Quantum Mechanical Constraints Research Articles

Parallel quantum computing simulations via quantum accelerator platform virtualization

Quantum circuit execution is a central task in quantum computation. Due to inherent quantum-mechanical constraints, quantum computing workflows often involve a considerable number of independent measurements over a large set of slightly different quantum circuits. Here we discuss a simple model for parallelizing such quantum circuit executions that is based on introducing a large array of virtual quantum processing units (mapped to HPC nodes in our case) as a parallel quantum computing platform. Implemented within the XACC framework, the model can readily take advantage of its backend-agnostic features, enabling parallel quantum computing/simulation over any target backend supported by XACC. We illustrate the performance of this approach by demonstrating strong scaling in two pertinent domain science problems, namely in computing the gradients for the multi-contracted variational quantum eigensolver and in data-driven quantum circuit learning, where we vary the number of qubits and the number of circuit layers. The latter simulation leverages the cuQuantum library to run efficiently on GPU-accelerated HPC platforms.

Frequency noise of laser gyros

Laser gyros are powerful tools used to test the predictions of the general theory of relativity. The precision of a measurement of the rotation rate with a laser gyro is limited by the frequency noise of the beat between two counterpropagating modes of a ring laser. The frequency noise of a single mode of a laser is limited by quantum mechanical constraints because it is related to the maximum precision with which the phase of a coherent state can be measured. If two modes are not correlated, the variance of the fluctuations of the difference of their frequencies is the sum of the variance of the frequency noise of the two modes. If the two modes are correlated, this result does not hold any longer. In this paper, we show that a laser gyro has mechanisms capable of dynamically locking the two modes together without forcing them to the same frequency. The lock of modes decouples the noise of the beat note from the frequency noise of the individual modes, thus allowing the realization of sub-shot noise laser gyros.

Magnetic Behavior of Trigonal (Bi-)pyramidal 3d8 Mononuclear Nanomagnets: The Case of [Ni(MDABCO)2Cl3]ClO4.

This paper attempts to shed light on the origin of the magnetic behavior specific to trigonal bi- and pyramidal 3d8 mono- and polynuclear nanomagnets. The focus lies on entirely unraveling the system's intrinsic microscopic mechanisms and fundamental quantum mechanical relations governing the underlying electron dynamics. To this end, we develop a self-consistent approach to characterize, in great detail, all electron correlations and the ensuing fine structure of the energy spectra of a broad class of 3d8 systems. The mathematical framework is based on the multiconfigurational self-consistent field method and is devised to account for prospective quantum mechanical constraints that may confine the electron orbital dynamics while preserving the properties of all measurable quantities. We successfully characterize the experimentally observed magnetic anisotropy properties of a slightly distorted trigonal bipyramidal Ni2+ coordination complex, demonstrating that such compounds do not exhibit intrinsic huge zero-field splitting and inherent giant magnetic anisotropy. We reproduce qualitatively and quantitatively the behavior of the low-field magnetic susceptibility, magnetization, low-, and high-field electron paramagnetic resonance spectroscopy measurements and provide an in-depth analysis of the obtained results.

Pauling’s rules for oxide-based minerals: A re-examination based on quantum mechanical constraints and modern applications of bond-valence theory to Earth materials

