Quantum Simulation of Dihedral Gauge Theories
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M Sohaib Alam↗
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Results for “quantum theory”
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On the Factorization of Secular Equations by Group Theory
Secular equation factorization in quantum mechanics of atoms, molecules, and crystals by group theory
FACTOR ANALYSIS↗
Applicability of perturbation theory to molecular problems.
Perturbation theory in molecular quantum physics using variational principles
PERTURBATION THEORY↗
Efficient Implementation for Unitary Coupled Cluster State Preparation for Near-Term Quantum Computers
Unitary coupled cluster theory (UCC) is a common wave function ansatz for quantum simulation of molecular electronic structure using the variational quantum eigenvalue solver (VQE). Even for small molecules using a double-ζ basis, the number of variational parameters required to minimize the electronic energy (i.e., optimize the circuit) is large and beyond the reach of current quantum computers. For example, a circuit simulating C2 using the UCCSD ansatz and the cc-pVDZ basis set with frozen-core will require over 10,000 variational parameters and a Hilbert space of over 10^(8) determinants. To make progress on simulating such molecular systems on near-term quantum computers, we explore how much of the optimization can be approximately prepared with classical simulation while reducing the number of optimization steps performed on a quantum device. Recently, Chen, Cheng, and Freericks [J. Chem. Theory Comput. 2021, 17, 841-847] presented an algorithm for the factorized form of the UCC ansatz that allows for efficient UCC optimizations on classical hardware. We flip the algorithm around and use it to prepare approximate quantum circuits for systems that require a large number of qubits to represent. We will present results from our implementation and discuss strategies for incorporating this implementation for algorithms involving near-term quantum computers.
Quantum Computing↗
Efficient Implementation for Unitary Coupled Cluster State Preparation for Near-Term Quantum Computers
Unitary coupled cluster theory (UCC) is a common wave function ansatz for quantum simulation of molecular electronic structure using the variational quantum eigenvalue solver (VQE). Even for small molecules using a double-ζ basis, the number of variational parameters required to minimize the electronic energy (i.e., optimize the circuit) is large and beyond the reach of current quantum computers. For example, a circuit simulating C2 using the UCCSD ansatz and the cc-pVDZ basis set with frozen-core will require over 10,000 variational parameters and a Hilbert space of over 10^(8) determinants. To make progress on simulating such molecular systems on near-term quantum computers, we explore how much of the optimization can be approximately prepared with classical simulation while reducing the number of optimization steps performed on a quantum device. Recently, Chen, Cheng, and Freericks [J. Chem. Theory Comput. 2021, 17, 841-847] presented an algorithm for the factorized form of the UCC ansatz that allows for efficient UCC optimizations on classical hardware. We flip the algorithm around and use it to prepare approximate quantum circuits for systems that require a large number of qubits to represent. We will present results from our implementation and discuss strategies for incorporating this implementation for algorithms involving near-term quantum computers.
Quantum Computing↗
Efficient Implementation for Unitary Coupled Cluster State Preparation for Near-Term Quantum Computers
Unitary coupled cluster theory (UCC) is a common wave function ansatz for quantum simulation of molecular electronic structure using the variational quantum eigenvalue solver (VQE). Even for small molecules using a double-ζ basis, the number of variational parameters required to minimize the electronic energy (i.e., optimize the circuit) is large and beyond the reach of current quantum computers. For example, a circuit simulating C2 using the UCCSD ansatz and the cc-pVDZ basis set with frozen-core will require over 10,000 variational parameters and a Hilbert space of over 10^8 determinants. To make progress on simulating such molecular systems on near-term quantum computers, we explore how much of the optimization can be approximately prepared with classical simulation while reducing the number of optimization steps performed on a quantum device. Recently, Chen, Cheng, and Freericks [J. Chem. Theory Comput. 2021, 17, 841-847] presented an algorithm for the factorized form of the UCC ansatz that allows for efficient UCC optimizations on classical hardware. We flip the algorithm around and use it to prepare approximate quantum circuits for systems that require a large number of qubits to represent. We will present results from our implementation and discuss strategies for incorporating this implementation for algorithms involving near-term quantum computers.
