Problems In Quantum Physics Research Articles

Towards the ultimate precision limits: An introduction to quantum metrology / Vers les limites ultimes de précision : une introduction à la métrologie quantique

These lectures will focus on quantum metrology, which aims to determine the ultimate precision limits in the estimation of parameters. It also helps to understand some basic problems in quantum physics, like for instance the energy-time uncertainty and its extension to noisy systems. Applications to several systems will be discussed, including phase estimation in optical interferometers, frequency estimation in atomic spectroscopy, force estimation, weak-value amplification, and the quantum s...

One-Shot Coherence Dilution

Manipulation and quantification of quantum resources are fundamental problems in quantum physics. In the asymptotic limit, coherence distillation and dilution have been proposed by manipulating infinite identical copies of states. In the nonasymptotic setting, finite data-size effects emerge, and the practically relevant problem of coherence manipulation using finite resources has been left open. This Letter establishes the one-shot theory of coherence dilution, which involves converting maximally coherent states into an arbitrary quantum state using maximally incoherent operations, dephasing-covariant incoherent operations, incoherent operations, or strictly incoherent operations. We introduce several coherence monotones with concrete operational interpretations that estimate the one-shot coherence cost-the minimum amount of maximally coherent states needed for faithful coherence dilution. Furthermore, we derive the asymptotic coherence dilution results with maximally incoherent operations, incoherent operations, and strictly incoherent operations as special cases. Our result can be applied in the analyses of quantum information processing tasks that exploit coherence as resources, such as quantum key distribution and random number generation.

Disentanglement via Entanglement: A Unified Method for Wannier Localization

The Wannier localization problem in quantum physics is mathematically analogous to finding a localized representation of a subspace corresponding to a nonlinear eigenvalue problem. While Wannier localization is well understood for insulating materials with isolated eigenvalues, less is known for metallic systems with entangled eigenvalues. Currently, the most widely used method for treating systems with entangled eigenvalues is to first obtain a reduced subspace (often referred to as disentanglement) and then to solve the Wannier localization problem by treating the reduced subspace as an isolated system. This is a multiobjective nonconvex optimization procedure, and its solution can depend sensitively on the initial guess. We propose a new method to solve the Wannier localization problem, avoiding the explicit use of an optimization procedure. Our method is robust and efficient, relies on few tunable parameters, and provides a unified framework for addressing problems with isolated and entangled eigenvalues.

Theoretical Perspectives of Spin Dynamics in Solid-State Nuclear Magnetic Resonance and Physics

Since the first demonstrations of nuclear magnetic resonance (NMR) in condensed matter in 1946, the field of NMR has yielded a continuous flow of conceptual advances and methodological innovations that continues today. Much progress has been made in the utilization of solid-state NMR to illuminate molecular structure and dynamics in systems not controllable by any other way. NMR deals with time-dependent perturbations of nuclear spin systems and solving the time-dependent Schrodinger equation is a central problem in quantum physics in general and solid-state NMR in particular. This theoretical perspective outlines the methods used to treat theoretical problems in solid-state NMR as well as the recent theoretical development of spin dynamics in NMR and physics. The purpose of this review is to unravel the versatility of theories in solid-state NMR and to present the recent theoretical developments of spin dynamics.

Wrong Potential Energy Term in Schrödinger’s Equation for Hydrogen Atom

Even after nine decades of successful run of the Quantum Mechanics (QM), different viewpoints on foundational problems of Quantum Physics are still being actively debated. That is because mathematical logic of QM often defies the physical intuition which constitutes the main spirit of Physics. De Broglie’s hypothesis of matter waves implied that the dynamic characteristics of a micro particle in motion, can be ascribed to the wave characteristics of the wavelet accompanying the particle. The Schrodinger equation models the matter-wave interactions through wavefunction ψ and effectively serves as the foundation of QM. Even though mathematical structure of the Schrodinger equation is sound and elegant, here we show a conceptual mistake in the development of this equation wherein the physical situation has not been correctly modeled in the equation. The Coulomb potential energy of the proton electron pair in Hydrogen atom is essentially the negative interaction energy between their superposed electrostatic fields which is inversely proportional to their instantaneous separation distance. Assuming the proton to be relatively fixed at the origin of an appropriate coordinate system, the potential energy of the orbiting electron will be a function of instantaneous position coordinates of the electron. This has not been properly modeled in the Schrodinger equation. The resulting errors in the solution have been quantitatively demonstrated in this paper. We have stressed the necessity of incorporating a specific correction in the potential energy term of the Schrodinger equation, after which it may facilitate the adoption of Bohmian QM.

