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Articles 1 - 30 of 1290
Full-Text Articles in Quantum Physics
High-Frequency Diode Effect In Superconducting Nb3Sn Microbridges, Sara Chahid, Serafim Teknowijoyo, Iris Mowgood, Armen Gulian
High-Frequency Diode Effect In Superconducting Nb3Sn Microbridges, Sara Chahid, Serafim Teknowijoyo, Iris Mowgood, Armen Gulian
Mathematics, Physics, and Computer Science Faculty Articles and Research
The superconducting diode effect has recently been reported in a variety of systems and different symmetry-breaking mechanisms have been examined. However, the frequency range of these potentially important devices still remains obscure. We investigated superconducting microbridges of Nb3Sn in out-of-plane magnetic fields; optimum magnetic fields of ∼10 mT generate ∼10% diode efficiency, while higher fields of ∼15–20 mT quench the effect. The diode changes its polarity with magnetic field reversal. We documented superconductive diode rectification at frequencies up to 100 kHz, the highest reported as of today. Interestingly, the bridge resistance during diode operation reaches a value that is a …
A Quantum Approach To Language Modeling, Constantijn Van Der Poel
A Quantum Approach To Language Modeling, Constantijn Van Der Poel
Dissertations, Theses, and Capstone Projects
This dissertation consists of six chapters. . . Chapter 1: We introduce language modeling, outline the software used for this thesis, and discuss related work. Chapter 2: We will unpack the transition from classical to quantum probabilities, as well as motivate their use in building a model to understand language-like datasets. Chapter 3: We motivate the Motzkin dataset, the models we will be investigating, as well as the necessary algorithms to do calculations with them. Chapter 4: We investigate our models’ sensitivity to various hyperparameters. Chapter 5: We compare the performance and robustness of the models. Chapter 6: We conclude …
"Semiclassical Mastermind", Curtis Bair, Alexa S. Cunningham, Joshua Qualls
"Semiclassical Mastermind", Curtis Bair, Alexa S. Cunningham, Joshua Qualls
Posters-at-the-Capitol
Games are often used in the classroom to teach mathematical and physical concepts. Yet the available activities used to introduce quantum mechanics are often overwhelming even to upper-level students. Further, the "games" in question range in focus and complexity from superficial introductions to games where quantum strategies result in decidedly nonclassical advantages, making it nearly impossible for people interested in quantum mechanics to have a simple introduction to the topic. In this talk, we introduce a straightforward and newly developed "Semiclassical Mastermind" based on the original version of mastermind but replace the colored pegs with 6 possible qubits (x+, x-, …
Gluon Transverse-Momentum-Dependent Distributions From Large-Momentum Effective Theory, Ruilin Zhu, Yao Ji, Jian-Hui Zhang, Shuai Zhao
Gluon Transverse-Momentum-Dependent Distributions From Large-Momentum Effective Theory, Ruilin Zhu, Yao Ji, Jian-Hui Zhang, Shuai Zhao
Physics Faculty Publications
We demonstrate that gluon transverse-momentum-dependent parton distribution functions (TMDPDFs) can be extracted from lattice calculations of appropriate Euclidean correlations in large-momentum effective theory (LaMET). Based on perturbative calculations of gluon unpolarized and helicity TMDPDFs, we present a matching formula connecting them and their LaMET counterparts, where the latter are renormalized in a scheme facilitating lattice calculations and converted to the MS ¯ scheme. The hard matching kernel is given up to one-loop level. We also show that the perturbative result is independent of the prescription used for the pinch-pole singularity in the relevant correlations. Our results offer a guidance for …
Prospects For 𝛾*𝛾* → 𝜋𝜋 Via Lattice Qcd, Raúl Briceño, Andrew W. Jackura, Arkaitz Rodas, Juan V. Guerrero
Prospects For 𝛾*𝛾* → 𝜋𝜋 Via Lattice Qcd, Raúl Briceño, Andrew W. Jackura, Arkaitz Rodas, Juan V. Guerrero
Physics Faculty Publications
The 𝛾*𝛾* → 𝜋𝜋 scattering amplitude plays a key role in a wide range of phenomena, including understanding the inner structure of scalar resonances as well as constraining the hadronic contributions to the anomalous magnetic moment of the muon. In this work, we explain how the infinite-volume Minkowski amplitude can be constrained from finite-volume Euclidean correlation functions. The relationship between the finite-volume Euclidean correlation functions and the desired amplitude holds up to energies where 3𝜋 states can go on shell, and is exact up to exponentially small corrections that scale like 𝒪(e−m𝜋L), where L is the spatial extent …
Observation Of Correlations Between Spin And Transverse Momenta In Back-To-Back Dihadron Production At Clas12, H. Avakian, T.B. Hayward, A. Kotzinian, W.R. Armstrong, H. Atac, C. Ayerbe Gayoso, L. Baashen, N.A. Balzell, L. Barion, M. Bashkanov, M. Battaglieri, I. Bedlinskiy, B. Benkel, F. Benmokhtar, A. Bianconi, L. Biondo, A. S. Biselli, M. Bondi, S. Boiarinov, M. Zurek, Et Al.
