scholarly journals Simulating arbitrary pair-interactions by a given Hamiltonian: graph-theoretical bounds on the time-complexity

2002 ◽  
Vol 2 (2) ◽  
pp. 117-132
Author(s):  
P. Wocjan ◽  
D. Janzing ◽  
T. Beth
Keyword(s):  
Quantum Computer ◽  
Pair Interaction ◽  
Hamiltonian Graph ◽  
Lower And Upper Bounds ◽  
Convex Optimization Problem ◽  
Minimal Time ◽  
Natural Time ◽  
Separability Problem ◽  
Time Overhead ◽  
Pair Interactions

We consider a quantum computer consisting of n spins with an arbitrary but fixed pair-interaction Hamiltonian and describe how to simulate other pair-interactions by interspersing the natural time evolution with fast local transformations. Calculating the minimal time overhead of such a simulation leads to a convex optimization problem. Lower and upper bounds on the minimal time overhead are derived in terms of chromatic indices of interaction graphs and spectral majorization criteria. These results classify Hamiltonians with respect to their computational power. For a specific Hamiltonian, namely \sigma_z\otimes\sigma_z-interactions between all spins, the optimization is mathematically equivalent to a separability problem of n-qubit density matrices. We compare the complexity defined by such a quantum computer with the usual gate complexity.

Quantum algorithm for measuring the energy of n qubits with unknown pair-interactions

2002 ◽  
Vol 2 (3) ◽  
pp. 198-207
Author(s):  
D. Janzing
Keyword(s):  
Quantum State ◽  
Quantum Computer ◽  
Quantum Algorithm ◽  
Pair Interaction ◽  
Phase Estimation ◽  
Solid States ◽  
Energy Gaps ◽  
Large N ◽  
Conditional Transformation ◽  
Essential Assumption

The well-known algorithm for quantum phase estimation requires that the considered unitary is available as a conditional transformation depending on the quantum state of an ancilla register. We present an algorithm converting an unknown n-qubit pair-interaction Hamiltonian into a conditional one such that standard phase estimation can be applied to measure the energy. Our essential assumption is that the considered system can be brought into interaction with a quantum computer. For large n the algorithm could still be applicable for estimating the density of energy states and might therefore be useful for finding energy gaps in solid states.

scholarly journals Associated Probabilities in Interactive MADM under Discrimination q-Rung Picture Linguistic Environment

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2337
Author(s):  
Gia Sirbiladze
Keyword(s):  
Choquet Integral ◽  
Pair Interaction ◽  
Small Degree ◽  
Aggregation Operators ◽  
Fuzzy Measure ◽  
Weighted Averaging ◽  
Location Selection ◽  
Multi Attribute Decision Making ◽  
The Difference ◽  
Pair Interactions

In some multi-attribute decision-making (MADM) models studying attributes’ interactive phenomena is very important for the minimizing decision risks. Usually, the Choquet integral type aggregations are considered in such problems. However, the Choquet integral aggregations do not consider all attributes’ interactions; therefore, in many cases, when these interactions are revealed in less degree, they do not perceive these interactions and their utility in MADM problems is less useful. For the decision of this problem, we create the Choquet integral-based new aggregation operators’ family which considers all pair interactions between attributes. The problem under the discrimination q-rung picture linguistic and q-rung orthopair fuzzy environments is considered. Construction of a 2-order additive fuzzy measure (TOAFM) involves pair interaction indices and importance values of attributes of a MADM model. Based on the attributes’ pair interactions for the identification of associated probabilities of a 2-order additive fuzzy measure, the Shapley entropy maximum principle is used. The associated probabilities q-rung picture linguistic weighted averaging (APs-q-RPLWA) and the associated probabilities q-rung picture linguistic weighted geometric (APs-q-RPLWG) aggregation operators are constructed with respect to TOAFM. For an uncertainty pole of experts’ evaluations on attributes regarding the possible alternatives, the associated probabilities of a fuzzy measure are used. The second pole of experts’ evaluations as arguments of the aggregation operators by discrimination q-rung picture linguistic values is presented. Discrimination q-rung picture linguistic evaluations specify the attribute’s dominant, neutral and non-dominant impacts on the selection of concrete alternative from all alternatives. Constructed operators consider the all relatedness between attributes in any consonant attribute structure. Main properties on the rightness of extensions are showed: APs-q-RPLWA and APs-q-RPLWG operators match with q-rung picture linguistic Choquet integral averaging and geometric operators for the lower and upper capacities of order two. The conjugation among the constructed operators is also considered. Connections between the new operators and the compositions of dual triangular norms (Tp,Spq) and (Tmin,Smax) are also constructed. Constructed operators are used in evaluation of a selection reliability index (SRI) of candidate service centers in the facility location selection problem, when small degree interactions are observed between attributes. In example MADM, the difference in optimal solutions is observed between the Choquet integral aggregation operators and their new extensions. The difference, however, is due to the need to use indices of all interactions between attributes.