Multichannel scattering problem with a nonseparable angular part as a boundary-value problem.

We have developed an efficient computational method for solving the quantum multichannel scattering problem with a nonseparable angular part. The use of the nondirect product discrete-variable representation, suggested and developed by V. Melezhik, gives us an accurate approximation for the angular part of the desired wave function and, eventually, for the scattering parameters. Subsequent reduction of the problem to the boundary-value problem with well-defined block-band matrix of equation coefficients permits us to use efficient standard algorithms for its solution. We demonstrate the numerical efficiency, flexibility, and good convergence of the computational scheme in a quantitative description of the Feshbach resonances in pair collisions occurring in atomic traps and the scattering in strongly anisotropic traps. The method can also be used for the investigation of further actual problems in quantum physics. A natural extension is a description of spin-orbit coupling, intensively investigated in ultracold gases, and dipolar confinement-induced resonances.

Interpretation and Decoherence: A Contribution to the Debate Vassallo & Esfeld Versus Crull

Two recent papers appeared in FOOP disagree regarding the role played by in quantum physics. On the one hand, Elise Crull considers that decoherence, by itself, solves many conceptual problems in quantum physics, with no need of interpretative considerations. On the other hand, Antonio Vassallo and Michael Esfeld reply by correctly claiming that, although is a powerful tool to deal with conceptual problems, it does not dispense us from interpreting the formalism. In this brief note we want to contribute to the debate with further considerations from another viewpoint. In this work we show that the discussions versus revolve around whether the theory of requires interpretive considerations to solve the measurement problem. In general, those discussions take the theory of for granted, as if it would not involve any difficulty. Therefore, they commonly focus on the interpretation wing: even in the case that the open system decoheres in a given basis, the whole closed system is still in a superposition and, thus, without an adequate interpretation, it cannot be said that the observables defined by that basis behave classically. Here we have focused on the decoherence wing: given the conceptual challenges that the theory must face and the alternative approaches to the orthodox view, the understanding of the very phenomenon of still requires a great deal of interpretive work.

An adaptive Galerkin method for the time-dependent complex Schrödinger equation

Nonlinear time-dependent Schrödinger equations (NLSE) model several important problems in quantum physics and morphogenesis. Recently, vortex lattice formation were experimentally found in Bose–Einstein condensate and Fermi superfluids, which are modeled by adding a rotational term in the NLSE equation. Numerical solutions have been computed by using separate approaches for time and space variables. If we see the complex equation as a system, wave methods can be used.In this article, we consider finite element approximations using continuous Galerkin schemes in time and space by adaptive mesh balancing both errors. To get this balance, we adapt the dual weighted residual method used for wave equations and estimates of error indicators for adaptive space–time finite element discretization. The results show how important is dynamic refinement to control the degrees of freedom in space.

Criticality in two-dimensional quantum systems: Tensor network approach

Determination and characterization of criticality in two-dimensional (2D) quantum many-body systems belong to the most important challenges and problems of quantum physics. In this paper we propose an efficient scheme to solve this problem by utilizing the infinite projected entangled pair state (iPEPS), and tensor network (TN) representations. We show that the criticality of a 2D state is faithfully reproduced by the ground state (dubbed as boundary state) of a one-dimensional effective Hamiltonian constructed from its iPEPS representation. We demonstrate that for a critical state the correlation length and the entanglement spectrum of the boundary state are essentially different from those of a gapped iPEPS. This provides a solid indicator that allows to identify the criticality of the 2D state. Our scheme is verified on the resonating valence bond (RVB) states on kagom\'e and square lattices, where the boundary state of the honeycomb RVB is found to be described by a $c=1$ conformal field theory. We apply our scheme also to the ground state of the spin-1/2 XXZ model on honeycomb lattice, illustrating the difficulties of standard variational TN approaches to study the critical ground states. Our scheme is of high versatility and flexibility, and can be further applied to investigate the quantum criticality in many other phenomena, such as finite-temperature and topological phase transitions.

Monitoring of the Process of System Information Broadcasting in Time.

One of the problems of quantum physics is how a measurement turns quantum, noncopyable data, towards copyable classical knowledge. We use the quantum state discrimination in a central system model to show how its evolution leads to the broadcasting of the information, and how orthogonalization and decoherence factors allow us to monitor the distance of the state in question to the one perfectly broadcasting information, in any moment of time not just asymptotically. We illustrate this in the spin-spin model where the distance is shown to be typically small and provide the related time scales.