Observation Of Correlations Between Spin And Transverse Momenta In Back-To-Back Dihadron Production At Clas12, H. Avakian, T.B. Hayward, A. Kotzinian, W.R. Armstrong, H. Atac, C. Ayerbe Gayoso, L. Baashen, N.A. Balzell, L. Barion, M. Bashkanov, M. Battaglieri, I. Bedlinskiy, B. Benkel, F. Benmokhtar, A. Bianconi, L. Biondo, A. S. Biselli, M. Bondi, S. Boiarinov, M. Zurek, Et Al.
Physics Faculty Publications
We report the first measurements of deep inelastic scattering spin-dependent azimuthal asymmetries in back-to-back dihadron electroproduction in the deep inelastic scattering process. In this reaction, two hadrons are produced in opposite hemispheres along the z axis in the virtual photon-target nucleon center-of-mass frame, with the first hadron produced in the current-fragmentation region and the second in the target-fragmentation region. The data were taken with longitudinally polarized electron beams of 10.2 and 10.6 GeV incident on an unpolarized liquid-hydrogen target using the CLAS12 spectrometer at Jefferson Lab. Observed nonzero sinΔϕ modulations in ep→e'pπ+ X events, where Δϕ is the difference …
A Multidimensional Study Of The Structure Function Ratio Σlt'/ Σ₀ From Hard Exclusive 𝜋⁺ Electro-Production Off Protons In The Gpd Regime, S. Diehl, A. Kim, K. Joo, P. Achenbach, Z. Akbar, M. J. Amaryan, H. Atac, H. Avagyan, C. Ayerbe Gayoso, L. Baashen, L. Barion, M. Bashkanov, M. Battaglieri, I. Bedlinsky, B. Benkel, F. Benmokhtar, A. Bianconi, A. S. Biselli, M. Bondi, W.A. Booth, M. Zurek, Et Al.
A Multidimensional Study Of The Structure Function Ratio Σlt'/ Σ₀ From Hard Exclusive 𝜋⁺ Electro-Production Off Protons In The Gpd Regime, S. Diehl, A. Kim, K. Joo, P. Achenbach, Z. Akbar, M. J. Amaryan, H. Atac, H. Avagyan, C. Ayerbe Gayoso, L. Baashen, L. Barion, M. Bashkanov, M. Battaglieri, I. Bedlinsky, B. Benkel, F. Benmokhtar, A. Bianconi, A. S. Biselli, M. Bondi, W.A. Booth, M. Zurek, Et Al.
Physics Faculty Publications
A multidimensional extraction of the structure function ratio from the hard exclusive →ep → e'n𝜋+ reaction above the resonance region has been performed. The study was done based on beam-spin asymmetry measurements using a 10.6 GeV incident electron beam on a liquid-hydrogen target and the CLAS12 spectrometer at Jefferson Lab. The measurements focus on the very forward regime (t/Q2≪ 1) with a wide kinematic range of in the valence regime (0.17 < 𝓍B < 0.55), and virtualities ranging from 1.5 GeV2 up to 6 GeV2. The results and their comparison to theoretical models based on Generalized Parton Distributions demonstrate the sensitivity to chiral-odd …
Golay Codes And Quantum Contextuality, Mordecai Waegell, P. K. Aravind
Golay Codes And Quantum Contextuality, Mordecai Waegell, P. K. Aravind
Mathematics, Physics, and Computer Science Faculty Articles and Research
It is shown that the codewords of the binary and ternary Golay codes can be converted into rays in RP23 and RP11 that provide proofs of the Kochen-Specker theorem in real state spaces of dimensions 24 and 12, respectively. Some implications of these results are discussed.
