arXiv subjects

Michael McGuigan

Publications and source records attributed to Michael McGuigan.

At least 19 recordsLinked to original sources

arXiv2023

Quantum Cosmology and Black Hole Interiors in Nonsupersymmetric String Theory and Canonical Gravity

In this paper we study black hole interior solutions and cosmologies in different dimensions using tools from canonical gravity and nonsupersymmetric string quantum cosmology. We find that the quantum wave functions associated with these solutions can be related to each other by a specific choice of variables. In a more realistic four dimensional setting we combine canonical gravity and nonsupersymmetric string orbifold compactifications. We discuss the classical solutions and the corresponding wave functions involving inflation, the Higgs field, dark matter and hidden gauge sectors in these models. Finally we discuss string aspects of these models such as duality, massive modes, and nonperturbative approaches such as Matrix theory and holography near the singularity.

hep-th↗

arXiv2023

Two Matrix Model, the Riemann Hypothesis and Master Matrix Obstruction

We identify the Riemann Xi function as the Baker-Akhiezer function for a (p,1) two matrix model as p goes to infinity. We solve the two matrix model using biorthogonal polynomials and study the zeros of the polynomials in the double scaling limit as N goes to infinity. We find zeros off the critical line at finite N which possibly go to infinity as N goes to infinity. We study other Baker-Akhiezer functions whose zeros are known to be on a critical line using the two matrix model technique and find the zeros on the critical line in those cases. We study other L-functions using the two matrix model and compare the biorthogonal method with other approaches to the two matrix model such as the master matrix approach and saddle point method. In cases where there are zeros off the critical line the master matrix approach encounters an obstruction to the solution to a quenched master matrix.

math.NT↗

arXiv2023

Quantum Computing and the Riemann Hypothesis

Quantum computing is a promising new area of computing with quantum algorithms offering a potential speedup over classical algorithms if fault tolerant quantum computers can be built. One of the first applications of the classical computer was to the study of the Riemann hypothesis and quantum computers may be applied to this problem as well. In this paper we apply the Quantum Fourier Transform (QFT) to study three functions with non-trivial zeros obeying a version of the Riemann hypothesis. We perform our quantum computations with six qubits, but more qubits can be used if quantum error correction allows the QFT algorithm to scale. We represent these functions as ground state wave functions transformed to momentum space. We show how to obtain these functions as states in supersymmetric quantum mechanics. Finally we discuss the relation of these functions to (p,1) Random two matrix models at large N.

quant-ph↗

arXiv2023

Infinity Wars: Three Types of Singularities in Non-supersymmetric Canonical Gravity and String Theory

We discuss three separate types of infinities that occur in non-supersymmetric canonical gravity and string theory. We consider UV perturbative singularities in non-supersymmetric gravity coupled to matter and how these are related to loop corrections to beta functions for non-supersymmetric strings. Next we consider classical cosmological singularities that occur in these equations and discuss a specific singular cosmology of Dudas and Mourad for non-supersymmetric string theory. Finally we discuss the infinities that occur in quantum cosmology associated with topology change and discuss how non-supersymmetric string quantum cosmology can be used to address them.

hep-th↗

arXiv2022

A Matrix Big Bang on a Quantum Computer

M-theory is a mysterious theory that seeks to unite different string theories in one lower dimension. The most studied example is eleven dimensional but other dimensions have been considered. The non-critical M-theories seek to unite different non-critical string theories. From the point of view of computing, non-critical M-theories should be simpler to simulate as they have fewer fields than eleven dimensional M-theory. The simplicity of non-critical M-theory carries over to quantum computing and we show that the quantum simulation requires fewer qubits and Pauli terms than critical M-theory. As an example quantum calculation we study the quantum computation of the ground state energy of Matrix models of non-critical M-theory in 3d in the finite difference and oscillator basis and compare the accuracy, number of qubits and number of Pauli terms of the different basis using the Variational Quantum Eigensolver (VQE) algorithm. We study non-critical M- Theory solutions with space-time singularities referred to as a "Matrix Big Bang" on the Quantum Computer using the Evolution of Hamiltonian (EOH) quantum algorithm using the Trotter approximation and compare the accuracy and results the can be obtained using quantum computation. Finally we consider the BRST quantization of the 3d M-theory Matrix model using quantum computation and compute BRST invariant states by studying the BRST Laplacian using the VQE algorithm.