Solving the quantum many-body problem with artificial neural networks.

The challenge posed by the many-body problem in quantum physics originates from the difficulty of describing the nontrivial correlations encoded in the exponential complexity of the many-body wave function. Here we demonstrate that systematic machine learning of the wave function can reduce this complexity to a tractable computational form for some notable cases of physical interest. We introduce a variational representation of quantum states based on artificial neural networks with a variable number of hidden neurons. A reinforcement-learning scheme we demonstrate is capable of both finding the ground state and describing the unitary time evolution of complex interacting quantum systems. Our approach achieves high accuracy in describing prototypical interacting spins models in one and two dimensions.

Vers les limites ultimes de précision : une introduction à la métrologie quantique

Luiz Davidovich, Instituto de Fisica, Universidade Federal do Rio de Janeiro These lectures will focus on quantum metrology, which aims to determine the ultimate precision limits in the estimation of parameters. It also helps to understand some basic problems in quantum physics, like for instance the energy-time uncertainty and its extension to noisy systems. Applications to several systems will be discussed, including phase estimation in optical interferometers, frequency estimation in atom...

Reply to "Comment on 'Fractional quantum mechanics' and 'Fractional Schrödinger equation' ".

The fractional uncertainty relation is a mathematical formulation of Heisenberg's uncertainty principle in the framework of fractional quantum mechanics. Two mistaken statements presented in the Comment have been revealed. The origin of each mistaken statement has been clarified and corrected statements have been made. A map between standard quantum mechanics and fractional quantum mechanics has been presented to emphasize the features of fractional quantum mechanics and to avoid misinterpretations of the fractional uncertainty relation. It has been shown that the fractional probability current equation is correct in the area of its applicability. Further studies have to be done to find meaningful quantum physics problems with involvement of the fractional probability current density vector and the extra term emerging in the framework of fractional quantum mechanics.

Exploring the quantum speed limit with computer games.

Humans routinely solve problems of immense computational complexity by intuitively forming simple, low-dimensional heuristic strategies. Citizen science (or crowd sourcing) is a way of exploiting this ability by presenting scientific research problems to non-experts. 'Gamification'--the application of game elements in a non-game context--is an effective tool with which to enable citizen scientists to provide solutions to research problems. The citizen science games Foldit, EteRNA and EyeWire have been used successfully to study protein and RNA folding and neuron mapping, but so far gamification has not been applied to problems in quantum physics. Here we report on Quantum Moves, an online platform gamifying optimization problems in quantum physics. We show that human players are able to find solutions to difficult problems associated with the task of quantum computing. Players succeed where purely numerical optimization fails, and analyses of their solutions provide insights into the problem of optimization of a more profound and general nature. Using player strategies, we have thus developed a few-parameter heuristic optimization method that efficiently outperforms the most prominent established numerical methods. The numerical complexity associated with time-optimal solutions increases for shorter process durations. To understand this better, we produced a low-dimensional rendering of the optimization landscape. This rendering reveals why traditional optimization methods fail near the quantum speed limit (that is, the shortest process duration with perfect fidelity). Combined analyses of optimization landscapes and heuristic solution strategies may benefit wider classes of optimization problems in quantum physics and beyond.

Physics: Quantum problems solved through games.

Humans are better than computers at performing certain tasks because of their intuition and superior visual processing. Video games are now being used to channel these abilities to solve problems in quantum physics. See Letter p.210 This paper from a team at Aarhus University, Denmark, describes the development of Quantum Moves, an online platform that brings the power of citizen science and game-playing to optimization problems in quantum physics. Jacob Sherson and colleagues have designed a game in which players are asked to find optimal ways of moving optical tweezers in a quantum computing architecture. While brute-force numerical optimization of this problem fails, the players' solutions provide a basis for an optimization method superior to traditional methods. Quantum physics has the reputation of being difficult and unintuitive, but this study shows that even here player intuition can lead to new scientific insights.

Efficient computation of spontaneous emission dynamics in arbitrary photonic structures

Defining a quantum mechanical wavefunction for photons is one of the remaining open problems in quantum physics. Thus quantum states of light are usually treated within the realm of second quantization. Consequently, spontaneous emission (SE) in arbitrary photonic media is often described by Fock space Hamiltonians. Here, we present a real space formulation of the SE process that can capture the physics of the problem accurately under different coupling conditions. Starting from first principles, we map the unitary evolution of a dressed two-level quantum emitter onto the problem of electromagnetic radiation from a self-interacting complex harmonic oscillator. Our formalism naturally leads to an efficient computational scheme of SE dynamics using finite difference time domain method without the need for calculating the photonic eigenmodes of the surrounding environment. In contrast to earlier investigations, our computational framework provides a unified numerical treatment for both weak and strong coupling regimes alike. We illustrate the versatility of our scheme by considering several different examples.

