IA Scholar Query: Fast Lattice Point Enumeration with Minimal Overhead.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgMon, 28 Nov 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help14402017
https://scholar.archive.org/work/uowfgqp7hzh2lltvflrcjwdtsm
Fresnel and Fraunhoffer diffraction-Polarization methods for the production of polarized light. Einstein's coefficients (expression for energy density). Requisites of a Laser system. Condition for laser action. Principle, Construction and working of He-Ne laser Holography-Principle of Recording and reconstruction of images. Propagation mechanism in optical fibers. Angle of acceptance. Numerical aperture. Types of optical fibers and modes of propagation. Attenuation, Block diagram discussion of point to point communication, applications. Module -4 10 hours Crystal Structure: Space lattice, Bravais lattice-Unit cell, primitive cell. Lattice parameters. Crystal systems. Direction and planes in a crystal. Miller indices. Expression for interplanar spacing. Coordination number. Atomic packing factors (SC, FCC, BCC). Bragg's law, Determination of crystal structure using Bragg's X-ray diffractometer. Polymorphism and Allotropy. Crystal Structure of Diamond. Module -5 10 hours ELEMENTS OF ELECTRONICS ENGINEERING Subject Code 17SEC13/23 IA Marks 50 Number of lecture hours/week 04 Exam Marks 50 Total number of lecture hours 50 Credits 04 Course Objectives: 1. To provide basic concepts D.C circuits and circuit analysis techniques 2. To provide knowledge on A.C circuit fundamental techniques 3. To understand construction and operation of BJT and Junction FET 4. Explain the different modes of communications from wired to wireless and the computing involved. 5. To provide fundamental knowledge of Digital Logic. Course Outcomes: CO1: Understand concepts of electrical circuits and elements. CO2: Apply basic electric laws in solving circuit problems. CO3: Analyse simple circuits containing transistors CO4: Understand concept of cellular wireless networks. CO5: Understand Number systems and design basic digital circuits.BTECH.MECHwork_uowfgqp7hzh2lltvflrcjwdtsmMon, 28 Nov 2022 00:00:00 GMT2021
https://scholar.archive.org/work/gze4zbzdt5a6xe6yg6qrijqlca
BTECH.ECEwork_gze4zbzdt5a6xe6yg6qrijqlcaMon, 28 Nov 2022 00:00:00 GMTQuantum Adversarial Learning in Emulation of Monte-Carlo Methods for Max-cut Approximation: QAOA is not optimal
https://scholar.archive.org/work/3w3yh4iinrca3frwos25z7bnji
One of the leading candidates for near-term quantum advantage is the class of Variational Quantum Algorithms, but these algorithms suffer from classical difficulty in optimizing the variational parameters as the number of parameters increases. Therefore, it is important to understand the expressibility and power of various ans\"atze to produce target states and distributions. To this end, we apply notions of emulation to Variational Quantum Annealing and the Quantum Approximate Optimization Algorithm (QAOA) to show that QAOA is outperformed by variational annealing schedules with equivalent numbers of parameters. Our Variational Quantum Annealing schedule is based on a novel polynomial parameterization that can be optimized in a similar gradient-free way as QAOA, using the same physical ingredients. In order to compare the performance of ans\"atze types, we have developed statistical notions of Monte-Carlo methods. Monte-Carlo methods are computer programs that generate random variables that approximate a target number that is computationally hard to calculate exactly. While the most well-known Monte-Carlo method is Monte-Carlo integration (e.g. Diffusion Monte-Carlo or path-integral quantum Monte-Carlo), QAOA is itself a Monte-Carlo method that finds good solutions to NP-complete problems such as Max-cut. We apply these statistical Monte-Carlo notions to further elucidate the theoretical framework around these quantum algorithms.Cem M. Unsal, Lucas T. Bradywork_3w3yh4iinrca3frwos25z7bnjiThu, 24 Nov 2022 00:00:00 GMTEnd-to-end resource analysis for quantum interior point methods and portfolio optimization
https://scholar.archive.org/work/qqjpiwjbavd7dmso7ufco4m674
We study quantum interior point methods (QIPMs) for second-order cone programming (SOCP), guided by the example use case of portfolio optimization (PO). We provide a complete quantum circuit-level description of the algorithm from problem input to problem output, making several improvements to the implementation of the QIPM. We report the number of logical qubits and the quantity/depth of non-Clifford T-gates needed to run the algorithm, including constant factors. The resource counts we find depend on instance-specific parameters, such as the condition number of certain linear systems within the problem. To determine the size of these parameters, we perform numerical simulations of small PO instances, which lead to concrete resource estimates for the PO use case. Our numerical results do not probe large enough instance sizes to make conclusive statements about the asymptotic scaling of the algorithm. However, already at small instance sizes, our analysis suggests that, due primarily to large constant pre-factors, poorly conditioned linear systems, and a fundamental reliance on costly quantum state tomography, fundamental improvements to the QIPM are required for it to lead to practical quantum advantage.Alexander M. Dalzell, B. David Clader, Grant Salton, Mario Berta, Cedric Yen-Yu Lin, David A. Bader, Nikitas Stamatopoulos, Martin J. A. Schuetz, Fernando G. S. L. Brandão, Helmut G. Katzgraber, William J. Zengwork_qqjpiwjbavd7dmso7ufco4m674Tue, 22 Nov 2022 00:00:00 GMTThe Circulating Library in Melbourne: its place in the book-trade and its influence on readers