AbstractSince their introduction in 1929, Pauling’s five rules have been used by scientists from many disciplines to rationalize and predict stable arrangements of atoms and coordination polyhedra in crystalline solids; amorphous materials such as silicate glasses and melts; nanomaterials, poorly crystalline solids; aqueous cation and anion complexes; and sorption complexes at mineral-aqueous solution interfaces. The predictive power of these simple yet powerful rules was challenged recently by George et al. (2020), who performed a statistical analysis of the performance of Pauling’s five rules for about 5000 oxide crystal structures. They concluded that only 13% of the oxides satisfy the last four rules simultaneously and that the second rule has the most exceptions. They also found that Pauling’s first rule is satisfied for only 66% of the coordination environments tested and concluded that no simple rule linking ionic radius to coordination environment will be predictive due to the variable quality of univalent radii.We address these concerns and discuss quantum mechanical calculations that complement Pauling’s rules, particularly his first (radius sum and radius ratio rule) and second (electrostatic valence rule) rules. We also present a more realistic view of the bonded radii of atoms, derived by determining the local minimum in the electron density distribution measured along trajectories between bonded atoms known as bond paths, i.e., the bond critical point (rc). Electron density at the bond critical point is a quantum mechanical observable that correlates well with Pauling bond strength. Moreover, a metal atom in a polyhedron has as many bonded radii as it has bonded interactions, resulting in metal and O atoms that may not be spherical. O atoms, for example, are not spherical in many oxide-based crystal structures. Instead, the electron density of a bonded oxygen is often highly distorted or polarized, with its bonded radius decreasing systematically from ~1.38 Å when bonded to highly electropositive atoms like sodium to 0.64 Å when bonded to highly electronegative atoms like nitrogen. Bonded radii determined for metal atoms match the Shannon (1976) radii for more electropositive atoms, but the match decreases systematically as the electronegativities of the M atoms increase. As a result, significant departures from the radius ratio rule in the analysis by George et al. (2020) is not surprising. We offer a modified, more fundamental version of Pauling’s first rule and demonstrate that the second rule has a one-to-one connection between the electron density accumulated between the bonded atoms at the bond critical point and the Pauling bond strength of the bonded interaction.Pauling’s second rule implicitly assumes that bond strength is invariant with bond length for a given pair of bonded atoms. Many studies have since shown that this is not the case, and Brown and Shannon (1973) developed an equation and a set of parameters to describe the relation between bond length and bond strength, now redefined as bond valence to avoid confusion with Pauling bond-strength. Brown (1980) used the valence-sum rule, together with the path rule and the valence-matching principle, as the three axioms of bond-valence theory (BVT), a powerful method for understanding many otherwise elusive aspects of crystals and also their participation in dynamic processes. We show how a priori bond-valence calculations can predict unstrained bond-lengths and how bond-valence mapping can locate low-Z atoms in a crystal structure (e.g., Li) or examine possible diffusion pathways for atoms through crystal structures.In addition, we briefly discuss Pauling’s third, fourth, and fifth rules, the first two of which concern the sharing of polyhedron elements (edges and faces) and the common instability associated with structures in which a polyhedron shares an edge or face with another polyhedron and contains high-valence cations. The olivine [α-(MgxFe1–x)2SiO4] crystal structure is used to illustrate the distortions from hexagonal close-packing of O atoms caused by metal-metal repulsion across shared polyhedron edges.We conclude by discussing several applications of BVT to Earth materials, including the use of BVT to: (1) locate H+ ions in crystal structures, including the location of protons in the crystal structures of nominally anhydrous minerals in Earth’s mantle; (2) determine how strongly bonded (usually anionic) structural units interact with weakly bonded (usually cationic) interstitial complexes in complex uranyl-oxide and uranyl-oxysalt minerals using the valence-matching principle; (3) calculate Lewis acid strengths of cations and Lewis base strengths of anions; (4) determine how (H2O) groups can function as bond-valence transformers by dividing one bond into two bonds of half the bond valence; (5) help characterize products of sorption reactions of aqueous cations (e.g., Co2+ and Pb2+) and oxyanions [e.g., selenate (Se6+O4)2− and selenite (Se4+O3)2−] at mineral-aqueous solution interfaces and the important role of protons in these reactions; and (6) help characterize the local coordination environments of highly charged cations (e.g., Zr4+, Ti4+, U4+, U5+, and U6+) in silicate glasses and melts.

QGOpt: Riemannian optimization for quantum technologies

Many theoretical problems in quantum technology can be formulated and addressed as constrained optimization problems. The most common quantum mechanical constraints such as, e.g., orthogonality of isometric and unitary matrices, CPTP property of quantum channels, and conditions on density matrices, can be seen as quotient or embedded Riemannian manifolds. This allows to use Riemannian optimization techniques for solving quantum-mechanical constrained optimization problems. In the present work, we introduce QGOpt, the library for constrained optimization in quantum technology. QGOpt relies on the underlying Riemannian structure of quantum-mechanical constraints and permits application of standard gradient based optimization methods while preserving quantum mechanical constraints. Moreover, QGOpt is written on top of TensorFlow, which enables automatic differentiation to calculate necessary gradients for optimization. We show two application examples: quantum gate decomposition and quantum tomography.

Observation of magnetically tunable Feshbach resonances in ultracold 23Na40K + 40K collisions.

Resonances in ultracold collisions involving heavy molecules are difficult to simulate theoretically and have proven challenging to detect. Here we report the observation of magnetically tunable Feshbach resonances in ultracold collisions between potassium-40 (40K) atoms and sodium-23-potassium-40 (23Na40K) molecules in the rovibrational ground state. We prepare the atoms and molecules in various hyperfine levels of their ground states and observe the loss of molecules as a function of the magnetic field. The atom-molecule Feshbach resonances are identified by observing an enhancement of the loss. We have observed 11 resonances in the magnetic field range of 43 to 120 gauss. The observed atom-molecule Feshbach resonances at ultralow temperatures probe the three-body potential energy surface with exceptional resolution and will help to improve understanding of ultracold collisions.