L k,s -Singular values and spectral radius of partially symmetric rectangular tensors

The real rectangular tensors arise from the strong ellipticity condition problem in solid mechanics and the entanglement problem in quantum physics. In this paper, we first study properties of lk,s-singular values of real rectangular tensors. Then, a necessary and sufficient condition for the positive definiteness of partially symmetric rectangular tensors is given. Furthermore, we show that the weak Perron-Frobenius theorem for nonnegative partially symmetric rectangular tensor keeps valid under some new conditions and we prove a maximum property for the largest lk,s-singular values of nonnegative partially symmetric rectangular tensor. Finally, we prove that the largest lk,s-singular value of nonnegative weakly irreducible partially symmetric rectangular tensor is still geometrically simple.

Entanglement and Nonlocality are Inequivalent for Any Number of Parties.

Understanding the relation between nonlocality and entanglement is one of the fundamental problems in quantum physics. In the bipartite case, it is known that these two phenomena are inequivalent, as there exist entangled states of two parties that do not violate any Bell inequality. However, except for a single example of an entangled three-qubit state that has a local model, almost nothing is known about such a relation in multipartite systems. We provide a general construction of genuinely multipartite entangled states that do not display genuinely multipartite nonlocality, thus proving that entanglement and nonlocality are inequivalent for any number of parties.

Algorithm 950

A hierarchy of semidefinite programming (SDP) relaxations approximates the global optimum of polynomial optimization problems of noncommuting variables. Generating the relaxation, however, is a computationally demanding task, and only problems of commuting variables have efficient generators. We develop an implementation for problems of noncommuting variables that creates the relaxation to be solved by SDPA--a high-performance solver that runs in a distributed environment. We further exploit the inherent sparsity of optimization problems in quantum physics to reduce the complexity of the resulting relaxations. Constrained problems with a relaxation of order two may contain up to a hundred variables. The implementation is available in Python. The tool helps solve such as finding the ground state energy or testing quantum correlations.

Digital quantum simulation goes to two fermions

In a recent work, a group of researchers led by Gui-Lu Long of Tsinghua University proposed a digital quantum simulation algorithm for the dynamics of interacting quantum systems in real space. They experimentally implemented the algorithm to simulate the dynamics of two interacting fermions using a nuclear magnetic resonance (NMR) setup [1]. Quantum simulation [2], inspired by the development of quantum computer, is one of the blossoming sub-fields in quantum information science. Efficient simulations of many-body quantum systems are generally difficult on classical computers due to the exponential growth of the required resource with the system size, while quantum computer has been proved to provide intrinsic advantages for such simulation tasks. Quantum simulation can be divided into two categories: analog simulation and digital simulation. An analog quantum simulator must have a sufficiently similar Hamiltonian to that of the target system to be simulated, and thus, on such quantum simulators, universal simulations of quantum systems cannot be realized [3]. In contrast, digital quantum simulation [4, 5] spares the requirement of similarity in Hamiltonians. A digital quantum simulator in principle can perform universal quantum simulations, and a quantum computer can play the role of a digital quantum simulator. A digital quantum simulation algorithm of a single-particle tunneling was proposed in 2012 [6]. Its first experimental realization was completed in 2013 [7]. Digital quantum simulations attract much attention recently. The simulation of real-space evolution of particles is one of the most attracting aspects among various quantum simulation tasks because of the fundamental role of real-space evolution problems in quantum physics. Investigation on the digital simulation of the quantum many-body spatial dynamics is difficult due to the large number of operations and qubits required. In the work of the Tsinghua team [1], they studied digital simulation of interacting quantum many-body dynamics, for both non-identical and identical particle systems. In identical particle systems, second quantization formalism was used. As a representative illustration, they proposed and experimentally realized a small-scale simulation for the temporal– spatial dynamics of a two-fermion system with Coulomb interactions using a three-qubit NMR quantum information processor. The experiment demonstrated the attracting or repelling nature between the particles due to attractive or repulsive interactions. This should be an indication that the simulation of many-body dynamics of small quantum systems is within reach of today’s small-scale quantum simulators with the help of digital quantum simulation algorithm, and quantum computers have promising superior powers in the simulation of complex quantum systems.