https://scholar.archive.org/work/zssw4cimrfd7flzjoup7pwywlq
Circulating libraries were small businesses that loaned books for a fee. The majority of the public had little access to affordable books, so the circulating libraries—although few in number in the nineteenth century—began to increase considerably from the 1920s when genre fiction became increasingly popular. Their number peaked in 1940 with over four hundred libraires in operation that loaned more than ten million books each year. This thesis examines the locations and operations of the circulating libraries throughout Melbourne, until the mid-1960s, when the rate supported council libraries provided free loans and assisted in the demise of the commercial library.PETER RUSSELL PEREYRAwork_zssw4cimrfd7flzjoup7pwywlqMon, 21 Nov 2022 00:00:00 GMTUAV Traffic Management : A Survey On Communication Security
https://scholar.archive.org/work/etxo5n7wwbgjtaugzxw34inaby
Unmanned Aerial Systems (UAS) have a wide variety of applications, and their development in terms of capabilities is continuously evolving. Many missions performed by an Unmanned Aerial Vehicle (UAV) require flying in public airspace. This requires very high safety standards, similar to those mandatory in commercial civil aviation. A safe UAV Traffic Management (UTM) requires several communication links between aircraft, their pilots and UTM systems. The integrity of these communication links is critical for the safety of operations. Several security requirements also have to be met on each of these links. Unfortunately, current cryptographic standards used over the internet are most often not suitable to UAS due to their limited resources and dynamic nature. This survey discusses the security required for every communication link in order to enable a safe traffic management. Research works focusing on the security of communication links using cryptographic primitives are then presented and discussed. Authentication protocols developed for UAVs or other constrained systems are compared and evaluated as solutions for UAS security. Symmetrical alternatives to the AES algorithm are also presented. Works to secure current UTM protocols such as ADS-B and RemoteID are discussed. The analysis reveals a need for the development of a complete secure architecture able to provide authentication and integrity to external systems (other aircraft, UTM systems...).Ridwane Aissaoui, Jean-Christophe Deneuville, Christophe Guerber, Alain Pirovanowork_etxo5n7wwbgjtaugzxw34inabyThu, 10 Nov 2022 00:00:00 GMTFoundations of Model-Based Deep Learning: Applications, Interpretability and Performance Guarantees
https://scholar.archive.org/work/jfeuqcvpkvesrh54c47ypqkmoe
In this thesis we lay the foundations of model-based deep learning with applications in various signal processing fields such as communication systems, compressive sensing, phase retrieval, radar signal processing, and image processing. Furthermore, we provide theoretical analysis of the proposed ideas, and specifically, presenting performance guarantees for the obtained model-based deep architectures.Shahin Khobahiwork_jfeuqcvpkvesrh54c47ypqkmoeTue, 08 Nov 2022 00:00:00 GMTThe Future of High Energy Physics Software and Computing
https://scholar.archive.org/work/epi7cx2rgbeo3jekkxchf6zwdm
Software and Computing (S&C) are essential to all High Energy Physics (HEP) experiments and many theoretical studies. The size and complexity of S&C are now commensurate with that of experimental instruments, playing a critical role in experimental design, data acquisition/instrumental control, reconstruction, and analysis. Furthermore, S&C often plays a leading role in driving the precision of theoretical calculations and simulations. Within this central role in HEP, S&C has been immensely successful over the last decade. This report looks forward to the next decade and beyond, in the context of the 2021 Particle Physics Community Planning Exercise ("Snowmass") organized by the Division of Particles and Fields (DPF) of the American Physical Society.V. Daniel Elvira, Steven Gottlieb, Oliver Gutsche, Benjamin Nachmanwork_epi7cx2rgbeo3jekkxchf6zwdmTue, 08 Nov 2022 00:00:00 GMTTailoring three-dimensional topological codes for biased noise
https://scholar.archive.org/work/lfefcrbir5f2bo33uefn2bkkpm
