Quantum Mechanical Wave Function Research Articles

Using gradient-based algorithms to determine ground-state energies on a quantum computer

Variational algorithms are promising candidates to be implemented on near-term quantum computers. In our work, we investigate the variational Hamiltonian ansatz (VHA), where a parametrized trial state of the quantum mechanical wave function is optimized to obtain the ground-state energy. In the VHA, the trial state is given by a noninteracting reference state modified by unitary rotations using generators that are part of the Hamiltonian describing the system. The lowest energy is obtained by optimizing the angles of those unitary rotations. A standard procedure to optimize the variational parameters is to use gradient-based algorithms. However, shot noise and the intrinsic noise of the quantum device affect the evaluation of the required gradients. We study how different methods for obtaining the gradient, specifically the finite-difference and the parameter-shift rule, are affected by shot noise and the noise of the quantum computer. To this end, we simulate a simple quantum circuit, as well as the two-site and six-site Hubbard models.

QMugs, quantum mechanical properties of drug-like molecules

Machine learning approaches in drug discovery, as well as in other areas of the chemical sciences, benefit from curated datasets of physical molecular properties. However, there currently is a lack of data collections featuring large bioactive molecules alongside first-principle quantum chemical information. The open-access QMugs (Quantum-Mechanical Properties of Drug-like Molecules) dataset fills this void. The QMugs collection comprises quantum mechanical properties of more than 665 k biologically and pharmacologically relevant molecules extracted from the ChEMBL database, totaling ~2 M conformers. QMugs contains optimized molecular geometries and thermodynamic data obtained via the semi-empirical method GFN2-xTB. Atomic and molecular properties are provided on both the GFN2-xTB and on the density-functional levels of theory (DFT, ωB97X-D/def2-SVP). QMugs features molecules of significantly larger size than previously-reported collections and comprises their respective quantum mechanical wave functions, including DFT density and orbital matrices. This dataset is intended to facilitate the development of models that learn from molecular data on different levels of theory while also providing insight into the corresponding relationships between molecular structure and biological activity.

Status of the Wave Function of Quantum Mechanics, or, What is Quantum Mechanics Trying to Tell Us?

The most debated status of the wave function of Quantum Mechanics is discussed in the light of the epistemological vs ontological opposition.

Could wavefunctions simultaneously represent knowledge and reality?

In discussion of the interpretation of quantum mechanics the terms ‘ontic’ and ‘epistemic’ are often used in the sense of pertaining to what exists, and pertaining to cognition or knowledge respectively. The terms are also often associated with the formal definitions given by Harrigan and Spekkens for the wavefunction in quantum mechanics to be psi -ontic or psi -epistemic in the context of the ontological models framework. The formal definitions are contradictories, so that the wavefunction can be either psi -epistemic or psi -ontic but not both. However, we argue, nothing about the informal ideas of epistemic and ontic interpretations rules out wavefunctions representing both reality and knowledge. The implications of the Pusey–Barrett–Rudolph theorem and many other issues may be rethought in the light of our analysis.

On local conservation of information content in Schwarzschild black holes

The central equations in classical general relativity are the Einstein Field equations, which accurately describe not only the generation of pseudo-Riemannian curvature by matter and radiation manifesting as gravitational effects, but more importantly mass-energy dynamics, evolution and distribution on the space-time manifold. Herein, we introduce a geometric phase in general relativity corresponding to Schwarzschild black hole information content. This quantity appropriately satisfies a local conservation law subject to minimal coupling, with other desirable properties such as the quantization of the black hole horizon in units of Planck area. The local conservation law is imposed by field equations, which not only contain the trace of Einstein Field equations, but also a complex-valued function with properties analogous to the quantum-mechanical wave function. Such success attests to the utility of the proposed field equations in capturing key aspects of quantum gravity theories.

