scholarly journals Quantum Simulations of Physics Problems

2003 ◽  
Vol 01 (02) ◽  
pp. 189-206 ◽  
Author(s):  
Rolando Somma ◽  
Gerardo Ortiz ◽  
Emanuel Knill ◽  
James Gubernatis
Keyword(s):  
Physical Properties ◽  
Hilbert Spaces ◽  
Correlation Functions ◽  
Physical System ◽  
Quantum Computer ◽  
Energy Spectra ◽  
Quantum Networks ◽  
Quantum Simulations ◽  
Physical Problems ◽  
Large Quantum

If a large Quantum Computer (QC) existed today, what type of physical problems could we efficiently simulate on it that we could not efficiently simulate on a classical Turing machine? In this paper we argue that a QC could solve some relevant physical "questions" more efficiently. The existence of one-to-one mappings between different algebras of observables or between different Hilbert spaces allow us to represent and imitate any physical system by any other one (e.g. a bosonic system by a spin-1/2 system). We explain how these mappings can be performed, and we show quantum networks useful for the efficient evaluation of some physical properties, such as correlation functions and energy spectra.

scholarly journals Quantum Attacks on Bitcoin, and How to Protect Against Them

Ledger ◽  
2018 ◽  
Vol 3 ◽  
Author(s):  
Divesh Aggarwal ◽  
Gavin Brennen ◽  
Troy Lee ◽  
Miklos Santha ◽  
Marco Tomamichel
Keyword(s):  
At Risk ◽  
Quantum Computer ◽  
Alternative Proof ◽  
Quantum Computers ◽  
Signature Scheme ◽  
Area At Risk ◽  
Signature Schemes ◽  
Near Term ◽  
Financial Transactions ◽  
Large Quantum

The key cryptographic protocols used to secure the internet and financial transactions of today are all susceptible to attack by the development of a sufficiently large quantum computer. One particular area at risk is cryptocurrencies, a market currently worth over 100 billion USD. We investigate the risk posed to Bitcoin, and other cryptocurrencies, by attacks using quantum computers. We find that the proof-of-work used by Bitcoin is relatively resistant to substantial speedup by quantum computers in the next 10 years, mainly because specialized ASIC miners are extremely fast compared to the estimated clock speed of near-term quantum computers. On the other hand, the elliptic curve signature scheme used by Bitcoin is much more at risk, and could be completely broken by a quantum computer as early as 2027, by the most optimistic estimates. We analyze an alternative proof-of-work called Momentum, based on finding collisions in a hash function, that is even more resistant to speedup by a quantum computer. We also review the available post-quantum signature schemes to see which one would best meet the security and efficiency requirements of blockchain applications.

RANDOM SURFACES AND THE LIOUVILLE THEORY

1992 ◽  
Vol 07 (15) ◽  
pp. 3403-3433 ◽  
Author(s):  
Y. KITAZAWA
Keyword(s):  
Black Holes ◽  
Physical Properties ◽  
Correlation Functions ◽  
Two Dimensions ◽  
Liouville Theory ◽  
View Point ◽  
Complete Understanding ◽  
Random Surfaces ◽  
Dimensional Gravity ◽  
The Continuum

We review the physical properties of random surfaces from the view point of the continuum Liouville theory. We shall summarize physical motivations of this subject and the field-theoretic treatment of the random surfaces. In the case of subcritical strings propagating in less than two dimensions, a complete understanding has been obtained recently through matrix models. We discuss the Liouville theory understanding of these results by studying the correlation functions. We also discuss promising avenues of further investigations such as black holes in 2-dimensional gravity and 3- and 4-dimensional string theory which may be relevant to Ising 3 and QCD 4.

scholarly journals Predicting permeability via statistical learning on higher-order microstructural information

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Magnus Röding ◽  
Zheng Ma ◽  
Salvatore Torquato
Keyword(s):  
Neural Networks ◽  
Physical Properties ◽  
Specific Surface ◽  
Correlation Functions ◽  
Quantitative Structure ◽  
Structure Property ◽  
Complex Materials ◽  
Structure Property Relationships ◽  
Quantitative Structure Property Relationships ◽  
Point Correlation