Tailored topological stabilizer codes in two dimensions have been shown to exhibit high storage threshold error rates and improved subthreshold performance under biased Pauli noise. Three-dimensional (3D) topological codes can allow for several advantages including a transversal implementation of non-Clifford logical gates, single-shot decoding strategies, parallelized decoding in the case of fracton codes as well as construction of fractal lattice codes. Motivated by this, we tailor 3D topological codes for enhanced storage performance under biased Pauli noise. We present Clifford deformations of various 3D topological codes, such that they exhibit a threshold error rate of 50% under infinitely biased Pauli noise. Our examples include the 3D surface code on the cubic lattice, the 3D surface code on a checkerboard lattice that lends itself to a subsystem code with a single-shot decoder, the 3D color code, as well as fracton models such as the X-cube model, the Sierpinski model and the Haah code. We use the belief propagation with ordered statistics decoder (BP-OSD) to study threshold error rates at finite bias. We also present a rotated layout for the 3D surface code, which uses roughly half the number of physical qubits for the same code distance under appropriate boundary conditions. Imposing coprime periodic dimensions on this rotated layout leads to logical operators of weight O(n) at infinite bias and a corresponding exp[-O(n)] subthreshold scaling of the logical failure rate, where n is the number of physical qubits in the code. Even though this scaling is unstable due to the existence of logical representations with O(1) low-rate Pauli errors, the number of such representations scales only polynomially for the Clifford-deformed code, leading to an enhanced effective distance.Eric Huang, Arthur Pesah, Christopher T. Chubb, Michael Vasmer, Arpit Duawork_lfefcrbir5f2bo33uefn2bkkpmThu, 03 Nov 2022 00:00:00 GMTImplementing a System for the Computation of Syntax Splittings for Total Preorders and for Conditional Knowledge Bases
https://scholar.archive.org/work/7wedfqklwzf5lbp2iybamig56e
In the context of knowledge representation and reasoning, the consideration of relevance plays a major role. The concept of syntax splitting has received an increasing amount of attention in recent years and has been investigated together with other contemporary methods. Originally formulated with respect to belief revision of belief sets, in 2017 Kern-Isberner and Brewka introduced the notion of syntax splitting for total preorders, and in 2020 KernIsberner et al. provided a basic notion of syntax splitting of conditional knowledge bases within the setting of non-monotonic reasoning. The work presented in this thesis extends the Java library InfOCF-Lib by the possibility to read and represent total preorders and to compute syntax splittings of epistemic states represented by total preorders as well as the unique finest syntax splitting of conditional knowledge bases in an automated way. For this purpose, the concept of splittability is introduced, which enables the calculation of syntax splittings for total preorders to be modelled and solved as a modified subset-sum problem. Moreover, with Makinson's notion of epistemic relevance, it is possible to calculate syntax splittings for conditional knowledge bases by considering the conditionals as epistemic knowledge that must not be split. This connection can be recognised and calculated by the transitive closure of the atoms in the conditionals. Based on these concepts, suitable algorithms are developed, implemented in InfOCF-Lib, and then evaluated whether concurrent processing brings a runtime advantage. To calculate syntax splittings for ranking functions, a basic approach is provided to model and solve this as a subset-sum problem as well.Bräuer, Beierle, Haldimannwork_7wedfqklwzf5lbp2iybamig56eWed, 02 Nov 2022 00:00:00 GMTNon-Abelian Floquet Spin Liquids in a Digital Rydberg Simulator
https://scholar.archive.org/work/7mbkey5vozhmbeagjmezjiadzu
Understanding topological matter is an outstanding challenge across several disciplines of physical science. Programmable quantum simulators have emerged as a powerful approach to studying such systems. While quantum spin liquids of paradigmatic toric code type have recently been realized in the laboratory, controlled exploration of topological phases with non-abelian excitations remains an open problem. We introduce and analyze a new approach to simulating topological matter based on periodic driving. Specifically, we describe a model for a so-called Floquet spin liquid, obtained through a periodic sequence of parallel quantum gate operations that effectively simulates the Hamiltonian of the non-abelian spin liquid in Kitaev's honeycomb model. We show that this approach, including the toolbox for preparation, control, and readout of topological states, can be efficiently implemented in state-of-the-art experimental platforms. One specific implementation scheme is based on Rydberg atom arrays and utilizes recently demonstrated coherent qubit transport combined with controlled-phase gate operations. We describe methods for probing the non-abelian excitations, and the associated Majorana zero modes, and simulate possible fusion and braiding experiments. Our analysis demonstrates the potential of programmable quantum simulators for exploring topological phases of matter. Extensions including simulation of Kitaev materials and lattice gauge theories are also discussed.Marcin Kalinowski, Nishad Maskara, Mikhail D. Lukinwork_7mbkey5vozhmbeagjmezjiadzuMon, 31 Oct 2022 00:00:00 GMTInvestigating Quantum Many-Body Systems with Tensor Networks, Machine Learning and Quantum Computers