quant-ph↗

arXiv2022

Quantum Computing for Rotating, Charged and String Theory Black Holes

The quantum mechanics of Rotating, Charged, de Sitter and String Theory black holes are of recent interest because of their peculiar thermodynamic properties, as well the mysterious nature of their microstates. A full quantum treatment of the operators involved in this systems could yield valuable information into their nature, similar to how quantum treatment yields valuable insight into atoms, molecules and elementary particles. We study four types of black holes using quantum computing, which include the 3D Rotating Banados-Teitelboim-Zanelli (BTZ) black hole, the 4D charged Reisner-Nordtrom (RN) black hole, the 4D charged Reisner-Nordstrom -de Sitter (RN-dS) black hole and the 2D charged string black hole. In these cases in addition to the Hamiltonian there is a Mass operator which plays an important role in describing the quantum states of the black hole. We compute the spectrum of these operators using classical and quantum computing. For quantum computing we use the Variational Quantum Eigensolver (VQE) which is hybrid classical-quantum algorithm that runs on near term quantum hardware. We perform our calculations using 4 qubits in both a harmonic oscillator and position basis, realizing the quantum operators of the black holes in terms of 16 x 16 matrices. For the 4 qubit case we find highly accurate results for the Mass eigenvalues for different values of the charge and angular momentum. For the 2D Charged String black hole we also use the VQE to compute the expectation value of the Hamiltonian constraint and the commutator of the Hamiltonian constraint with the mass operator and find excellent agreement with theoretical expectations.

quant-ph↗

arXiv2022

Superconformal Quantum Mechanics on a Quantum Computer

We investigate superconformal quantum mechanics (SCQM) on a quantum computer. We study the ground state of the mass deformed SCQM on a quantum computed using the Variational Quantum Eigensolver (VQE) using a one boson and one boson - one fermion Hilbert space with and without noise and compare the accuracy of the results. We study the Feynman path integral for SCQM using the Evolution of Hamiltonian (EOH) algorithm on the quantum computer using the Trotter-Suzuki approximation and compare with the exact result. We consider an N boson and N fermion version of SCQM given be the Supersymmetric Calogero-Moser-Sutherland (SCMS) model. We compare the ground state of SCMS theory obtained using the VQE computation with the exact solution. Finally we discuss the implications of the the numerical simulation of SCQM on a quantum computer for the simulation of quantum gravity in light of the Anti-de Sitter/Superconformal field theory (AdS/CFT) correspondence.

quant-ph↗

arXiv2022

Quantum Computing of Schwarzschild-de Sitter Black Holes and Kantowski-Sachs Cosmology

The quantum mechanics of Schwarzschild-de Sitter black holes is of great recent interest because of their peculiar thermodynamic properties as well as their realization in modern dark energy cosmology which indicates the presence of a small positive cosmological constant. We study Schwarzschild-de Sitter black holes and also the Kantowki-Sachs Cosmology using quantum computing. In these cases in addition to the Hamiltonian there is a Mass operator which plays an important role in describing the quantum states of the black hole and Kantowski-Sachs cosmology. We compute the spectrum of these operators using classical and quantum computing. For quantum computing we use the Variational Quantum Eigensolver which is hybrid classical-quantum algorithm that runs on near term quantum hardware. We perform our calculations using 4, 6 and 8 qubits in a harmonic oscillator basis, realizing the quantum operators of the Schwarzschild-de Sitter black hole and Kantowski-Sachs cosmology in terms of 16 x 16, 64 x 64 and 256 x 256 matrices respectively. For the 4 qubit case we find highly accurate results but for the other cases we find a more refined variational ansatz will be necessary to represent the quantum states of a Schwarzschild-de Sitter black hole or Kantowki-Sachs cosmology accurately on a quantum computer.

