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arXiv:2308.07515 · Materials Today Quantum

Universal quantum computing based on magnetic domain-wall qubits

Shuang Li, Xichao Zhang, Motohiko Ezawa, Yan Zhou

Published Apr 4, 2024• 5 citations
arXivHTMLPDF

Abstract

Quantum computers allow to solve efficiently certain problems that are intractable for classical computers. For the realization of a quantum computer, a qubit design as the basic building block is a nontrivial starting point. Within a nanoscale ferromagnetic domain wall stabilized by achiral energy, two degenerate chirality forms exist which can be regarded as the two qubit states. Our numerical demonstration shows that the manipulation of spin configurations of the ferromagnetic domain walls is governed by magnetic and electric fields for single-qubit quantum gates, while the Ising exchange coupling facilitates the two-qubit gates. The incorporation of these quantum gates permits universal quantum computation. Furthermore, we discuss the estimation of the coherence time, as well as the initialization and readout of the qubits. Our findings show a practical implementation of quantum computing architectures based on the domain-wall qubits in ferromagnetic materials.

DOI
10.1016/j.mtquan.2024.100005

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Quantum computers allow to solve efficiently certain problems that are intractable for classical computers. For the realization of a quantum computer, a qubit design as the basic building block is a nontrivial starting point. Within a nanoscale ferromagnetic domain wall stabilized by achiral energy, two degenerate chirality forms exist which can be regarded as the two qubit states. Our numerical demonstration shows that the manipulation of spin configurations of the ferromagnetic domain walls is governed by magnetic and electric fields for single-qubit quantum gates, while the Ising exchange coupling facilitates the two-qubit gates. The incorporation of these quantum gates permits universal quantum computation. Furthermore, we discuss the estimation of the coherence time, as well as the initialization and readout of the qubits. Our findings show a practical implementation of quantum computing architectures based on the domain-wall qubits in ferromagnetic materials.
Domain walls (DWs) on magnetic racetracks are at the core of the field of spintronics, providing a basic element for classical information processing. Here, we show that mobile DWs also provide a blueprint for large-scale quantum computers. Remarkably, these DW qubits showcase exceptional versatility, serving not only as stationary qubits, but also performing the role of solid-state flying qubits that can be shuttled in an ultrafast way. We estimate that the DW qubits are long-lived because they can be operated at sweet spots to reduce potential noise sources. Single-qubit gates are implemented by moving the DW, and two-qubit entangling gates exploit naturally emerging interactions between different DWs. These gates, sufficient for universal quantum computing, are fully compatible with current state-of-the-art experiments on racetrack memories. Further, we discuss possible strategies for qubit readout and initialization, paving the way toward future quantum computers based on mobile topological textures on magnetic racetracks.
Magnetic domain walls have long been pursued as carriers of classical information for storage and processing. With the ability to create, control, and probe domain walls at the nanoscale, they are recently recognized as an ideal platform for studying macroscopic quantum effects and provide a natural blueprint for building scalable quantum computing architectures. In particular, the experimentally demonstrated high mobility of domain walls makes them not only suitable as stationary qubits but also as flying qubits, which may offer advantages over currently explored quantum computing platforms. In this Perspective, we outline our current understanding of the essential ingredients and key requirements for realizing universal quantum computation based on magnetic domain walls. We highlight promising concrete material platforms and identify the experiments that are still needed to advance this concept. We also discuss the potential challenges and point to new opportunities in this emerging research direction at the interface between magnetism and quantum information science.
Nanoscale topological spin textures in magnetic systems are emerging as promising candidates for scalable quantum architectures. Despite their potential as qubits, previous studies have been limited to semiclassical approaches, leaving a critical gap: the lack of a fully quantum demonstration. Here, we address this challenge by employing the density matrix renormalization group (DMRG) method to establish domain wall (DW) qubits in coupled quantum spin-1/2 chains. We calculate the ground-state energies and excitation gaps of the system and find that DWs with opposite chiralities form a well-defined low-energy sector, distinctly isolated from higher excited states in the presence of anisotropies. This renders the chirality states suitable for encoding quantum information, serving as robust qubits. Interestingly, when a magnetic field is applied, we observe tunneling between quantum DW states with opposite chiralities. Through quantum simulations, we construct an effective qubit Hamiltonian that exhibits strongly anisotropic ggg factors, offering a way to implement single-qubit gates. Furthermore, we obtain an effective interacting Hamiltonian for two mobile DWs in coupled quantum spin chains from DMRG simulations, enabling the implementation of two-qubit gates. Single-qubit and two-qubit gates are also demonstrated in real-time simulations using the time-dependent variational principle. Our work represents a critical step from semiclassical constructions to a fully quantum demonstration of the potential of DW textures for scalable quantum computing, establishing a solid foundation for future quantum architectures based on topological magnetic textures.
We study the low energy states of finite spin chains with isotropic (Heisenberg) and anisotropic (XY and Ising-like) antiferromagnetic exchange interaction with uniform and nonuniform coupling constants. We show that for an odd number of sites a spin cluster qubit can be defined in terms of the ground state doublet. This qubit is remarkably insensitive to the placement and coupling anisotropy of spins within the cluster. One- and two-qubit quantum gates can be generated by magnetic fields and intercluster exchange, and leakage during quantum gate operation is small. Spin cluster qubits inherit the long decoherence times and short gate operation times of single spins. Control of single spins is hence not necessary for the realization of universal quantum gates.
We show that a wide range of spin clusters with antiferromagnetic intracluster exchange interaction allows one to define a qubit. For these spin cluster qubits, initialization, quantum gate operation, and readout are possible using the same techniques as for single spins. Quantum gate operation for the spin cluster qubit does not require control over the intracluster exchange interaction. Electric and magnetic fields necessary to effect quantum gates need only be controlled on the length scale of the spin cluster rather than the scale for a single spin. Here, we calculate the energy gap separating the logical qubit states from the next excited state and the matrix elements which determine quantum gate operation times. We discuss spin cluster qubits formed by one- and two-dimensional arrays of s=1/2s=1/2s=1/2 spins as well as clusters formed by spins s>1/2.s>1/2.s>1/2. We illustrate the advantages of spin cluster qubits for various suggested implementations of spin qubits and analyze the scaling of decoherence time with spin cluster size.
Quantum computation is a promising emerging technology, and by utilizing the principles of quantum mechanics, it is expected to achieve faster computations than classical computers for specific problems. There are two distinct architectures for quantum computation: gate-based quantum computers and quantum annealing. In gate-based quantum computation, we implement a sequence of quantum gates that manipulate qubits. This approach allows us to perform universal quantum computation, yet they pose significant experimental challenges for large-scale integration. On the other hand, with quantum annealing, the solution of the optimization problem can be obtained by preparing the ground state. Conventional quantum annealing devices with transverse-field Ising Hamiltonian, such as those manufactured by D-Wave Inc., achieving around 5000 qubits, are relatively more amenable to large-scale integration but are limited to specific computations. In this paper, we present a practical method for implementing universal quantum computation within the conventional quantum annealing architecture using the transverse-field Ising Hamiltonian. Our innovative approach relies on an adiabatic transformation of the Hamiltonian, changing from transverse fields to a ferromagnetic interaction regime, where the ground states become degenerate. Notably, our proposal is compatible with D-Wave devices, opening up possibilities for realizing large-scale gate-based quantum computers. This research bridges the gap between conventional quantum annealing and gate-based quantum computation, offering a promising path toward the development of scalable quantum computing platforms.