The Quantum Hologram Theory of Consciousness as a Framework for Altered States of Consciousness Research

We can learn more about how our reality is made and what non-ordinary states of consciousness are by studying the Quantum Hologram Theory of Physics and Consciousness (QHTC). The QHTC says that consciousness is not local and that altered states of consciousness can help us understand how our minds work in more than one way. That's what Schrödinger thought. He thought that the quantum mechanical wave function was a field of consciousness. QHTC is based on holographic theories for human consciousness. These theories say that the brain works like a hologram and that it processes images into interference patterns that are then turned into virtual images, just like a laser hologram. These quantum waves can store a lot of information, which our brains use to make our three-dimensional world. This article says that this last theory should be the main framework for research on altered states of consciousness, and it talks about how to get data for analysis and how to get into an altered state for possible experiments.

Modeling Electronic Response Properties with an Explicit-Electron Machine Learning Potential.

Explicit-electron force fields introduce electrons or electron pairs as semiclassical particles in force fields or empirical potentials, which are suitable for molecular dynamics simulations. Even though semiclassical electrons are a drastic simplification compared to a quantum-mechanical electronic wave function, they still retain a relatively detailed electronic model compared to conventional polarizable and reactive force fields. The ability of explicit-electron models to describe chemical reactions and electronic response properties has already been demonstrated, yet the description of short-range interactions for a broad range of chemical systems remains challenging. In this work, we present the electron machine learning potential (eMLP), a new explicit electron force field in which the short-range interactions are modeled with machine learning. The electron pair particles will be located at well-defined positions, derived from localized molecular orbitals or Wannier centers, naturally imposing the correct dielectric and piezoelectric behavior of the system. The eMLP is benchmarked on two newly constructed data sets: eQM7, an extension of the QM7 data set for small molecules, and a data set for the crystalline β-glycine. It is shown that the eMLP can predict dipole moments, polarizabilities, and IR-spectra of unseen molecules with high precision. Furthermore, a variety of response properties, for example, stiffness or piezoelectric constants, can be accurately reproduced.

Cutting cosmological correlators

The initial conditions of our universe appear to us in the form of a classical probability distribution that we probe with cosmological observations. In the current leading paradigm, this probability distribution arises from a quantum mechanical wavefunction of the universe. Here we ask what the imprint of quantum mechanics is on the late time observables. We show that the requirement of unitary time evolution, colloquially the conservation of probabilities, fixes the analytic structure of the wavefunction and of all the cosmological correlators it encodes. In particular, we derive in perturbation theory an infinite set of single-cut rules that generalize the Cosmological Optical Theorem and relate a certain discontinuity of any tree-level n-point function to that of lower-point functions. Our rules are closely related to, but distinct from the recently derived Cosmological Cutting Rules. They follow from the choice of the Bunch-Davies vacuum and a simple property of the (bulk-to-bulk) propagator and are astoundingly general: we prove that they are valid for fields with a linear dispersion relation and any mass, any integer spin and arbitrary local interactions with any number of derivatives. They also apply to general FLRW spacetimes admitting a Bunch-Davies vacuum, including de Sitter, slow-roll inflation, power-law cosmologies and even resonant oscillations in axion monodromy. We verify the single-cut rules in a number of non-trivial examples, including four massless scalars exchanging a massive scalar, as relevant for cosmological collider physics, four gravitons exchanging a graviton, and a scalar five-point function.

Is the electric potential physical?

In the yet-unmeasured electric Aharonov–Bohm effect, an electric potential influences the quantum mechanical wavefunction of charged matter—even in regions where the electric field vanishes.

No-Thing and Causality in Realistic Non-Standard Interpretations of the Quantum Mechanical Wave Function: Ex Nihilo Aliquid?

It has been shown that quantum mechanics in its orthodox interpretation violates four different formulations of causality principle endowed with empirical meaning. The present work aims to highlight how even a realistic non-standard interpretation of the theory conflicts with causality in its Cartesian formulation of the principle of the non-inferiority of causes over effects. Such an interpretation, which attributes some form of weak physical reality to the wave function (called empty wave, regarded as a zero-energy wave-like phenomenon), is a sort of precursor of the more recent so-called wavefunction realism. We also discuss a more radical realistic interpretation according to which physical properties can also be assigned to non-metaphysical relative nothing, seen as the simple absence of a particle such as a photon, but not of its corresponding state (no-photon), which is considered real. By interpreting the wave function collapse as a consequence of an interaction with empty waves or of a detection of the no-photon, we will highlight how more real physical effects can derive from lower causes, including relative nothing. Finally, we will show how these interpretations, while violating Cartesian causality in its two variants, do not seem to affect the validity of the principle of a rational explanation that nothing can derive from (absolute) nothing, which does not seem satisfied by the orthodox interpretation.

