We present an information geometric analysis of off-resonance effects on classes of exactly solvable generalized semi-classical Rabi systems. Specifically, we consider population transfer performed by four distinct off-resonant driving schemes specified by su(2; C) time-dependent Hamiltonian models. For each scheme, we study the consequences of a departure from the on-resonance condition in terms of both geodesic paths and geodesic speeds on the corresponding manifold of transition probability vectors. In particular, we analyze the robustness of each driving scheme against off-resonance effects. Moreover, we report on a possible tradeoff between speed and robustness in the driving schemes being investigated. Finally, we discuss the emergence of a different relative ranking in terms of performance among the various driving schemes when transitioning from on-resonant to off-resonant scenarios.
Effective Hamiltonians are often used in quantum physics, both in time dependent and time independent contexts. Analogies are drawn between the two usages, the discussion framed particularly for the geometric phase of a time-dependent Hamiltonian and for resonances as stationary states of a time-independent Hamiltonian.
We interpret quantum computing as a geometric evolution process by reformulating finite quantum systems via Connes' noncommutative geometry. In this formulation, quantum states are represented as noncommutative connections, while gauge transformations on the connections play a role of unitary quantum operations. Thereby, a geometrical model for quantum computation is presented, which is equivalent to the quantum circuit model. This result shows a geometric way of realizing quantum computing and as such, provides an alternative proposal of building a quantum computer.
Strong, fast pulses, called ``bang-bang'' controls can be used to eliminate the effects of system-environment interactions. This method for preventing errors in quantum information processors is treated here in a geometric setting which leads to an intuitive perspective. Using this geometric description, we clarify the notion of group symmetrization as an averaging technique, and provide a geometric picture for evaluating errors due to imperfect bang-bang controls. This will provide additional support for the usefulness of such controls as a means for providing more reliable quantum informatio…
Geometric quantum gates are performed by using the geometric phase, making them particularly robust to the pulse amplitude error due to the intrinsic global property. However, in many systems, such as the silicon-based spin qubits, the off-resonance error is the dominant noise, which can cause dephasing and is always difficult to deal with for a geometric gate. Thus how to deal with the off-resonance error is very significant for the application of the geometric gates. A recent work in \emph{Phy. Rev. Appl. 16, 044005 (2021)} reveals that by inserting two $π$-pulse dynamically corrected sequen…
We follow a generalized kinematic approach to compute the geometric phases acquired in both unitary and dissipative Jaynes-Cummings models, which provide a fully quantum description for a two-level system interacting with a single mode of the (cavity) electromagnetic field, in a perfect or dissipative cavity respectively. In the dissipative model, the non-unitary effects arise from the outflow of photons through the cavity walls and the incoherent pumping of the two-level system. Our approach allows to compare the geometric phases acquired in these models, leading to an exhaustive characteriza…
We provide a class of Bell diagonal entanglement witnesses displaying an additional local symmetry -- a maximal commutative subgroup of the unitary group U(n). Remarkably, this class of witnesses is parameterized by a torus being a maximal commutative subgroup of an orthogonal group SO(n-1). It is shown that a generic element from the class defines an indecomposable entanglement witness. The paper provides a geometric perspective for some aspects of the entanglement theory and an interesting interplay between group theory and block-positive operators.
We investigate the effects of counterrotating terms on geometric phase and its relation to the resonance of the Rabi model. We apply the unitary transformation with a single parameter to the Rabi model and obtain the transformed Hamiltonian involving multiple harmonic terms. By combining the counter-rotating-hybridized rotating-wave method with time-dependent perturbation theory, we solve systematically time evolution operator and then obtain the geometric phase of the two-level system. Our results are beyond adiabatic approximation and rotating-wave approximation (RWA). Higher-order harmonic …
In the radiation field of an optical waveguide, the Rayleigh scattering of photons is shown to result in a strongly velocity-dependent force on atoms. The pump field, which is injected in the fundamental branch of the waveguide, is favorably scattered by a moving atom into one of the transversely excited branches of propagating modes. All fields involved are far detuned from any resonances of the atom. For a simple polarizable particle, a linear friction force coefficient comparable to that of cavity cooling can be achieved.
Exploiting the notion of measurement-induced nonlocality [Phys.Rev. Lett. 106, 120401 (2011)], we introduce a new measure to quantify the nonbilocal correlation. We establish a simple relation between the nonlocal and nonbilocal measures for the arbitrary pure input states. Considering the mixed states as inputs, we derive two upper bounds of affinity-based nonbilocal measure. Finally, we have studied the nonbilocality of a different combinations of input states.