quant-ph↗

arXiv2021

Worldline Path Integrals for Gauge Fields and Quantum Computing

We study different aspects the worldline path integrals with gauge fields using quantum computing. We use the Variational Quantum Eigensolver (VQE) and Evolution of Hamiltonian (EOH) quantum algorithms and IBM QISKit to perform our computations. We apply these methods to the path integral of a particle moving in a Abelian and non-Abelian background gauge field associated with a constant magnetic field and the field of a chromo-magnetic field. In all cases we found excellent agreement with the classical computation. We also discuss the insertion of vertex operators into the worldline path integrals to study scattering and show how to represent them using unitary operators and quantum gates on near term quantum computers.

quant-ph↗

arXiv2021

Matrix Model simulations using Quantum Computing, Deep Learning, and Lattice Monte Carlo

Matrix quantum mechanics plays various important roles in theoretical physics, such as a holographic description of quantum black holes. Understanding quantum black holes and the role of entanglement in a holographic setup is of paramount importance for the development of better quantum algorithms (quantum error correction codes) and for the realization of a quantum theory of gravity. Quantum computing and deep learning offer us potentially useful approaches to study the dynamics of matrix quantum mechanics. In this paper we perform a systematic survey for quantum computing and deep learning approaches to matrix quantum mechanics, comparing them to Lattice Monte Carlo simulations. In particular, we test the performance of each method by calculating the low-energy spectrum.

quant-ph↗

arXiv2021

Quantum Walks, Feynman Propagators and Graph Topology on an IBM Quantum Computer

Topological data analysis is a rapidly developing area of data science where one tries to discover topological patterns in data sets to generate insight and knowledge discovery. In this project we use quantum walk algorithms to discover features of a data graph on which the walk takes place. This can be done faster on quantum computers where all paths can be explored using superposition. We begin with simple walks on a polygon and move up to graphs described by higher dimensional meshes. We use insight from the physics description of quantum walks defined in terms of probability amplitudes to go from one site on a graph to another distant site and show how this relates to the Feynman propagator or Kernel in the physics terminology. Our results from quantum computation using IBM's Qiskit quantum computing software were in good agreement with those obtained using classical computing methods.

quant-ph↗

arXiv2021

Quantum Computing for Inflationary, Dark Energy and Dark Matter Cosmology

Cosmology is in an era of rapid discovery especially in areas related to dark energy, dark matter and inflation. Quantum cosmology treats the cosmology quantum mechanically and is important when quantum effects need to be accounted for, especially in the very early Universe. Quantum computing is an emerging new method of computing which excels in simulating quantum systems. Quantum computing may have some advantages when simulating quantum cosmology, especially because the Euclidean action of gravity is unbounded from below, making the implementation of Monte Carlo simulation problematic. In this paper we present several examples of the application of quantum computing to cosmology. These include a dark energy model that is related to Kaluza-Klein theory, dark matter models where the dark sector is described by a self interacting gauge field or a conformal scalar field and an inflationary model with a slow roll potential. We implement quantum computations in the IBM QISKit software framework and show how to apply the Variational Quantum Eigensolver (VQE) and Evolution of Hamiltonian (EOH) algorithms to solve the Wheeler-DeWitt equation that can be used to describe the cosmology in the mini-superspace approximation. We find excellent agreement with classical computing results and describe the accuracy of the different quantum algorithms. Finally we discuss how these methods can be scaled to larger problems going beyond the mini-superspace approximation where the quantum computer may exceed the performance of classical computation.

quant-ph↗

arXiv2021

Effective Matrix Model for Gauge Theories at Finite Temperature and Density using Quantum Computing

We study the effective matrix model for for gauge fields and fermions on a quantum computer. We use the Variational Quantum Eigensolver (VQE) using IBM QISKit for the effective matrix model for SU(2) and SU(3) including fermions in the fundamental representation. For SU(2) we study the effects of finite temperature and nonzero chemical potential. In all cases we find excellent agreement with the classical computation.

quant-ph↗

arXiv2021

Z3 gauge theory coupled to fermions and quantum computing

We study the Z3 gauge theory with fermions on the quantum computer using the Variational Quantum Eigensolver (VQE) algorithm with IBM QISKit software. Using up to 9 qubits we are able to obtain accurate results for the ground state energy. Introducing nonzero chemical potential we are able to determine the Equation of State (EOS) for finite density on the quantum computer. We discuss possible realizations of quantum advantage for this system over classical computers with regards to finite density simulations and the fermion sign problem.