Brief get-togethers between NaK and K

Chemical Physics Cooling molecules to nanokelvin temperatures places them under the tightest quantum mechanical constraints. Studies in this intriguing regime have been limited to diatomics: Two cold atoms can be lured together into weakly associated Feshbach resonances, which lasers can then shift into a more stable molecular state. Yang et al. now report the observation of triatomic Feshbach resonances in ultracold collisions between potassium (K) atoms and sodium potassium (NaK) diatomics. The findings potentially set the stage for the preparation and study of ultracold triatomic molecules. Science , this issue p. [261][1] [1]: /lookup/doi/10.1126/science.aau5322

Communication: Constant uncertainty molecular dynamics: A simple and efficient algorithm to incorporate quantum nature into a real-time molecular dynamics simulation.

We propose a novel molecular dynamics (MD) algorithm for approximately dealing with a nuclear quantum dynamics in a real-time MD simulation. We have found that real-time dynamics of the ensemble of classical particles acquires quantum nature by introducing a constant quantum mechanical uncertainty constraint on its classical dynamics. The constant uncertainty constraint is handled by the Lagrange multiplier method and implemented into a conventional MD algorithm. The resulting constant uncertainty molecular dynamics (CUMD) is applied to the calculation of quantum position autocorrelation functions on quartic and Morse potentials. The test calculations show that CUMD gives better performance than ring-polymer MD because of the inclusion of the quantum zero-point energy during real-time evolution as well as the quantum imaginary-time statistical effect stored in an initial condition. The CUMD approach will be a possible starting point for new real-time quantum dynamics simulation in condensed phase.

On the Remarkable Features of the Lower Limits of Charge and the Radiated Energy of Antennas as Predicted by Classical Electrodynamics

Electromagnetic energy radiated by antennas working in both the frequency domain and time domain is studied as a function of the charge associated with the current in the antenna. The frequency domain results, obtained under the assumption of sinusoidal current distribution, show that, for a given charge, the energy radiated within a period of oscillation increases initially with L/λ and then starts to oscillate around a steady value when L/λ > 1. The results show that for the energy radiated by the antenna to be equal to or larger than the energy of one photon, the oscillating charge in the antenna has to be equal to or larger than the electronic charge. That is, U ≥ hν or UT ≥ h ⇒ q ≥ e, where U is the energy dissipated over a period, ν is the frequency of oscillation, T is the period, h is Planck’s constant, q is the rms value of the oscillating charge, and e is the electronic charge. In the case of antennas working in the time domain, it is observed that UΔt ≥ h/4π ⇒ q ≥ e, where U is the total energy radiated, Δt is the time over which the energy is radiated, and q is the charge transported by the current. It is shown that one can recover the time–energy uncertainty principle of quantum mechanics from this time domain result. The results presented in this paper show that when quantum mechanical constraints are applied to the electromagnetic energy radiated by a finite antenna as estimated using the equations of classical electrodynamics, the electronic charge emerges as the smallest unit of free charge in nature.

Embedding Quantum into Classical: Contextualization vs Conditionalization

We compare two approaches to embedding joint distributions of random variables recorded under different conditions (such as spins of entangled particles for different settings) into the framework of classical, Kolmogorovian probability theory. In the contextualization approach each random variable is “automatically” labeled by all conditions under which it is recorded, and the random variables across a set of mutually exclusive conditions are probabilistically coupled (imposed a joint distribution upon). Analysis of all possible probabilistic couplings for a given set of random variables allows one to characterize various relations between their separate distributions (such as Bell-type inequalities or quantum-mechanical constraints). In the conditionalization approach one considers the conditions under which the random variables are recorded as if they were values of another random variable, so that the observed distributions are interpreted as conditional ones. This approach is uninformative with respect to relations between the distributions observed under different conditions because any set of such distributions is compatible with any distribution assigned to the conditions.