scholarly journals Variational Quantum Fidelity Estimation

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 248 ◽  
Author(s):  
Marco Cerezo ◽  
Alexander Poremba ◽  
Lukasz Cincio ◽  
Patrick J. Coles
Keyword(s):  
Phase Transitions ◽  
Quantum Computer ◽  
Quantum Phase Transitions ◽  
Upper Bounds ◽  
Low Rank ◽  
Matrix Elements ◽  
Lower And Upper Bounds ◽  
Classical Algorithm ◽  
Largest Eigenvalues ◽  
Quantum Fidelity

Computing quantum state fidelity will be important to verify and characterize states prepared on a quantum computer. In this work, we propose novel lower and upper bounds for the fidelity F(ρ,σ) based on the ``truncated fidelity'' F(ρm,σ), which is evaluated for a state ρm obtained by projecting ρ onto its m-largest eigenvalues. Our bounds can be refined, i.e., they tighten monotonically with m. To compute our bounds, we introduce a hybrid quantum-classical algorithm, called Variational Quantum Fidelity Estimation, that involves three steps: (1) variationally diagonalize ρ, (2) compute matrix elements of σ in the eigenbasis of ρ, and (3) combine these matrix elements to compute our bounds. Our algorithm is aimed at the case where σ is arbitrary and ρ is low rank, which we call low-rank fidelity estimation, and we prove that no classical algorithm can efficiently solve this problem under reasonable assumptions. Finally, we demonstrate that our bounds can detect quantum phase transitions and are often tighter than previously known computable bounds for realistic situations.

scholarly journals On the Schrödinger spectrum of a hydrogen atom with electrostatic Bopp–Landé–Thomas–Podolsky interaction between electron and proton

2019 ◽  
Vol 34 (26) ◽  
pp. 1950146 ◽  
Author(s):  
Holly K. Carley ◽  
Michael K.-H. Kiessling ◽  
Volker Perlick
Keyword(s):  
Hydrogen Atom ◽  
Electrostatic Field ◽  
Energy Levels ◽  
Rest Mass ◽  
Pair Interaction ◽  
Precision Measurements ◽  
Field Energy ◽  
Text Line ◽  
Lower And Upper Bounds ◽  
Structure Splitting

The Schrödinger spectrum of a hydrogen atom, modeled as a two-body system consisting of a point electron and a point proton, changes when the usual Coulomb interaction between point particles is replaced with an interaction which results from a modification of Maxwell’s law of the electromagnetic vacuum. Empirical spectral data thereby impose bounds on the theoretical parameters involved in such modified vacuum laws. In the present paper the vacuum law proposed, in the 1940s, by Bopp, Landé–Thomas, and Podolsky (BLTP) is scrutinized in such a manner. The BLTP theory hypothesizes the existence of an electromagnetic length scale of nature — the Bopp length [Formula: see text] —, to the effect that the electrostatic pair interaction deviates significantly from Coulomb’s law only for distances much shorter than [Formula: see text]. Rigorous lower and upper bounds are constructed for the Schrödinger energy levels of the hydrogen atom, [Formula: see text], for all [Formula: see text] and [Formula: see text]. The energy levels [Formula: see text], [Formula: see text], and [Formula: see text] are also computed numerically and plotted versus [Formula: see text]. It is found that the BLTP theory predicts a nonrelativistic correction to the splitting of the Lyman-[Formula: see text] line in addition to its well-known relativistic fine-structure splitting. Under the assumption that this splitting does not go away in a relativistic calculation, it is argued that present-day precision measurements of the Lyman-[Formula: see text] line suggest that [Formula: see text] must be smaller than [Formula: see text]. Finite proton size effects are found not to modify this conclusion. As a consequence, the electrostatic field energy of an elementary point charge, although finite in BLTP electrodynamics, is much larger than the empirical rest mass ([Formula: see text]) of an electron. If, as assumed in all “renormalized theories” of the electron, the empirical rest mass of a physical electron is the sum of its bare rest mass and its electrostatic field energy, then in BLTP electrodynamics the electron has to be assigned a negative bare rest mass.

