimized. We study how the disorder in the couplings affects the state transfer fidelity depending on the disorder model and strength as well as the chain type and length. We show that the desired level of fidelity and transfer time are important factors in designing a chain. In particular we demonstrate that transfer efficiency comparable or better than that of the most robust engineered systems can also be reached in chains with modified boundaries without the demanding engineering of a large number of couplings.
Abstract Quantum state transfer (QST) is a fundamental requirement for scalable quantum computation, where fast and reliable communication between distant subsystems is essential. In this work, we present a protocol for QST in linear Ising chains. 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.
The transmission of quantum states through spin chains is an important element in the implementation of quantum information technologies. Speed and fidelity of transfer are the main objectives which have to be achieved by the devices even in the presence of imperfections which are unavoidable in any manufacturing process. To reach these goals, several kinds of spin chains have been suggested, which differ in the degree of fine-tuning, or engineering, of the system parameters. In this work we present a systematic study of two important classes of such chains. In one class only the spin couplings at the ends of the chain have to be adjusted to a value different from the bulk coupling constant, while in the other class every coupling has to have a specific value. We demonstrate that configurations from the two different classes may perform similarly when subjected to the same kind of disorder in spite of the large difference in the engineering effort necessary to prepare the system. We identify the system features responsible for these similarities and we perform a detailed study of the transfer fidelity as a function of chain length and disorder strength, yielding empirical scaling laws for the fidelity which are similar for all kinds of chain and all disorder models. These results are helpful in identifying the optimal spin chain for a given quantum information transfer task. In particular, they help in judging whether it is worthwhile to engineer all couplings in the chain as compared to adjusting only the boundary couplings.
Shortening the operation time of implementing scheme and reducing the influence of harmful factors have always been the research objectives pursued by people. Based on invariant-based reverse engineering, we present a general scheme for implementing robust population transfer in a three-level system via optimal shortcut to adiabatic passage. The systematic error sensitivity is introduced to measure the robustness of the process. The smooth Rabi frequencies are expressed with some coefficients, which are also related to the systematic error sensitivity and the population of intermediate state. When the amplitude of control field is given, the transfer can be optimized within as small systematic error sensitivity as possible, i.e., the robustness against systematic errors is further improved by choosing suitable correlation coefficient. Additionally, we apply the technique to achieve robust excitation fluctuation transfer between two membranes in an optomechanical system. The relation between the fidelity of excitation fluctuation transfer and variation of effective optomechanical coupling strengths is analysed. Numerical result shows that the fidelity keeps over 0.95 even if the coupling strengths deviates from 20% of the theoretical value. Moreover, comparison with existing literature [Opt. Express29, 7998 (2021)10.1364/OE.417343], the proposed scheme possesses stronger robustness against variations of effective optomechanical coupling strengths and lower population of unwanted states. The idea may provide a promising approach for quantum information processing.