J Wayne Mullinax↗
Rotational excitation of HCN by collisions
Rate constants for the rotational excitation of HCN by collisions with He atoms at temperatures below 100 K were computed from first principles and are presented in tabular form. The potential energy surface was obtained by using the uniform electron gas model of Gordon and Kim (1972) and then joined smoothly to the asymptotic long-range perturbation theory potential valid at large separations. Quantum close-coupling theory was used to analyze the collision dynamics. Individual rates are believed to be accurate to within 50% above 30 K and within a factor of two below 20 K. The results should be extendable to excitation by collision with H2 and may therefore be of value in the study of interstellar clouds.
Green, S.↗
Quantum algorithms for lattice phi^4 theory
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M Sohaib Alam↗
Space QUEST Mission Proposal: Experimentally Testing Decoherence Due to Gravity
Models of quantum systems on curved space-times lack sufficient experimental verification. Some speculative theories suggest that quantum properties, such as entanglement, may exhibit entirely different behavior to purely classical systems. By measuring this effect or lack thereof, we can test the hypotheses behind several such models. For instance, as predicted by Ralph and coworkers [T C Ralph, G J Milburn, and T Downes, Phys. Rev. A, 79(2):22121, 2009; T C Ralph and J Pienaar, New Journal of Physics, 16(8):85008, 2014], a bipartite entangled system could decohere if each particle traversed through a different gravitational field gradient. We propose to study this effect in a ground to space uplink scenario. We extend the above theoretical predictions of Ralph and coworkers and discuss the scientific consequences of detecting/failing to detect the predicted gravitational decoherence. We present a detailed mission design of the European Space Agency's (ESA) Space QUEST (Space - Quantum Entanglement Space Test) mission, and study the feasibility of the mission schema.
Entanglement↗
Perturbation theory of the constrained variational method in molecular quantum mechanics.
Energy minimization for trial wave function constrained to give expectation value of operator
PERTURBATION THEORY↗
Experimental verification of the photodiode theory of SIS mixers
The authors describe the characterization and interpretation of the performance of SIS receivers within the framework of the photodiode theory of mixing. The quantum efficiency plays a dominant role in the theory, and a simple method of accurately measuring this parameter is presented. It is demonstrated that the quantum efficiency measurements can be conveniently made on a standard radio astronomy receiver and combined with the usual hot and cold load characterization to improve the understanding of the receiver's performance. The measurements verify that the photodiode theory of mixing accurately describes the receiver noise even at local-oscillator power levels well above the linear response range. The results for receivers operating at 100 and 240 GHz verify the utility of this approach. These methods should also prove useful in evaluating submillimeter receivers.
Woody, David P.↗
Semiclassical S-matrix theory of vibrationally inelastic collisions between two diatomic molecules
We derive a semiclassical S matrix for vibrationally inelastic collisions between two diatomic molecules, assuming a collinear geometry. Our theory incorporates a quantum mechanical superposition principle with classical dynamics and, as such, is an extension of the atom-diatomic molecule theory of Miller. The several approximations to the S matrix differ in the complexity with which the interference between various classical trajectories is treated. We report numerical calculations for H2-D2 and D2-D2 collisions based on two different interaction potentials. The cruder approximations yield transition probabilities which agree with exact quantum mechanical results to within a factor of 2. More sophisticated approximations to the S matrix yield excellent quantitative agreement with the quantum calculations.