Fourier Acceleration In The Linear Sigma Model, Cameron Cianci
Fourier Acceleration In The Linear Sigma Model, Cameron Cianci
Honors Scholar Theses
The linear sigma model is a low energy effective model of Quantum Chromodynamics. This model mimics the breaking of chiral symmetry both spontaneously and explicitly through the quark condensate and pion mass matrix respectively. Fourier acceleration is a method that can be implemented in the Hybrid Monte-Carlo algorithm which decreases autocorrelations due to critical slowing down through tuning the mass parameters in the HMC algorithm. Fourier acceleration is applied to the linear sigma model with a novel mass estimation procedure, by assuming the modes behave approximately like simple harmonic oscillators. The masses are chosen by sampling the expectation values of …
What Is Nonclassical About Uncertainty Relations?, Lorenzo Catani, Matthew S. Leifer, Giovanni Scala, David Schmid, Robert W. Spekkens
What Is Nonclassical About Uncertainty Relations?, Lorenzo Catani, Matthew S. Leifer, Giovanni Scala, David Schmid, Robert W. Spekkens
Mathematics, Physics, and Computer Science Faculty Articles and Research
Uncertainty relations express limits on the extent to which the outcomes of distinct measurements on a single state can be made jointly predictable. The existence of nontrivial uncertainty relations in quantum theory is generally considered to be a way in which it entails a departure from the classical worldview. However, this perspective is undermined by the fact that there exist operational theories which exhibit nontrivial uncertainty relations but which are consistent with the classical worldview insofar as they admit of a generalized-noncontextual ontological model. This prompts the question of what aspects of uncertainty relations, if any, cannot be realized in …
Two-Step Single Qubit Gates For Superconducting Qubits, Edward Takyi
Two-Step Single Qubit Gates For Superconducting Qubits, Edward Takyi
Open Access Theses & Dissertations
Why quantum information processing? Contemporary manipulation and transmission of information is executed through physical machines (computers, routers, scanners, etc.) in which Classical Mechanics is used to describe the embodiment and transformation of information. However, the physical theory of the world is not Classical Mechanics. And so, there is no reason to suppose that machines following the laws of Classical Mechanics would have the same computational power like quantum machines. Quantum computers would break the rules of classical computers and they would be able solve problems that are intractable on conventional supercomputers.
In order to fabricate quantum computers and make significant …
The Impact Of A Nuclear Disturbance On A Space-Based Quantum Network, Alexander Miloshevsky
The Impact Of A Nuclear Disturbance On A Space-Based Quantum Network, Alexander Miloshevsky
Doctoral Dissertations
Quantum communications tap into the potential of quantum mechanics to go beyond the limitations of classical communications. Currently, the greatest challenge facing quantum networks is the limited transmission range of encoded quantum information. Space-based quantum networks offer a means to overcome this limitation, however the performance of such a network operating in harsh conditions is unknown. This dissertation analyzes the capabilities of a space-based quantum network operating in a nuclear disturbed environment. First, performance during normal operating conditions is presented using Gaussian beam modeling and atmospheric modeling to establish a baseline to compare against a perturbed environment. Then, the DEfense …
Gate-Controlled Quantum Dots In Two-Dimensional Tungsten Diselenide And One-Dimensional Tellurium Nanowires, Shiva Davari Dolatabadi
Gate-Controlled Quantum Dots In Two-Dimensional Tungsten Diselenide And One-Dimensional Tellurium Nanowires, Shiva Davari Dolatabadi
Graduate Theses and Dissertations
This work focuses on the investigation of gate-defined quantum dots in two-dimensional transition metal dichalcogenide tungsten diselenide (WSe2) as a means to unravel mesoscopic physical phenomena such as valley-contrasting physics in WSe2 flakes and its potential application as qubit, as well as realizing gate-controlled quantum dots based on elementaltellurium nanostructures which may unlock the topological nature of the host material carriers such as Weyl states in tellurium nanowires.The fabrication and characterization of gate-defined hole quantum dots in monolayer and bilayer WSe2 are reported. The gate electrodes in the device design are located above and below the WSe2 nanoflakes to accumulate …
High Fidelity Universal Gates Performed On A Continuously-Decoupled Coherence Enhanced Transmon Qubit, Michael Senatore
High Fidelity Universal Gates Performed On A Continuously-Decoupled Coherence Enhanced Transmon Qubit, Michael Senatore