No-Forcing and No-Matching Theorems for Classical Probability Applied to Quantum Mechanics

Correlations of spins in a system of entangled particles are inconsistent with Kolmogorov’s probability theory (KPT), provided the system is assumed to be non-contextual. In the Alice–Bob EPR paradigm, non-contextuality means that the identity of Alice’s spin (i.e., the probability space on which it is defined as a random variable) is determined only by the axis $$\alpha _{i}$$ chosen by Alice, irrespective of Bob’s axis $$\beta _{j}$$ (and vice versa). Here, we study contextual KPT models, with two properties: (1) Alice’s and Bob’s spins are identified as $$A_{ij}$$ and $$B_{ij}$$ , even though their distributions are determined by, respectively, $$\alpha _{i}$$ alone and $$\beta _{j}$$ alone, in accordance with the no-signaling requirement; and (2) the joint distributions of the spins $$A_{ij},B_{ij}$$ across all values of $$\alpha _{i},\beta _{j}$$ are constrained by fixing distributions of some subsets thereof. Of special interest among these subsets is the set of probabilistic connections, defined as the pairs $$\left( A_{ij},A_{ij'}\right) $$ and $$\left( B_{ij},B_{i'j}\right) $$ with $$\alpha _{i}\not =\alpha _{i'}$$ and $$\beta _{j}\not =\beta _{j'}$$ (the non-contextuality assumption is obtained as a special case of connections, with zero probabilities of $$A_{ij}\not =A_{ij'}$$ and $$B_{ij}\not =B_{i'j}$$ ). Thus, one can achieve a complete KPT characterization of the Bell-type inequalities, or Tsirelson’s inequalities, by specifying the distributions of probabilistic connections compatible with those and only those spin pairs $$\left( A_{ij},B_{ij}\right) $$ that are subject to these inequalities. We show, however, that quantum-mechanical (QM) constraints are special. No-forcing theorem says that if a set of probabilistic connections is not compatible with correlations violating QM, then it is compatible only with the classical–mechanical correlations. No-matching theorem says that there are no subsets of the spin variables $$A_{ij},B_{ij}$$ whose distributions can be fixed to be compatible with and only with QM-compliant correlations.

On the Chan-Das gauge for the calculation of molecular magnetizabilities

It is proven that the common origin gauge proposed by Chan and Das for the calculation of molecular magnetizabilities within the conventional approach using gaugeless basis sets, i.e., the center of electronic charge, does not minimize the van Vleck paramagnetic contribution to the diagonal tensor components, unless the Arrighini-Maestro-Moccia sum rules for gauge invariance, and charge conservation are satisfied. Additional quantum mechanical constraints for extremum values of formally diamagnetic and paramagnetic contributions have also been obtained for magnetizabilities calculated via procedures allowing for a continuous translation of the origin of the current density.

INFORMATION TRANSFER IN INDIVIDUAL QUANTUM MEASUREMENTS

The information transfer in quantum measurements between the measured object Ω and measuring system [Formula: see text] is studied. It was found that due to the quantum-mechanical (QM) constraints, the information about the purity of Ω state is not transferred to [Formula: see text] during the measurement of arbitrary Ω observable V. As a result, [Formula: see text] can not discriminate the pure and mixed Ω ensembles with the same [Formula: see text]. It is shown that such information constraints induce the appearance of stochasticity in the measurement of Ω pure ensemble, so that [Formula: see text] would detect the random a "pointer" coordinates qi; their distribution obeys Born rule. The influence of [Formula: see text] decoherence by its environment is studied, it is shown that the account of its effects does not change this result principally.

Comment on “Two-way protocols for quantum cryptography with a nonmaximally entangled qubit pair”

Three protocols of quantum cryptography with a nonmaximally entangled qubit pair [Phys. Rev. A 80, 022323 (2009)] were recently proposed by Shimizu, Tamaki, and Fukasaka. The security of these protocols is based on the quantum-mechanical constraint for a state transformation between nonmaximally entangled states. However, we find that the second protocol is vulnerable under the correlation-elicitation attack. An eavesdropper can obtain the encoded bit $M$ although she has no knowledge about the random bit $R$.

On one asymptotic property of time-shift quantum cryptography

One of the basic results of classical information theory is that error-free information transmission is possible even through an imperfect binary communication channel with noise up to an error of Qc = 1/2. There is a fundamental and applied question of whether quantum-mechanical constraints can ensure error-free classical-information transmission with quantum states and, moreover, guarantee the security of distributed keys up to the theoretical limit in the error Qc. It has been shown that the secure key distribution is possible up to the error Qc in the asymptotic limit of a large number of bases.

Efficient estimation algorithm for ARMA, exponential and other trigonometric model with quantum constraints

A new estimation algorithm has been developed here, which refers to covariance shaping least square estimation (CSLS) based on the quantum mechanical concepts and constraints. The algorithm has been applied to ARMA, complex exponential, sine, cosine and sinc models with various parameter values. The same models can be applied with white Gaussian noise, which estimates the bias in the parameter and the validity of the uncertainty can be analysed. For optimal quantum measurement design, the performance of the CSLS estimator is developed, discussed and compared with LS, Shrunken and Ridge estimators for different applications. The results suggest that the CSLS estimator can outperform from others at low-to-moderate signal-to-noise ratio.