Cohen, S. C.↗
Theory of collision effects on line shapes using a quantum mechanical description of the atomic center of mass motion - Application to lasers
Quantum mechanical treatment of atomic center of mass motion in theory of collision effects on line shapes
Berman, P. R.↗
Theory and Development of Position-Sensitive Quantum Calorimeters
Quantum calorimeters are being developed as imaging spectrometers for future X-ray astrophysics observatories. Much of the science to be done by these instruments could benefit greatly from larger focal-plane coverage of the detector (without increasing pixel size). An order of magnitude more area will greatly increase the science throughput of these future instruments. One of the main deterrents to achieving this goal is the complexity of the readout schemes involved. We have devised a way to increase the number of pixels from the current baseline designs by an order of magnitude without increasing the number of channels required for readout. The instrument is a high energy resolution, distributed-readout imaging spectrometer called a Position-Sensitive Transition-Edge Sensor (POST). A POST is a quantum calorimeter consisting of two Transition-Edge Sensors (TESS) on the ends of a long absorber capable of one-dimensional imaging spectroscopy. Comparing rise time and energy information from the two TESS, the position of the event in the POST is determined. The energy of the event is inferred from the sum of the two pulses. We have developed a generalized theoretical formalism for distributed-readout calorimeters and apply it to our devices. We derive the noise theory and calculate the theoretical energy resolution of a POST. Our calculations show that a 7-pixel POST with 6 keV saturation energy can achieve 2.3 eV resolution, making this a competitive design for future quantum calorimeter instruments. For this thesis we fabricated 7- and 15-pixel POSTS using Mo/Au TESs and gold absorbers, and moved from concept drawings on scraps of napkins to a 32 eV energy resolution at 1.5 keV, 7-pixel POST calorimeter.
Figueroa-Feliciano, Enectali↗
Recent developments in perturbation theory
Rayleigh-Schroeder perturbation theory - degenerate and non-degenerate states - quantum chemistry - other perturbation equations
PERTURBATION THEORY↗
Benchmark calculations of thermal reaction rates. I - Quantal scattering theory
The thermal rate coefficient for the prototype reaction H + H2 yields H2 + H with zero total angular momentum is calculated by summing, averaging, and numerically integrating state-to-state reaction probabilities calculated by time-independent quantum-mechanical scattering theory. The results are very carefully converged with respect to all numerical parameters in order to provide high-precision benchmark results for confirming the accuracy of new methods and testing their efficiency.
Chatfield, David C.↗
Second International Workshop on Harmonic Oscillators
The Second International Workshop on Harmonic Oscillators was held at the Hotel Hacienda Cocoyoc from March 23 to 25, 1994. The Workshop gathered 67 participants; there were 10 invited lecturers, 30 plenary oral presentations, 15 posters, and plenty of discussion divided into the five sessions of this volume. The Organizing Committee was asked by the chairman of several Mexican funding agencies what exactly was meant by harmonic oscillators, and for what purpose the new research could be useful. Harmonic oscillators - as we explained - is a code name for a family of mathematical models based on the theory of Lie algebras and groups, with applications in a growing range of physical theories and technologies: molecular, atomic, nuclear and particle physics; quantum optics and communication theory.
Han, Daesoo↗
Light ion components of the galactic cosmic rays: Nuclear interactions and transport theory
Light nuclei are present in the primary galactic cosmic rays (GCR) and are produced in thick targets due to projectile or target fragmentation from both nucleon and heavy induced reactions. In the primary GCR, He-4 is the most abundant nucleus after H-1. However, there are also a substantial fluxes of H-2 and He-3. In this paper we describe theoretical models based on quantum multiple scattering theory for the description of light ion nuclear interactions. The energy dependence of the light ion fragmentation cross section is considered with comparisons of inclusive yields and secondary momentum distributions to experiments described. We also analyze the importance of a fast component of lights ions from proton and neutron induced target fragementation. These theoretical models have been incorporated into the cosmic ray transport code HZETRN and will be used to analyze the role of shielding materials in modulating the production and the energy spectrum of light ions.
Cucinotta, F. A.↗