Converting translation operators into plane polar and spherical coordinates and their use in determining quantum-mechanical wavefunctions in a representation-independent fashion

Quantum mechanics is often developed in the position representation, but this is not necessary, and one can perform calculations in a representation-independent fashion, even for wavefunctions. In this work, we illustrate how one can determine wavefunctions, aside from normalization, using only operators and how those operators act on state vectors. To do this in plane polar and spherical coordinates requires one to convert the translation operator into those coordinates. As examples of this approach, we illustrate the solution of the Coulomb problem in two and three dimensions without needing to express any operators in position space.

The equation for the wavefunction in nonrelativistic quantum mechanics*

The equation for the wavefunction in nonrelativistic quantum mechanics*

Thermal Equilibrium Distribution in Infinite-Dimensional Hilbert Spaces

The thermal equilibrium distribution over quantum-mechanical wave functions is a so-called Gaussian adjusted projected (GAP) measure, $GAP(\rho_\beta)$, for a thermal density operator $\rho_\beta$ at inverse temperature $\beta$. More generally, $GAP(\rho)$ is a probability measure on the unit sphere in Hilbert space for any density operator $\rho$ (i.e., a positive operator with trace 1). In this note, we collect the mathematical details concerning the rigorous definition of $GAP(\rho)$ in infinite-dimensional separable Hilbert spaces. Its existence and uniqueness follows from Prohorov's theorem on the existence and uniqueness of Gaussian measures in Hilbert spaces with given mean and covariance. We also give an alternative existence proof. Finally, we give a proof that $GAP(\rho)$ depends continuously on $\rho$ in the sense that convergence of $\rho$ in the trace norm implies weak convergence of $GAP(\rho)$.

Probing the Planck scale: the modification of the time evolution operator due to the quantum structure of spacetime

The propagator which evolves the wave-function in non-relativistic quantum mechanics, can be expressed as a matrix element of a time evolution operator: i.e. GNR(x) = 〈x2|UNR(t)|x1〉 in terms of the orthonormal eigenkets |x〉 of the position operator. In quantum field theory, it is not possible to define a conceptually useful single-particle position operator or its eigenkets. It is also not possible to interpret the relativistic (Feynman) propagator GR(x) as evolving any kind of single-particle wave-functions. In spite of all these, it is indeed possible to express the propagator of a free spinless particle, in quantum field theory, as a matrix element 〈x2|UR(t)|x1〉 for a suitably defined time evolution operator and (non-orthonormal) kets |x〉 labeled by spatial coordinates. At mesoscopic scales, which are close but not too close to Planck scale, one can incorporate quantum gravitational corrections to the propagator by introducing a zero-point-length. It turns out that even this quantum-gravity-corrected propagator can be expressed as a matrix element 〈x2|UQG(t)|x1〉. I describe these results and explore several consequences. It turns out that the evolution operator UQG(t) becomes non-unitary for sub-Planckian time intervals while remaining unitary for time interval is larger than Planck time. The results can be generalized to any ultrastatic curved spacetime.

Cosmological constant caused by observer-induced boundary condition

The evolution of the wave function in quantum mechanics is deterministic like that of classical waves. Only when we bring in observers the fundamentally different quantum reality emerges. Similarly the introduction of observers changes the nature of spacetime by causing a split between past and future, concepts that are not well defined in the observer-free world. The induced temporal boundary leads to a resonance condition for the oscillatory vacuum solutions of the metric in Euclidean time. It corresponds to an exponential de Sitter evolution in real time, which can be represented by a cosmological constant , where r u is the radius of the particle horizon at the epoch when the observer exists. For the present epoch we get a value of Λ that agrees with the observed value within 2σ of the observational errors. This explanation resolves the cosmic coincidence problem. Our epoch in cosmic history does not herald the onset of an inflationary phase driven by some dark energy. We show that the observed accelerated expansion that is deduced from the redshifts is an ‘edge effect’ due to the observer-induced boundary and not representative of the intrinsic evolution. The new theory satisfies the BBN (Big Bang nucleosynthesis) and CMB (cosmic microwave background) observational constraints equally well as the concordance model of standard cosmology. There is no link between the dark energy and dark matter problems. Previous conclusions that dark matter is mainly non-baryonic are not affected.

