Towards Practical Quantum Simulation of Quantum Field Theories
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M Sohaib Alam↗
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Hidden Statistics Approach to Quantum Simulations
Recent advances in quantum information theory have inspired an explosion of interest in new quantum algorithms for solving hard computational (quantum and non-quantum) problems. The basic principle of quantum computation is that the quantum properties can be used to represent structure data, and that quantum mechanisms can be devised and built to perform operations with this data. Three basic non-classical properties of quantum mechanics superposition, entanglement, and direct-product decomposability were main reasons for optimism about capabilities of quantum computers that promised simultaneous processing of large massifs of highly correlated data. Unfortunately, these advantages of quantum mechanics came with a high price. One major problem is keeping the components of the computer in a coherent state, as the slightest interaction with the external world would cause the system to decohere. That is why the hardware implementation of a quantum computer is still unsolved. The basic idea of this work is to create a new kind of dynamical system that would preserve the main three properties of quantum physics superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods. In other words, such a system would reinforce the advantages and minimize limitations of both quantum and classical aspects. Based upon a concept of hidden statistics, a new kind of dynamical system for simulation of Schroedinger equation is proposed. The system represents a modified Madelung version of Schroedinger equation. It preserves superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods. Such an optimal combination of characteristics is a perfect match for simulating quantum systems. The model includes a transitional component of quantum potential (that has been overlooked in previous treatment of the Madelung equation). The role of the transitional potential is to provide a jump from a deterministic state to a random state with prescribed probability density. This jump is triggered by blowup instability due to violation of Lipschitz condition generated by the quantum potential. As a result, the dynamics attains quantum properties on a classical scale. The model can be implemented physically as an analog VLSI-based (very-large-scale integration-based) computer, or numerically on a digital computer. This work opens a way of developing fundamentally new algorithms for quantum simulations of exponentially complex problems that expand NASA capabilities in conducting space activities. It has been illustrated that the complexity of simulations of particle interaction can be reduced from an exponential one to a polynomial one.
Zak, Michail↗
Introduction to Quantum Simulation
This viewgraph presentation addresses the problem of efficiently simulating the evolution of a quantum system. The contents include: 1) Quantum Simulation; 2) Extracting Answers from Quantum Simulations; 3) Quantum Fourier Transform; 4) Eigenvalue Estimation; 5) Fermionic Simulations.
quantum simulation↗
Improved Fermion Hamiltonians for Quantum Simulation
The Symanzik improvement program has been quite successful in classical simulations of quantum chromodynamics allowing calculations to be performed at coarser lattice spacings and with reduced computational resource costs. It is expected that improved Hamiltonians will be essential to simulate lattice field theories using quantum computers. In this work I will discuss the formulation of an ASQTAD and HISQ Hamiltonian amenable for quantum simulations. I will also show preliminary results that demonstrate significant tree-level contributions are removed in the spectrum of the 1 flavor Schwinger model.
quantum computing↗
Quantum simulation of the yellow emission band of CsXe
Quantum spectral simulations of the yellow excimer emission band of CsXe are presented. Synthetic spectra as a function of wave number are calculated for the 2 Sigma 1/2 + (7s) - 2 Sigma 1/2 + (6s) transition by the use of the equation of Tellinghuisen et al. (1976) with a theoretical potential for the ground state and a Morse potential curve with an electron frequency of 32/cm for the excited state. Results based on emission studies at 450 K and 200 and 800 torr, are found to be consistent with absorption studies. The undulatory structure observed in the spectrum is attributed not to the vibrational spacing in the excited state, but rather to a characteristic reflection structure associated with nearly parallel upper and lower potential curves.
Tellinghuisen, J.↗
Effectively Leveraging NISQ Hardware for Quantum Simulations of Gauge Theories
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Noisy Intermediate Scale Quantum Computer↗
2D Quantum Simulation of MOSFET Using the Non Equilibrium Green's Function Method
The objectives this viewgraph presentation summarizes include: (1) the development of a quantum mechanical simulator for ultra short channel MOSFET simulation, including theory, physical approximations, and computer code; (2) explore physics that is not accessible by semiclassical methods; (3) benchmarking of semiclassical and classical methods; and (4) study other two-dimensional devices and molecular structure, from discretized Hamiltonian to tight-binding Hamiltonian.
Svizhenko, Alexel↗
Improved Fermion Hamiltonians for Quantum Simulations
Constructing improved hamiltonians for gauge theories coupled to fermonic matter will be important for improving continuum limit extrapolations of quantum computations. In this talk we will present a formulation for simulating ASQTAD fermions for lattice computation and provide fault tolerant resource costs in terms of primitive group operations. We additionally show that the scaling of energies with respect to the lattice spacing are better than for the unimproved Hamiltonian for toy models.
Quantum Algorithms↗
Improved Fermion Hamiltonians for Quantum Simulations
Constructing improved hamiltonians for gauge theories coupled to fermonic matter will be important for improving continuum limit extrapolations of quantum computations. In this talk we will present a formulation for simulating ASQTAD fermions for lattice computation and provide fault tolerant resource costs in terms of primitive group operations. We additionally show that the scaling of energies with respect to the lattice spacing are better than for the unimproved Hamiltonian for toy models.
