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arXiv:2112.05223 · Journal of Physics Communications

Electronic control and switching of entangled spin state using anisotropy and exchange in the three-particle paradigm

Eric D. Switzer, X.-G. Zhang, Talat Shahnaz Rahman

Published Jul 1, 2022• 5 citations
arXivHTMLPDF

Abstract

Abstract We explore the control and switching of the entangled spin states of multi-spin particle qubit coupled to an electron using a three-particle spin model described by S i (i = 1, 2, 3), in which S 1 = 1 2 is an electron and S 2,3 can have any spin with both exchange coupling and magnetic anisotropy. We derive a general formula for the existence of a switching (DJ) resonance for any spin S 2,3. We further contrast the entanglement switching mechanisms for the S 2,3 = 1 2 and S 2,3 = 1 spin models. We find that while the onsite magnetic anisotropy in the case of S 2,3 > 1 2 allows full control of their spin states via interaction with S 1, in order to achieve acceptable control of a Bloch vector within the S 2,3 = 1 2 model, additional mechanisms, such as anisotropic exchange coupling, are required.

DOI
10.1088/2399-6528/ac7e1d

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Abstract We explore the control and switching of the entangled spin states of multi-spin particle qubit coupled to an electron using a three-particle spin model described by S i (i = 1, 2, 3), in which S 1 = 1 2 is an electron and S 2,3 can have any spin with both exchange coupling and magnetic anisotropy. We derive a general formula for the existence of a switching (DJ) resonance for any spin S 2,3. We further contrast the entanglement switching mechanisms for the S 2,3 = 1 2 and S 2,3 = 1 spin models. We find that while the onsite magnetic anisotropy in the case of S 2,3 > 1 2 allows full control of their spin states via interaction with S 1, in order to achieve acceptable control of a Bloch vector within the S 2,3 = 1 2 model, additional mechanisms, such as anisotropic exchange coupling, are required.
We explore the three-particle spin model of an S1=12{S}_{1}=\frac{1}{2}S1​=21​ particle (e.g., an electron) interacting with two spin-coupled S2,3{S}_{\text{2,3}}S2,3​ particles with exchange coupling and magnetic anisotropy. We show that in the case of S2,3=1{S}_{2,3}=1S2,3​=1 particles, the coupled particle entanglement states can be prepared, controlled, and read by the S1{S}_{1}S1​ particle. We also find that for particular resonance conditions of the magnetic anisotropy strength DDD and exchange coupling strength JJJ, the entanglement state-switching behavior is maximized and is robust against a range of anisotropic application of the exchange coupling.
Pairwise exchange couplings have long been the standard mechanism for entangling spin qubits in semiconductor systems. However, implementing quantum circuits based on pairwise exchange gates often requires a lengthy sequence of elementary gate operations. In this work, we present an alternative approach: multi-qubit entangling gate operations that simultaneously drive the exchange couplings between multiple pairs of spin qubits. We explore three spin qubit systems in linear or triangular configurations. We derive analytical expressions for these multi-exchange entangling operations and demonstrate how to use the resulting three-qubit gates to construct quantum circuits capable of generating standard entangled states such as GHZ and W states, and the Toffoli gate, by optimizing control parameters. Our results show that this multi-qubit strategy significantly reduces the number of required operations, offering a pathway to more efficient, shallower, and more coherent circuits for spin-qubit processors.
Electrical control of single spin qubits is a major frontier for nanoscale, high-speed, and scalable quantum devices. Yet, extending it to highly shielded rare-earth 4f electrons remains an experimental challenge across solid-state platforms. Here we demonstrate all-electrical coherent control of a single Er electron spin, which is exchange-coupled to a nearby Ti atom. Scanning tunneling microscopy-based electron spin resonance with three-dimensional magnetic-field control enables comprehensive mapping of the resonance and Rabi frequencies, revealing pronounced anisotropies in both the Er g-tensor and the Er-Ti exchange interaction. The electrical modulation of the anisotropic Er-Ti coupling results in an efficient drive of the Er spin, allowing us to achieve near-gigahertz Rabi frequencies - a ten-fold improvement over the present record for rare-earth spin qubits. By establishing anisotropic exchange as a general resource for electrically accessing shielded rare-earth spins, our results open a new route to ultrafast and local control of rare-earth spins in solid-state quantum devices.
In the last years, the electron spin in quantum dots has become a most promising candidate for the realization of qubits, the basic element for quantum computation. In quantum dot spin qubits the exchange interaction implements a fundamental two qubit gate, which originates in the Coulomb interaction and the Pauli principle. Compared to single qubit gates, the exchange based gates are much faster and easier to control locally, motivating the solely exchange energy based quantum computation. The control is based on the exponential sensitivity of the exchange energy on the interparticle distance. Manipulation then can proceed, for example, shifting the single particle states electrically or compressing them magnetically. The practical manipulation schemes require quantitative knowledge of the exchange energy. The spin-orbit interaction plays an important role in this nano-system. Indeed the usual exchange interaction changes its magnitude, while a new term, called anisotropic exchange, appears. In this thesis we propose an accurate effective spin Hamiltonian for modeling spin-orbit-induced spin dynamics in the presence of the magnetic field. We have also performed numerically exact calculations of the isotropic and anisotropic exchange coupling in realistic two-electron GaAs coupled quantum dots in the presence of both Dresselhaus and Bychkov-Rashba spin-orbit interactions. The numerics allow us to establish the goodness of our model and to see the limits of previous statements. Furthermore we find that in zero magnetic field the second-order spin-orbit effects are absent at all interdot couplings.
A two-electron system confined in two coupled semiconductor quantum dots is investigated as a candidate for performing quantum logic operations with spin qubits. We study different processes of swapping the electron spins by a controlled switching on and off of the exchange interaction. The resulting spin swap corresponds to an elementary operation in quantum-information processing. We perform direct simulations of the time evolution of the two-electron system. Our results show that, in order to obtain the full interchange of spins, the exchange interaction should change smoothly in time. The presence of jumps and spikes in the time characteristics of the confinement potential leads to a considerable increase of the spin-swap time. We propose several mechanisms to modify the exchange interaction by changing the confinement potential profile and discuss their advantages and disadvantages.
The exchange coupling between quantum dot spin qubits is isotropic, which restricts the types of quantum gates that can be formed. Here, we propose a method for controlling anisotropic interactions between spins arranged in a bus geometry. The symmetry is broken by an external magnetic field, resulting in XXZ-type interactions that can efficiently generate maximally entangled Greenberger-Horne-Zeilinger states or universal gate sets for exchange-only quantum computing. We exploit the XXZ couplings to propose a qubit scheme, based on double dots.