Dissertations - ALL
Decoherence is the primary limiting factor for the utility of modern qubits and qubit networks; most chiefly, pure dephasing which limits the operational time any gate-sequence can produce a high-fidelity result. In this dissertation, I present the results of my experiment, performing fast, high fidelity, universal single-qubit gates, on a qubit which has been decoupled from pure dephasing resulting from environmental noise. This technique can expand operational ranges of qubits–such as allowing the high-coherence operation of a flux-tunable qubit far away from its flux-insensitive sweet-spot; broadening our selection of viable qubits by making otherwise low-coherence qubits operable with high coherence, …
Non-Inertial Quantum Clock Frames Lead To Non-Hermitian Dynamics, Ismael L. Paiva, Amit Te'eni, Bar Y. Peled, Eliahu Cohen, Yakir Aharonov
Non-Inertial Quantum Clock Frames Lead To Non-Hermitian Dynamics, Ismael L. Paiva, Amit Te'eni, Bar Y. Peled, Eliahu Cohen, Yakir Aharonov
Mathematics, Physics, and Computer Science Faculty Articles and Research
The operational approach to time is a cornerstone of relativistic theories, as evidenced by the notion of proper time. In standard quantum mechanics, however, time is an external parameter. Recently, many attempts have been made to extend the notion of proper time to quantum mechanics within a relational framework. Here, we use similar ideas combined with the relativistic mass-energy equivalence to study an accelerating massive quantum particle with an internal clock system. We show that the ensuing evolution from the perspective of the particle’s internal clock is non-Hermitian. This result does not rely on specific implementations of the clock. As …
Compilation Optimizations To Enhance Resilience Of Big Data Programs And Quantum Processors, Travis D. Lecompte
Compilation Optimizations To Enhance Resilience Of Big Data Programs And Quantum Processors, Travis D. Lecompte
LSU Doctoral Dissertations
Modern computers can experience a variety of transient errors due to the surrounding environment, known as soft faults. Although the frequency of these faults is low enough to not be noticeable on personal computers, they become a considerable concern during large-scale distributed computations or systems in more vulnerable environments like satellites. These faults occur as a bit flip of some value in a register, operation, or memory during execution. They surface as either program crashes, hangs, or silent data corruption (SDC), each of which can waste time, money, and resources. Hardware methods, such as shielding or error correcting memory (ECM), …
Symmetry Breaking Effects In Low-Dimensional Quantum Systems, Ke Wang
Symmetry Breaking Effects In Low-Dimensional Quantum Systems, Ke Wang
Doctoral Dissertations
Quantum criticality in low-dimensional quantum systems is known to host exotic behaviors. In quantum one-dimension (1D), the emerging conformal group contains infinite generators, and conformal techniques, e.g., operator product expansion, give accurate and universal descriptions of underlying systems. In quantum two-dimension (2D), the electronic interaction causes singular corrections to Fermi-liquids characteristics. Meanwhile, the Dirac fermions in topological 2D materials can greatly enrich emerging phenomena. In this thesis, we study the symmetry-breaking effects of low-dimensional quantum criticality. In 1D, we consider two cases: time-reversal symmetry (TRS) breaking in the Majorana conformal field theory (CFT) and the absence of conformal symmetry in …
Reservoir Engineering Of Multi-Photon States In Circuit Quantum Electrodynamics, Jeffrey M. Gertler
Reservoir Engineering Of Multi-Photon States In Circuit Quantum Electrodynamics, Jeffrey M. Gertler
Doctoral Dissertations
The field of experimental quantum information has made significant progress towards useful computation but has been handicapped by the dissipative nature of physical qubits. Except for unwieldy and unrealized topological qubits, all quantum information systems experience natural dissipation, which limits the time scale for useful computation. However, this same dissipation, which induces errors requiring quantum error correction (QEC), can be used as a resource to perform a variety of important and unrealized tasks. In this thesis I discuss research into three uses of dissipation: manifold stabilization, state transfer, and QEC. With reservoir engineering, these tasks can be addressed in an …
Anomalous Transport, Quasiperiodicity, And Measurement Induced Phase Transitions, Utkarsh Agrawal
Anomalous Transport, Quasiperiodicity, And Measurement Induced Phase Transitions, Utkarsh Agrawal
Doctoral Dissertations