Dipole oscillator strength distributions, properties and dispersion energies for the dimethyl, diethyl and methyl–propyl ethers1

Isotropic dipole oscillator strength distributions (DOSDs) have been constructed for the dimethyl, diethyl and methyl–propyl ether molecules through the use of quantum mechanical constraint techniques and experimental dipole oscillator strength data. The constraints are furnished by molar refractivity data and the Thomas–Reiche–Kuhn sum rule. The DOSDs are used to obtain recommended values for a variety of isotropic dipole oscillator strength sums, logarithmic dipole oscillator strength sums, and mean excitation energies for the molecules. Pseudo-DOSDs for the ethers are also constructed and used to obtain reliable results for the isotropic dipole–dipole dispersion energy coefficients for all two-body interactions of the ethers with each other and with fifty other species. In addition reliable results are also obtained for the triple–dipole dispersion energy coefficients for all three-body interactions involving the ethers. 1Dedicated to Anthony Stone, an excellent scientist and friend, on the occasion of his 70th birthday.

Dipole oscillator strength distributions, properties, and dispersion energies for ethylene, propene, and 1-butene

A recommended isotropic dipole oscillator strength distribution (DOSD) has been constructed for the ethylene molecule through the use of quantum mechanical constraint techniques and experimental dipole oscillator strength (DOS) data; the DOS data employed are recent experimental results not available at the time of the original constrained DOSD analysis of this molecule. The constraints are furnished by molar refractivity data and the Thomas–Reiche–Kuhn sum rule. The DOSD is used to evaluate a variety of isotropic dipole oscillator strength sums, logarithmic dipole oscillator strength sums, and mean excitation energies for ethylene. Pseudo-DOSDs for this molecule, and for propene and 1–butene, which are based on an earlier constrained DOSD analysis for these molecules, are developed. They are used to obtain reliable results for the isotropic dipole–dipole dispersion-energy coefficients C6, for the interactions of the alkenes with each other and with 47 other species, and the triple-dipole dispersion-energy coefficients C9 for interactions involving any triple of molecules taken from ethylene, propene, and 1–butene.Key words: alkenes, dipole properties, pseudo-states, dipole–dipole and triple-dipole dispersion energies, long-range additive, non-additive interaction energies.

Dipole Oscillator Strength Distributions and Properties for Methanol, Ethanol and Propan-1-ol and Related Dispersion Energies

Recommended isotropic dipole oscillator strength distributions (DOSDs) have been constructed for the methanol and ethanol molecules through the use of quantum mechanical constraint techniques and experimental dipole oscillator strength (DOS) data; the DOS data employed are recent experimental results not available at the time of the original constrained DOSD analysis of these molecules. The constraints are furnished by molar refractivity data and the Thomas-Reiche-Kuhn sum rule. The DOSDs are used to evaluate a variety of isotropic dipole oscillator strength sums, logarithmic dipole oscillator strength sums, and mean excitation energies for the molecules. Pseudo-DOSDs for these molecules, and for propan-1-ol based on an earlier constrained DOSD analysis for this molecule, are also presented. They are used to obtain reliable results for the isotropic dipole-dipole dispersion energy coefficients C6, for the interactions of the alcohols with each other and with 36 other species, and the triple-dipole dispersion energy coefficients C9for interactions involving any triple of molecules involving methanol, ethanol and propan-1-ol.

A phase-space method for the Bose–Hubbard model: application to mean-field models

We present a phase-space method for the Bose–Hubbard model based on the Q-function representation. In particular, we consider two model Hamiltonians in the mean-field approximation; the first is the standard ‘one-site’ model where quantum tunnelling is approximated entirely using mean-field terms; the second ‘two-site’ model explicitly includes tunnelling between two adjacent sites while treating tunnelling with other neighbouring sites using the mean-field approximation. The ground state is determined by minimizing the classical energy functional subject to quantum mechanical constraints, which take the form of uncertainty relations. For each model Hamiltonian, we compare the ground state results from the Q-function method with the exact numerical solution. The results from the Q-function method, which are easy to compute, give a good qualitative description of the main features of the Bose–Hubbard model including the superfluid to Mott insulator. We find the quantum mechanical constraints dominate the problem and show there are some limitations of the method particularly in the weak lattice regime.