scholarly journals THE ROLE OF INTERACTION BETWEEN PRESCHOOL AGE TWINS’ IN THE DEVELOPMENT OF THEIR SELF-AWARENESS

2021 ◽  
pp. 58-62
Author(s):  
A. S. Kuzmina ◽  
◽  
E. S. Prisendorf ◽  
Keyword(s):  
Monozygotic Twins ◽  
Pair Interaction ◽  
Preschool Age ◽  
Self Awareness ◽  
Dizygotic Twins ◽  
Pair Interactions

The article reveals the role of intra-pair behavior of twins in the development of their self-awareness in preschool age. The twin personality is understood as a special social developmental situation that determines the formation of twins. This situation is associated with the emergence of special intra-pair interactions that determine the development of self-awareness of preschoolers. In pairs of di- and monozygotic twins, a different nature of intra-pair interaction is possible; it is interconnected with the development of self-awareness of preschoolers. Dizygotic twins are more competitive, and monozygotic twins are more cooperative.

scholarly journals Ion-Pair Interaction and Hydrogen Bonds as Main Features of Protein Thermostability in Mutated T1 Recombinant Lipase Originating from Geobacillus zalihae

Molecules ◽  
2020 ◽  
Vol 25 (15) ◽  
pp. 3430
Author(s):  
Siti Nor Hasmah Ishak ◽  
Nor Hafizah Ahmad Kamarudin ◽  
Mohd Shukuri Mohamad Ali ◽  
Adam Thean Chor Leow ◽  
Raja Noor Zaliha Raja Abd. Rahman
Keyword(s):  
Hydrogen Bonds ◽  
Melting Temperature ◽  
Tertiary Structure ◽  
Pair Interaction ◽  
Ion Pair ◽  
Recombinant Lipase ◽  
Biophysical Study ◽  
Comparative Structure ◽  
Β Sheet ◽  
Pair Interactions

A comparative structure analysis between space- and an Earth-grown T1 recombinant lipase from Geobacillus zalihae had shown changes in the formation of hydrogen bonds and ion-pair interactions. Using the space-grown T1 lipase validated structure having incorporated said interactions, the recombinant T1 lipase was re-engineered to determine the changes brought by these interactions to the structure and stability of lipase. To understand the effects of mutation on T1 recombinant lipase, five mutants were developed from the structure of space-grown T1 lipase and biochemically characterized. The results demonstrate an increase in melting temperature up to 77.4 °C and 76.0 °C in E226D and D43E, respectively. Moreover, the mutated lipases D43E and E226D had additional hydrogen bonds and ion-pair interactions in their structures due to the improvement of stability, as observed in a longer half-life and an increased melting temperature. The biophysical study revealed differences in β-Sheet percentage between less stable (T118N) and other mutants. As a conclusion, the comparative analysis of the tertiary structure and specific residues associated with ion-pair interactions and hydrogen bonds could be significant in revealing the thermostability of an enzyme with industrial importance.

THREE-SPIN CORRELATION OF THE ISING MODEL ON A KAGOMÉ LATTICE

1990 ◽  
Vol 04 (01) ◽  
pp. 123-130 ◽  
Author(s):  
K. Y. LIN ◽  
B. H. CHEN
Keyword(s):  
Ising Model ◽  
Spin Correlation ◽  
Pair Interaction ◽  
Kagome Lattice ◽  
Spin Correlations ◽  
Kagomé Lattice ◽  
Pair And Triplet Interactions ◽  
Isotropic Pair ◽  
Pair Interactions

Several local three-spin correlations are derived for the Ising model on a Kagomé lattice with anisotropic pair interactions. Three-spin correlation for three spins surrounding a triangle is derived for the Kagomé lattice Ising model with isotropic pair and triplet interactions at a particular temperature determined by pair interaction only.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

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