With the advent of the noisy-intermediate scale quantum (NISQ) era quantum computers are increasingly becoming a reality of the near future. Though universal computation still seems daunting, a great part of the excitement is about using quantum simulators to solve fundamental problems in fields ranging from quantum gravity to quantum many-body systems. This so-called second quantum revolution rests on two pillars. First, the ability to have precise control over experimental degrees of freedom is crucial for the realization of NISQ devices. Significant progress in the control and manipulation of qubits, atoms, and ions, as well as their interactions, has not …
Characterization Of Superconducting Hardware For Implementing Quantum Stabilizers, Kenneth Richard Dodge
Characterization Of Superconducting Hardware For Implementing Quantum Stabilizers, Kenneth Richard Dodge
Dissertations - ALL
Superconducting qubits are one of the leading approaches being investigated for building a scalable quantum computer. In the presence of external noise and perturbations plus local microscopic fluctuations and dissipation in the qubit environment, arbitrary quantum states will decohere, leading to bit-flip and phase-flip errors of the qubit. In order to build a fault-tolerant quantum computer that can preserve and process quantum information in the presence of noise and dissipation, one must implement some form of quantum error correction. Stabilizer operations are at the heart of quantum error correction and are typically implemented in software-controlled entangling gates and measurements of …
Classification Of Pixel Tracks To Improve Track Reconstruction From Proton-Proton Collisions, Kebur Fantahun, Jobin Joseph, Halle Purdom, Nibhrat Lohia
Classification Of Pixel Tracks To Improve Track Reconstruction From Proton-Proton Collisions, Kebur Fantahun, Jobin Joseph, Halle Purdom, Nibhrat Lohia
SMU Data Science Review
In this paper, machine learning techniques are used to reconstruct particle collision pathways. CERN (Conseil européen pour la recherche nucléaire) uses a massive underground particle collider, called the Large Hadron Collider or LHC, to produce particle collisions at extremely high speeds. There are several layers of detectors in the collider that track the pathways of particles as they collide. The data produced from collisions contains an extraneous amount of background noise, i.e., decays from known particle collisions produce fake signal. Particularly, in the first layer of the detector, the pixel tracker, there is an overwhelming amount of background noise that …
Methods For Bioconjugation Of Biochemical Sensors Based On Metallic Nanoparticles, Jacob Rolin
Methods For Bioconjugation Of Biochemical Sensors Based On Metallic Nanoparticles, Jacob Rolin
Summer Community of Scholars Posters (RCEU and HCR Combined Programs)
No abstract provided.
Control Of Nonlinear Properties Of Van Der Waals Materials, Rezlind Bushati
Control Of Nonlinear Properties Of Van Der Waals Materials, Rezlind Bushati
Dissertations, Theses, and Capstone Projects
Van der Waals materials are a broad class of materials that exhibit unique optoelectronic properties. They provide a rich playground for which they can be integrated into current on-chip devices due to their nanometer-scale size, and be utilized for studying fundamental physics. Strong coupling of emitters to microcavities provides many opportunities for new exotic physics through the formation of hybrid quasi-particles exciton-polaritons. This thesis
focuses on exploring and enhancing nonlinearity of van der Waals materials through strongly coupling to microcavities. By taking advantage of the stacking order of TMDs, we show intense second-harmonic generation from bulk, centrosymmetric TMD systems. In …
Wideband And Relativistic Superradiance In Astrophysics, Christopher M. Wyenberg
Wideband And Relativistic Superradiance In Astrophysics, Christopher M. Wyenberg
Electronic Thesis and Dissertation Repository
In the quantum phenomenon of superradiance (SR) a population of inverted particles evolves, through its interaction with the quantized vacuum radiation field, into a highly entangled state capable of generating much greater radiative emission than predicted by the independent spontaneous decay of its constituent particles. The phenomenon has recently been applied to transient astrophysical processes but has thus far been restricted to particles sharing a common velocity. This thesis researches the effects of astrophysical velocity distributions upon SR, which are distinct from conventional regimes of the quantum optics literature in that they may possess extremely wide bandwidths, turbulent statistical properties, …
Magnetic Skyrmions Unwrapped, Alexey Kovalev
Magnetic Skyrmions Unwrapped, Alexey Kovalev
Alexey Kovalev Papers
Experiments with chiral magnets may hold the key to a better understanding of fundamental aspects of transformations between different skyrmionic states, necessary for magnetic memory and logic applications to become a reality.