Signatures of possible surface states in TaAs

A signature property of Weyl semimetals is the existence of topologically protected surface states - arcs in momentum space that connect Weyl points in the bulk. However, the presence of bulks states makes detection of surface contributions to the transport challenging. Here we present a magnetoresistance study of high-quality samples of the prototypical Weyl semimetal, TaAs. By measuring the Shubnikov de Haas effect, we reveal the presence of a two-dimensional cyclotron orbit. This orbit is quantitatively consistent with the interference of coherent quasiparticles traversing two distinct Fermi arcs on the [001] crystallographic surface. The observation of this effect suggests that high magnetic fields can be used to study not only the transport properties of Fermi arcs, but also the interference of their quantum mechanical wavefunctions.

Quantum Trajectories for the Dynamics in the Exact Factorization Framework: A Proof-of-Principle Test.

In the framework of the exact factorization of the time-dependent electron-nuclear wave function, we investigate the possibility of solving the nuclear time-dependent Schrödinger equation based on trajectories. The nuclear equation is separated in a Hamilton-Jacobi equation for the phase of the wave function, and a continuity equation for its (squared) modulus. For illustrative adiabatic and nonadiabatic one-dimensional models, we implement a procedure to follow the evolution of the nuclear density along the characteristics of the Hamilton-Jacobi equation. Those characteristics are referred to as quantum trajectories, since they are generated via ordinary differential equations similar to Hamilton's equations, but including the so-called quantum potential, and they can be used to reconstruct exactly the quantum-mechanical nuclear wave function, provided infinite initial conditions are propagated in time.

Position Measurements and the Empirical Status of Particles in Bohmian Mechanics

The article addresses the debate about the empirical status of particles versus wave functions in Bohmian quantum mechanics. It thereby clarifies questions and misconceptions about the role of the particles in the measurement process, the (un)reliability of position measurements (surrealistic trajectories), and the limited empirical access to particle positions (absolute uncertainty). Taking the ontological commitment of Bohmian mechanics seriously, all relevant empirical results follow from an analysis of the theory in terms of particle motions. Finally, we address the question of why particle motions rather than patterns in the wave function would be the supervenience base of conscious experience.

Tunable Flux Vortices in Two-Dimensional Dirac Superconductors.

The nontrivial geometry encoded in the quantum mechanical wave function has important consequences for both noninteracting and interacting systems. Yet, our understanding of the relationship between geometrical effects in noninteracting systems and their interacting counterparts is far from complete. Here, we demonstrate how the single-particle Berry curvature associated with the normal phase in two dimensions modifies the fluxoid quantization of a Bardeen-Cooper-Schrieffer superconductor. A discussion of the experimental scenarios where this anomalous quantization is expected is provided. Our work demonstrates the importance of variational Ansätze in making a clear connection between the Berry phases of single-particle and many-body wave functions.

Determining odd from even

Quantum Information The parity of a quantum mechanical wave function simply tells you if there is an odd or even number of excitations in the system it describes. Without the need to know the exact number of excitations within a system, being able to measure changes in parity is important and can be exploited in operations such as quantum error correction and stabilizing quantum communication protocols. Besse et al . demonstrate a detector that can determine the parity of a propagating microwave field. Using a superconducting phase qubit embedded in a cavity, they show that they can engineer the system such that transmission of the microwaves is conditional on there being an odd or even number of microwave photons in the radiation field. The simplicity of the detector design should have applications across a broad range of setups for quantum information processing. Phys. Rev. X 10 , 011046 (2020).