Erik Joseph Gustafson↗
Improved Fermion Hamiltonians for Quantum Simulations
Constructing improved hamiltonians for gauge theories coupled to fermonic matter will be important for improving continuum limit extrapolations of quantum computations. In this talk we will present a formulation for simulating ASQTAD fermions for lattice computation and provide fault tolerant resource costs in terms of primitive group operations. We additionally show that the scaling of energies with respect to the lattice spacing are better than for the unimproved Hamiltonian for toy models.
Erik Gustafson↗
Quantum Simulation of Dihedral Gauge Theories
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M Sohaib Alam↗
Quantum Simulation of Dihedral Gauge Theories
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M Sohaib Alam↗
A Quantum Algorithm to Simulate Open Quantum Systems
Given the advent of quantum algorithms for a wide array of problems in linear algebra and machine learning, it is important to develop general methods for the simulation of arbitrary (ie non-unitary) operators on quantum hardware. In this talk, we present a novel quantum algorithm based on the quantum singular value transformation (QSVT) to apply an arbitrary operator K to some input state and subsequently estimate the expectation value of some observable. Our construction then immediately yields a route to estimating observables of states undergoing open quantum dynamics, whose effect is captured by a set of non-unitary Kraus operators. Our algorithm succeeds deterministically given the Sz-Nagy dilation, and we provide details on the algorithm's query and gate complexity, numerical verification, and comparisons with prior methods.
Quantum computing↗
A Quantum Algorithm to Simulate Open Quantum Systems
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quantum algorithm↗
Quantum Entanglement Molecular Absorption Spectrum Simulator
Quantum Entanglement Molecular Absorption Spectrum Simulator (QE-MASS) is a computer program for simulating two photon molecular-absorption spectroscopy using quantum-entangled photons. More specifically, QE-MASS simulates the molecular absorption of two quantum-entangled photons generated by the spontaneous parametric down-conversion (SPDC) of a fixed-frequency photon from a laser. The two-photon absorption process is modeled via a combination of rovibrational and electronic single-photon transitions, using a wave-function formalism. A two-photon absorption cross section as a function of the entanglement delay time between the two photons is computed, then subjected to a fast Fourier transform to produce an energy spectrum. The program then detects peaks in the Fourier spectrum and displays the energy levels of very short-lived intermediate quantum states (or virtual states) of the molecule. Such virtual states were only previously accessible using ultra-fast (femtosecond) laser systems. However, with the use of a single-frequency continuous wave laser to produce SPDC photons, and QEMASS program, these short-lived molecular states can now be studied using much simpler laser systems. QE-MASS can also show the dependence of the Fourier spectrum on the tuning range of the entanglement time of any externally introduced optical-path delay time. QE-MASS can be extended to any molecule for which an appropriate spectroscopic database is available. It is a means of performing an a priori parametric analysis of entangled photon spectroscopy for development and implementation of emerging quantum-spectroscopic sensing techniques. QE-MASS is currently implemented using the Mathcad software package.
Nguyen, Quang-Viet↗
Automistic Simulation of Quantum Dots Including Strain and Bandstructure and Full Band Simulation of Hole Transport in 1-D Heterostructures
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quantum dots strain tight binding hole transport↗
Efficient Multi-Dimensional Simulation of Quantum Confinement Effects in Advanced MOS Devices
We investigate the density-gradient (DG) transport model for efficient multi-dimensional simulation of quantum confinement effects in advanced MOS devices. The formulation of the DG model is described as a quantum correction to the classical drift-diffusion model. Quantum confinement effects are shown to be significant in sub-100nm MOSFETs. In thin-oxide MOS capacitors, quantum effects may reduce gate capacitance by 25% or more. As a result, the inclusion or quantum effects in simulations dramatically improves the match between C-V simulations and measurements for oxide thickness down to 2 nm. Significant quantum corrections also occur in the I-V characteristics of short-channel (30 to 100 nm) n-MOSFETs, with current drive reduced by up to 70%. This effect is shown to result from reduced inversion charge due to quantum confinement of electrons in the channel. Also, subthreshold slope is degraded by 15 to 20 mV/decade with the inclusion of quantum effects via the density-gradient model, and short channel effects (in particular, drain-induced barrier lowering) are noticeably increased.
Biegel, Bryan A.↗
Efficient Multi-Dimensional Simulation of Quantum Confinement Effects in Advanced MOS Devices
We investigate the density-gradient (DG) transport model for efficient multi-dimensional simulation of quantum confinement effects in advanced MOS devices. The formulation of the DG model is described as a quantum correction ot the classical drift-diffusion model. Quantum confinement effects are shown to be significant in sub-100nm MOSFETs. In thin-oxide MOS capacitors, quantum effects may reduce gate capacitance by 25% or more. As a result, the inclusion of quantum effects may reduce gate capacitance by 25% or more. As a result, the inclusion of quantum effects in simulations dramatically improves the match between C-V simulations and measurements for oxide thickness down to 2 nm. Significant quantum corrections also occur in the I-V characteristics of short-channel (30 to 100 nm) n-MOSFETs, with current drive reduced by up to 70%. This effect is shown to result from reduced inversion charge due to quantum confinement of electrons in the channel. Also, subthreshold slope is degraded by 15 to 20 mV/decade with the inclusion of quantum effects via the density-gradient model, and short channel effects (in particular, drain-induced barrier lowering) are noticeably increased.
Biegel, Bryan A.↗