High-fidelity quantum operations are a key requirement for fault-tolerant quantum information processing. In electron spin resonance, manipulation of the quantum spin is usually achieved with time-dependent microwave fields. In contrast to the conventional dynamic approach, adiabatic geometric phase operations are expected to be less sensitive to certain kinds of noise and field inhomogeneities. Here, we investigate such phase gates applied to electron spins both through simulations and experiments, showing that the adiabatic geometric phase gate is indeed inherently robust against inhomogenei…
In a previous paper it has been shown that the interference of the first and second order pole of the Green's function at an exceptional point, as well as the interference of the first order poles in the vicinity of the exceptional point, gives rise to asymmetric scattering cross section profiles. In the present paper we demonstrate that these line profiles are indeed well described by the Beutler-Fano formula, and thus are genuine Fano resonances. Also further away from the exceptional points excellent agreement can be found by introducing energy dependent Fano parameters.
Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled logic gates by controlled dynamics of qubits. In controlled dynamics, one qubit undergoes coherent evolution and acquires appropriate phase, depending on the state of other qubits. If the evolution is geometric, then the phase acquired depend only on the geometry of the path executed, and is robust against certain types of errors. This phenomenon leads to an inh…
Calibrating the Role of Entanglement in Variational Quantum Algorithms from a Geometric Perspective
School of Physics, Beihang University（北京航空航天大学物理学院）；School of Applied Science, Beijing Information Science and Technology University（北京信息科技大学应用科学学院）；Shenzhen Institute of Beihang University（北京航空航天大学深圳研究院）；School of Future Technology, Henan University（河南大学未来技术学院）；School of Instrument Science and Opto-Electronics Engineering, Beijing Information Science and Technology University（北京信息科技大学仪器科学与光电工程学院）
A new aspect of understanding a Fano absorption spectrum is presented in terms of the complex spectral analysis. The absorption spectrum of an impurity embedded in semi-infinite superlattice is investigated. The boundary condition on the continuum causes a large energy dependence of the self-energy, enhances the nonlinearity of the eigenvalue problem of the effective Hamiltonian, yielding several nonanalytic resonance states. The overall spectral features is perfectly reproduced by the direct transitions to these discrete resonance states. Even with a single optical transition path the spectru…
The classical combinatorial problem of $36$ officers has no solution, as there are no Graeco-Latin squares of order six. The situation changes if one works in a quantum setup and allows for superpositions of classical objects and admits entangled states. We analyze the recently found solution to the quantum version of the Euler's problem from a geometric point of view. The notion of a non-displaceable manifold embedded in a larger space is recalled. This property implies that any two copies of such a manifold, like two great circles on a sphere, do intersect. Existence of a quantum Graeco-Lati…
The objective of this article is to introduce the tools to analyze the contrast imaging problem in Nuclear Magnetic Resonance. Optimal trajectories can be selected among extremal solutions of the Pontryagin Maximum Principle applied to this Mayer type optimal problem. Such trajectories are associated to the question of extremizing the transfer time. Hence the optimal problem is reduced to the analysis of the Hamiltonian dynamics related to singular extremals and their optimality status. This is illustrated by using the examples of cerebrospinal fluid / water and grey / white matter of cerebrum…
We describe a design to implement a two-qubit geometric phase gate, by which a pair of electrons confined in adjacent quantum dots are entangled. The entanglement is a result of the Coulomb exchange interaction between the optically excited exciton-polaritons and the localized spins. This optical coupling, resembling the electron-electron Ruderman-Kittel-Kasuya-Yosida (RKKY) inter- actions, offers high speed, high fidelity two-qubit gate operation with moderate cavity quality factor Q. The errors due to the finite lifetime of the polaritons can be minimized by optimizing the optical pulse para…
Geometric phase from encircling an exceptional point of a quantum resonance in the complex-scaling method
Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所跨学科理论与数学科学中心）；Department of Physics, Kyushu University（九州大学物理系）
We present a gravitational quantum dynamics theory that combines quantum field theory for particle dynamics in space-time with classical Einstein's general relativity in a non-Riemannian Finsler space. This approach is based on the geometrization of quantum mechanics proposed in ref. [1] and combines quantum and gravitational effects into a global curvature of the Finsler space induced by the quantum potential associated to the matter quantum fields. In order to make this theory compatible with general relativity, the quantum effects are described in the framework of quantum field theory, wher…
Quantum metrology holds the promise of an early practical application of quantum technologies, in which measurements of physical quantities can be made with much greater precision than what is achievable with classical technologies. In this review, we collect some of the key theoretical results in quantum parameter estimation by presenting the theory for the quantum estimation of a single parameter, multiple parameters, and optical estimation using Gaussian states. We give an overview of results in areas of current research interest, such as Bayesian quantum estimation, noisy quantum metrology…
