28 research outputs found
Realization of universal nonadiabatic geometric control on decoherence-free qubits in the XY model
No full textA fundamental requirement of quantum information processing is the protection from the adverse effects of decoherence and noise. Decoherence-free subspaces and geometric processing are important steps of quantum information protection. Here, we provide a new experimentally feasible scheme to combine decoherence-free subspaces with nonadiabatic geometric manipulations to attain a universal quantum computation. The proposed scheme is different from previous proposals and is based on the typical XY interaction coupling, which can be set up in various nano-engineered systems and therefore open up for realization of nonadiabatic holonomic quantum computation in decoherence-free subspaces
Universal non-adiabatic geometric manipulation of pseudo-spin charge qubits
No full textReliable quantum information processing requires high-fidelity universal manipulation of quantum systems within the characteristic coherence times. Non-adiabatic holonomic quantum computation offers a promising approach to implement fast, universal, and robust quantum logic gates particularly useful in nano-fabricated solid-state architectures, which typically have short coherence times. Here, we propose an experimentally feasible scheme to realize high-speed universal geometric quantum gates in nano-engineered pseudo-spin charge qubits. We use a system of three coupled quantum dots containing a single electron, where two computational states of a double quantum dot charge qubit interact through an intermediate quantum dot. The additional degree of freedom introduced into the qubit makes it possible to create a geometric model system, which allows robust and efficient single-qubit rotations through careful control of the inter-dot tunneling parameters. We demonstrate that a capacitive coupling between two charge qubits permits a family of non-adiabatic holonomic controlled two-qubit entangling gates, and thus provides a promising procedure to maintain entanglement in charge qubits and a pathway toward fault-tolerant universal quantum computation. We estimate the feasibility of the proposed structure by analyzing the gate fidelities to some extent
Numerical solution of quantum Landau-Lifshitz-Gilbert equation
No full textThe classical Landau-Lifshitz-Gilbert (LLG) equation has long served as a cornerstone for modeling magnetization dynamics in magnetic systems, yet its classical nature limits its applicability to inherently quantum phenomena such as entanglement and nonlocal correlations. Inspired by the need to incorporate quantum effects into spin dynamics, recently a quantum generalization of the LLG equation is proposed [Phys. Rev. Lett. 133, 266704 (2024)] which captures essential quantum behavior in many-body systems. In this work, we develop a robust numerical methodology tailored to this quantum LLG framework that not only handles the complexity of quantum many-body systems but also preserves the intrinsic mathematical structures and physical properties dictated by the equation. We apply the proposed method to a class of quantum systems with a moderate number of spins that host host topological states of matter, and demonstrate rich quantum behavior, including the emergence of long-time entangled states. This approach opens a pathway toward reliable simulations of quantum magnetism beyond classical approximations, potentially leading to new discoveries.The authors contributed equally to this work</p
Non-Abelian geometric phases in a system of coupled quantum bits
No full textA common strategy to measure the Abelian geometric phase for a qubit is to let it evolve along an ‘orange slice’ shaped path connecting two antipodal points on the Bloch sphere by two different semi- great circles. Since the dynamical phases vanish for such paths, this allows for direct measurement of the geometric phase. Here, we generalize the orange slice setting to the non-Abelian case. The proposed method to measure the non-Abelian geometric phase can be implemented in a cyclic chain of four qubits with controllable interactions.</p
Entangling power of holonomic gates in atom-based systems
No full textEntanglement is one of the main resources of quantum computation, and entangling power of a quantum system is a crucial element in the universality and efficiency of a proposed architecture for realization of quantum processing. Our goal here is to study the entangling power of holonomic gates in some particular systems. We explore the holonomy-induced entanglement, by means of nonadiabatic quantum holonomies, through different types of interactions in atom-based systems, namely, the tripod-type interaction induced by the quantum Zeno effect between three-level atoms, as well as the Λ-type interaction arising from dipole–dipole or van der Waals forces between high-lying states of two-level atoms in systems consisting of N optically trapped identical atoms. Our analysis shows that although the two schemes provide completely separate classes of entangling gates, both schemes permit for full entangling power and also in the sense of quantum efficiency both families of entanglers consist of holonomic gates that have the same efficiency in quantum algorithms. Besides, we observe that holonomy-induced entanglement characteristics remarkably depend on the interaction configuration of the system.</p
Non-Abelian geometric phases in a system of coupled quantum bits
No full text10.1103/PhysRevA.89.022117Physical Review A - Atomic, Molecular, and Optical Physics892-PLRA