Abstract Quantitative structure–property relationships are crucial for the understanding and prediction of the physical properties of complex materials. For fluid flow in porous materials, characterizing the geometry of the pore microstructure facilitates prediction of permeability, a key property that has been extensively studied in material science, geophysics and chemical engineering. In this work, we study the predictability of different structural descriptors via both linear regressions and neural networks. A large data set of 30,000 virtual, porous microstructures of different types, including both granular and continuous solid phases, is created for this end. We compute permeabilities of these structures using the lattice Boltzmann method, and characterize the pore space geometry using one-point correlation functions (porosity, specific surface), two-point surface-surface, surface-void, and void-void correlation functions, as well as the geodesic tortuosity as an implicit descriptor. Then, we study the prediction of the permeability using different combinations of these descriptors. We obtain significant improvements of performance when compared to a Kozeny-Carman regression with only lowest-order descriptors (porosity and specific surface). We find that combining all three two-point correlation functions and tortuosity provides the best prediction of permeability, with the void-void correlation function being the most informative individual descriptor. Moreover, the combination of porosity, specific surface, and geodesic tortuosity provides very good predictive performance. This shows that higher-order correlation functions are extremely useful for forming a general model for predicting physical properties of complex materials. Additionally, our results suggest that artificial neural networks are superior to the more conventional regression methods for establishing quantitative structure–property relationships. We make the data and code used publicly available to facilitate further development of permeability prediction methods.

scholarly journals Application of Quantum Computing to Biochemical Systems: A Look to the Future

2020 ◽  
Vol 8 ◽  
Author(s):  
Hai-Ping Cheng ◽  
Erik Deumens ◽  
James K. Freericks ◽  
Chenglong Li ◽  
Beverly A. Sanders
Keyword(s):  
Quantum Computing ◽  
Physical System ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Active Regions ◽  
Quantum Computers ◽  
The Future ◽  
Biochemical Systems ◽  
Near Term ◽  
Different Levels

Chemistry is considered as one of the more promising applications to science of near-term quantum computing. Recent work in transitioning classical algorithms to a quantum computer has led to great strides in improving quantum algorithms and illustrating their quantum advantage. Because of the limitations of near-term quantum computers, the most effective strategies split the work over classical and quantum computers. There is a proven set of methods in computational chemistry and materials physics that has used this same idea of splitting a complex physical system into parts that are treated at different levels of theory to obtain solutions for the complete physical system for which a brute force solution with a single method is not feasible. These methods are variously known as embedding, multi-scale, and fragment techniques and methods. We review these methods and then propose the embedding approach as a method for describing complex biochemical systems, with the parts not only treated with different levels of theory, but computed with hybrid classical and quantum algorithms. Such strategies are critical if one wants to expand the focus to biochemical molecules that contain active regions that cannot be properly explained with traditional algorithms on classical computers. While we do not solve this problem here, we provide an overview of where the field is going to enable such problems to be tackled in the future.

scholarly journals ON THE CONSTRUCTION OF CORRELATION FUNCTIONS FOR THE INTEGRABLE SUPERSYMMETRIC FERMION MODELS

2006 ◽  
Vol 20 (05) ◽  
pp. 505-549 ◽  
Author(s):  
SHAO-YOU ZHAO ◽  
WEN-LI YANG ◽  
YAO-ZHONG ZHANG
Keyword(s):  
Correlation Function ◽  
Physical Properties ◽  
Correlation Functions ◽  
Recent Progress ◽  
Integrable Models ◽  
Thermodynamical Limit ◽  
Point Correlation ◽  
Point Correlation Function ◽  
The Creation ◽  
Scalar Products

We review the recent progress on the construction of the determinant representations of the correlation functions for the integrable supersymmetric fermion models. The factorizing F-matrices (or the so-called F-basis) play an important role in the construction. In the F-basis, the creation (and the annihilation) operators and the Bethe states of the integrable models are given in completely symmetric forms. This leads to the determinant representations of the scalar products of the Bethe states for the models. Based on the scalar products, the determinant representations of the correlation functions may be obtained. As an example, in this review, we give the determinant representations of the two-point correlation function for the Uq(gl(2|1)) (i.e. q-deformed) supersymmetric t-J model. The determinant representations are useful for analyzing physical properties of the integrable models in the thermodynamical limit.

scholarly journals SU(2) hadrons on a quantum computer via a variational approach