quant-ph↗

arXiv2021

Casimir energy with chiral fermions on a quantum computer

In this paper we discuss the computation of Casimir energy on a quantum computer. The Casimir energy is an ideal quantity to calculate on a quantum computer as near term hybrid classical quantum algorithms exist to calculate the ground state energy and the Casimir energy gives physical implications for this quantity in a variety of settings. Depending on boundary conditions and whether the field is bosonic or fermionic we illustrate how the Casimir energy calculation can be set up on a quantum computer and calculated using the Variational Quantum Eigensolver algorithm with IBM QISKit. We compare the results based on a lattice regularization with a finite number of qubits with the continuum calculation for free boson fields, free fermion fields and chiral fermion fields. We use a regularization method introduced by Bergman and Thorn to compute the Casimir energy of a chiral fermion. We show how the accuracy of the calculation varies with the number of qubits. We show how the number of Pauli terms which are used to represent the Hamiltonian on a quantum computer scales with the number of qubits. We discuss the application of the Casimir calculations on quantum computers to cosmology, nanomaterials, string models, Kaluza Klein models and dark energy.

quant-ph↗

arXiv2021

Morse Potential on a Quantum Computer for Molecules and Supersymmetric Quantum Mechanics

In this paper we discuss the Morse potential on a quantum computer. The Morse potential is useful to describe diatomic molecules and has a finite number of bound states which can be measured through spectroscopy. It is also a example of an exactly soluble potential using supersymmetric quantum mechanics. Using the the supersymmetric quantum mechanics formalism one can derive a heirachy of Hamiltonians such that the ground state of the next rung on the heirarchy yeids the first excited state of the hamiltonian below it. Using this method one can determine all the states of the Morse potential by calculating all the ground states of the sequence of Hamiltonians in the heirarchy. We use the IBM QISKit software together with the Variational Quantum Eiegensolver (VQE) algorithm to calculate the ground state and first excited state energy of the Morse potential and find agreement with the exact expression for the bound state energies of the Morse Potential. We analyze different optimizers to study the numerical effect on the calculations. Finally we perform quantum computations for diatomic and triatomic molecules to illustrate the application of these techniques on near term quantum computers and find excellent agreement with experimental data.

quant-ph↗

arXiv2020

Pandemic modeling and the renormalization group equations: Effect of contact matrices, fixed points and nonspecific vaccine waning

In this paper we find common features between the equations that are used for pandemic or epidemic modeling and the renormalization group equations that are used in high energy physics. Some of these features include the relation of contact matrices in pandemic modeling and operator mixing in the renormalization group equations. Another common feature are the use of flow diagrams and the study of fixed points both in pandemic modeling and in evolution under renormalization group equations. We illustrate these relations through the study of some cases of interest to the current COVID-19 pandemic. These include pandemic modeling with mixing between different age groups and also contact matrices associated with contact between countries. For the final example we study the effect on mortality of waning from nonspecific vaccines which are designed to combat different pathogens but nevertheless may lessen the severity and mortality of COVID-19 infections.

q-bio.QM↗

arXiv2020

Riemann Hypothesis, Modified Morse Potential and Supersymmetric Quantum Mechanics

In this paper we discuss various potentials related to the Riemann zeta function and the Riemann Xi function. These potentials are modified versions of Morse potentials and can also be related to modified forms of the radial harmonic oscillator and modified Coulomb potential. We use supersymmetric quantum mechanics to construct their ground state wave functions and the Fourier transform of the ground state to exhibit the Riemann zeros. This allows us to formulate the Riemann hypothesis in terms of the location of the nodes of the ground state wave function in momentum space. We also discuss the relation these potentials to one and two matrix integrals and construct a few orthogonal polynomials associated with the matrix models. We relate the Schrodinger equation in momentum space to and finite difference equation in momentum space with an infinite number of terms. We computed the uncertainty relations associated with these potentials and ground states as well as the Shannon Information entropy and compare with the unmodified Morse and harmonic oscillator potentials. Finally we discuss the extension of these methods to other functions defined by a Dirichlet series such as the the Ramanujan zeta function.

math-ph↗