With the aim of developing computing devices that operate with low power dissipation, scientists have been pursuing the idea of encoding information in magnetic states. Specifically, skyrmions, which can be thought of as whirl-like states of magnetic moments, are promising candidates for this purpose. The advantage of skyrmions lies in their topological protection, a property implying that only a ‘global’ system modification can erase a skyrmion. Realizations of …
Characterizing The Single-Photon State: Quantum Physics Experiments With Single-Photon Sensitivity, Sheldon Lee Field
Characterizing The Single-Photon State: Quantum Physics Experiments With Single-Photon Sensitivity, Sheldon Lee Field
University Honors Theses
Coincidence-counting and spontaneous parametric downconversion are central to introductory quantum mechanical experimentation but have remained largely out of reach of undergraduate physics instructors. This thesis summarizes the theory behind light polarization, spontaneous parametric downconversion, birefringent refractive indices, and an affordable self-contained photon coincidence counting unit (CCU). A method for implementing a CCU to demonstrate downconversion is presented, and empirical results are provided.
Quantum Computational Simulations For Condensed Matter Systems, Trevor Alan Keen
Quantum Computational Simulations For Condensed Matter Systems, Trevor Alan Keen
Doctoral Dissertations
In condensed matter physics, and especially in the study of strongly correlated electron systems, numerical simulation techniques are crucial to determine the properties of the system including interesting phases of matter that arise from electron-electron interactions. Many of these interesting phases of matter, including but not limited to Mott-insulating materials and possibly high-temperature superconducting systems, can be modeled by the Hubbard model. Although it is one of the simplest models to include electron-electron interactions, it cannot be solved analytically in more than one dimension and thus numerical techniques must be employed. Although there have been great strides in classical numerical …
Overcoming Atmospheric Effects In Quantum Cryptography, Brian Joseph Rollick
Overcoming Atmospheric Effects In Quantum Cryptography, Brian Joseph Rollick
Doctoral Dissertations
Quantum Computers will have the potential to greatly assist us in problems such as searching, optimization and even drug discovery. Unfortunately, among these newfound capabilities is one which allows one to break RSA encryption in orders of magnitude less time. One promising countermeasure to secure our communication today and in the future is the one time pad, although it is very difficult to generate and distribute. Quantum Key Distribution offers a practical method for two authenticated parties to generate a key. Whereby the parties, Alice and Bob, share quantum states and use physical laws to place an upper bound on …
Optimization Of Quantum Circuits Using Spin Bus Multiqubit Gates For Quantum Dots, Miguel Gonzalo Rodriguez
Optimization Of Quantum Circuits Using Spin Bus Multiqubit Gates For Quantum Dots, Miguel Gonzalo Rodriguez
Open Access Theses & Dissertations
The current conventional method for designing quantum circuits is to employ a number of single- and two-qubit gates, which often necessitate a lengthy sequence, imposing severe constraints on quantum coherence and quantum circuit complexity. Coupling multiple spin qubits to a common spin chain can result in a generically multiqubit gate. It is demonstrated that the multiqubit gate can substantially reduce the depth of quantum circuits and establish multiqubit entanglement considerably more quickly.
Quantum Computing Simulation Of The Hydrogen Molecule System With Rigorous Quantum Circuit Derivations, Yili Zhang
Quantum Computing Simulation Of The Hydrogen Molecule System With Rigorous Quantum Circuit Derivations, Yili Zhang
All Graduate Plan B and other Reports
Quantum computing has been an emerging technology in the past few decades. It utilizes the power of programmable quantum devices to perform computation, which can solve complex problems in a feasible time that is impossible with classical computers. Simulating quantum chemical systems using quantum computers is one of the most active research fields in quantum computing. However, due to the novelty of the technology and concept, most materials in the literature are not accessible for newbies in the field and sometimes can cause ambiguity for practitioners due to missing details.
This report provides a rigorous derivation of simulating quantum chemistry …