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Yasar Y. Atas ◽  
Jinglei Zhang ◽  
Randy Lewis ◽  
Amin Jahanpour ◽  
Jan F. Haase ◽  
...  
Keyword(s):  
Gauge Theory ◽  
Nuclear Physics ◽  
Variational Approach ◽  
Gauge Theories ◽  
Quantum Computer ◽  
Quantum Computers ◽  
Abelian Gauge ◽  
Quantum Simulations ◽  
Sign Problem ◽  
Matter Fields

AbstractQuantum computers have the potential to create important new opportunities for ongoing essential research on gauge theories. They can provide simulations that are unattainable on classical computers such as sign-problem afflicted models or time evolutions. In this work, we variationally prepare the low-lying eigenstates of a non-Abelian gauge theory with dynamically coupled matter on a quantum computer. This enables the observation of hadrons and the calculation of their associated masses. The SU(2) gauge group considered here represents an important first step towards ultimately studying quantum chromodynamics, the theory that describes the properties of protons, neutrons and other hadrons. Our calculations on an IBM superconducting platform utilize a variational quantum eigensolver to study both meson and baryon states, hadrons which have never been seen in a non-Abelian simulation on a quantum computer. We develop a hybrid resource-efficient approach by combining classical and quantum computing, that not only allows the study of an SU(2) gauge theory with dynamical matter fields on present-day quantum hardware, but further lays out the premises for future quantum simulations that will address currently unanswered questions in particle and nuclear physics.

Quantum theory, the Church–Turing principle and the universal quantum computer

1985 ◽  
Vol 400 (1818) ◽  
pp. 97-117 ◽  
Keyword(s):  
Quantum Theory ◽  
Complexity Theory ◽  
Turing Machine ◽  
Physical System ◽  
Quantum Computer ◽  
Physical Principle ◽  
Universal Turing Machine ◽  
Universal Quantum ◽  
Computing Machines ◽  
The Church

It is argued that underlying the Church–Turing hypothesis there is an implicit physical assertion. Here, this assertion is presented explicitly as a physical principle: ‘every finitely realizible physical system can be perfectly simulated by a universal model computing machine operating by finite means’. Classical physics and the universal Turing machine, because the former is continuous and the latter discrete, do not obey the principle, at least in the strong form above. A class of model computing machines that is the quantum generalization of the class of Turing machines is described, and it is shown that quantum theory and the 'universal quantum computer’ are compatible with the principle. Computing machines resembling the universal quantum computer could, in principle, be built and would have many remarkable properties not reproducible by any Turing machine. These do not include the computation of non-recursive functions, but they do include ‘quantum parallelism’, a method by which certain probabilistic tasks can be performed faster by a universal quantum computer than by any classical restriction of it. The intuitive explanation of these properties places an intolerable strain on all interpretations of quantum theory other than Everett’s. Some of the numerous connections between the quantum theory of computation and the rest of physics are explored. Quantum complexity theory allows a physically more reasonable definition of the ‘complexity’ or ‘knowledge’ in a physical system than does classical complexity theory.

Mathematical modeling of the correlation function and the energy spectra of the noise modulation function

2021 ◽  
pp. 77-92
Author(s):  
В.И. Воловач
Keyword(s):  
Mathematical Modeling ◽  
Correlation Function ◽  
Energy Spectrum ◽  
Correlation Functions ◽  
Narrow Band ◽  
Energy Spectra ◽  
Discrete Component ◽  
Modulation Function ◽  
Interference Modulation ◽  
Multiplicative Interference

Рассмотрены и проанализированы вопросы, связанные с математическим моделированием корреляционных функций и энергетических спектров функции помеховой модуляции. Показано, что при воздействии на сигнал узкополосной мультипликативной помехи в энергетическом спектре функции помеховой модуляции присутствует дискретная составляющая, мощность которой зависит от глубины фазовых искажений. При импульсно-флуктуационной модулирующей помехе с детерминированным тактовым интервалом энергетический спектр функции помеховой модуляции представляет собой сумму непрерывной и дискретной частей. The issues related to mathematical modeling of correlation functions and energy spectra of the noise modulation function are considered and analyzed. It is shown that when a signal is affected by a narrow-band multiplicative interference, a discrete component is present in the energy spectrum of the interference modulation function, the power of which depends on the depth of the phase distortion. In the case of pulse-fluctuating modulating interference with a deterministic clock interval, the energy spectrum of the interference modulation function is the sum of the continuous and discrete parts.

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