Conceptual aspects of geometric quantum computation
No full textGeometric quantum computation is the idea that geometric phases can be used to implement quantum gates, i.e., the basic elements of the Boolean network that forms a quantum computer. Although originally thought to be limited to adiabatic evolution, controlled by slowly changing parameters, this form of quantum computation can as well be realized at high speed by using nonadiabatic schemes. Recent advances in quantum gate technology have allowed for experimental demonstrations of different types of geometric gates in adiabatic and nonadiabatic evolution. Here, we address some conceptual issues that arise in the realizations of geometric gates. We examine the appearance of dynamical phases in quantum evolution and point out that not all dynamical phases need to be compensated for in geometric quantum computation. We delineate the relation between Abelian and non-Abelian geometric gates, and find an explicit physical example where the two types of gates coincide. We identify differencies and similarities between adiabatic and nonadiabatic realizations of quantum computation based on non-Abelian geometric phases. </p
Quantum Holonomy for Many-Body Systems and Quantum Computation
No full textThe research of this Ph. D. thesis is in the field of Quantum Computation and Quantum Information. A key problem in this field is the fragile nature of quantum states. This be comes increasingly acute when the number of quantum bits (qubits) grows in order to perform large quantum computations. It has been proposed that geometric (Berry) phases may be a useful tool to overcome this problem, because of the inherent robustness of such phases to random noise. In the thesis we investigate geometric phases and quantum holonomies (matrix-valued geometric phases) in many-body quantum systems, and elucidate the relationship between these phases and the quantum correlations present in the systems. An overall goal of the project is to assess the feasibility of using geometric phases and quantum holonomies to build robust quantum gates, and investigate their behavior when the size of a quantum system grows, thereby gaining insights into large-scale quantum computation. In a first project we study the Uhlmann holonomy of quantum states for hydrogen-like atoms. We try to get into a physical interpretation of this geometric concept by analyzing its relation with quantum correlations in the system, as well as by comparing it with different types of geometric phases such as the standard pure state geometric phase, Wilczek-Zee holonomy, Lévay geometric phase and mixed-state geometric phases. In a second project we establish a unifying connection between the geometric phase and the geometric measure of entanglement in a generic many-body system, which provides a universal approach to the study of quantum critical phenomena. This approach can be tested experimentally in an interferometry setup, where the geometric measure of entanglement yields the visibility of the interference fringes, whereas the geometric phase describes the phase shifts. In a third project we propose a scheme to implement universal non-adiabatic holonomic quantum gates, which can be realized in novel nano-engineered systems such as quantum dots, molecular magnets, optical lattices and topological insulators. In a fourth project we propose an experimentally feasible approach based on “orange slice” shaped paths to realize non- Abelian geometric phases, which can be used particularly for geometric manipulation of qubits. Finally, we provide a physical setting for realizing non-Abelian off-diagonal geometric phases. The proposed setting can be implemented in a cyclic chain of four qubits with controllable nearest-neighbor interactions. Our proposal seems to be within reach in various nano-engineered systems and therefore opens up for first experimental test of the non-Abelian off-diagonal geometric phase.</p
Temperature-anisotropy conjugate magnon squeezing in antiferromagnets
No full textQuantum squeezing is an essential asset in the field of quantum science and
technology. In this study, we investigate the impact of temperature and
anisotropy on squeezing of quantum fluctuations in two-mode magnon states
within uniaxial antiferromagnetic materials. Through our analysis, we discover
that the inherent nonlinearity in these bipartite magnon systems gives rise to
a conjugate magnon squeezing effect across all energy eigenbasis states, driven
by temperature and anisotropy. We show that temperature induces amplitude
squeezing, whereas anisotropy leads to phase squeezing. In addition, we observe
that the two-mode squeezing characteristic of magnon eigenenergy states is
associated with amplitude squeezing. This highlights the constructive impact of
temperature and the destructive impact of anisotropy on two-mode magnon
squeezing. Nonetheless, our analysis shows that the destructive effect of
anisotropy is bounded. We demonstrate this by showing that, at a given
temperature, the squeezing of the momentum (phase) quadrature (or equivalently,
the stretching of the position (amplitude) quadrature) approaches a constant
function of anisotropy after a finite value of anisotropy. Moreover, our study
demonstrates that higher magnon squeeze factors can be achieved at higher
temperatures, smaller levels of anisotropy, and closer to the Brillouin zone
center. All these characteristics are specific to low-energy magnons in the
uniaxial antiferromagnetic materials that we examine here