https://scholar.archive.org/work/wszjs55s4bepdm4lzqjixf7wku
We perform quantum simulation on classical and quantum computers and set up a machine learning framework in which we can map out phase diagrams of known and unknown quantum many-body systems in an unsupervised fashion. The classical simulations are done with state-of-the-art tensor network methods in one and two spatial dimensions. For one dimensional systems, we utilize matrix product states (MPS) that have many practical advantages and can be optimized using the efficient density matrix renormalization group (DMRG) algorithm. The data for two dimensional systems is obtained from entangled projected pair states (PEPS) optimized via imaginary time evolution. Data in form of observables, entanglement spectra, or parts of the state vectors from these simulations, is then fed into a deep learning (DL) pipeline where we perform anomaly detection to map out the phase diagram. We extend this notion to quantum computers and introduce quantum variational anomaly detection. Here, we first simulate the ground state and then process it in a quantum machine learning (QML) manner. Both simulation and QML routines are performed on the same device, which we demonstrate both in classical simulation and on a physical quantum computer hosted by IBM.Korbinian Kottmannwork_wszjs55s4bepdm4lzqjixf7wkuThu, 20 Oct 2022 00:00:00 GMTStatistical Decoding 2.0: Reducing Decoding to LPN
https://scholar.archive.org/work/gsx5p3qdvzfwxpdtv34kdtucfq
The security of code-based cryptography relies primarily on the hardness of generic decoding with linear codes. The best generic decoding algorithms are all improvements of an old algorithm due to Prange: they are known under the name of information set decoders (ISD). A while ago, a generic decoding algorithm which does not belong to this family was proposed: statistical decoding. It is a randomized algorithm that requires the computation of a large set of parity-checks of moderate weight, and uses some kind of majority voting on these equations to recover the error. This algorithm was long forgotten because even the best variants of it performed poorly when compared to the simplest ISD algorithm. We revisit this old algorithm by using parity-check equations in a more general way. Here the parity-checks are used to get LPN samples with a secret which is part of the error and the LPN noise is related to the weight of the parity-checks we produce. The corresponding LPN problem is then solved by standard Fourier techniques. By properly choosing the method of producing these low weight equations and the size of the LPN problem, we are able to outperform in this way significantly information set decodings at code rates smaller than 0.3. It gives for the first time after 60 years, a better decoding algorithm for a significant range which does not belong to the ISD family.Kevin Carrier, Thomas Debris-Alazard, Charles Meyer-Hilfiger, Jean-Pierre Tillichwork_gsx5p3qdvzfwxpdtv34kdtucfqMon, 17 Oct 2022 00:00:00 GMTA Review of Beamforming Technologies for Ultra-Massive MIMO in Terahertz Communications
https://scholar.archive.org/work/o7hbhjtehreaxjimtjzrkygghy
Terahertz (THz) communications with a frequency band 0.1-10 THz are envisioned as a promising solution to future high-speed wireless communication. Although with tens of gigahertz available bandwidth, THz signals suffer from severe free-spreading loss and molecular-absorption loss, which limit the wireless transmission distance. To compensate for the propagation loss, the ultra-massive multiple-input-multiple-output (UM-MIMO) can be applied to generate a high-gain directional beam by beamforming technologies. In this paper, a review of beamforming technologies for THz UM-MIMO systems is provided. Specifically, we first present the system model of THz UM-MIMO and identify its channel parameters and architecture types. Then, we illustrate the basic principles of beamforming via UM-MIMO and introduce the schemes of beam training and beamspace MIMO for THz communications. Moreover, the spatial-wideband effect and frequency-wideband effect in the THz beamforming are introduced. The intelligent-reflecting-surface (IRS)-assisted joint beamforming and multi-user beamforming in THz UM-MIMO systems are discussed, respectively. Further, we present the corresponding fabrication techniques and illuminate the emerging applications benefiting from THz beamforming. Open challenges and future research directions on THz UM-MIMO systems are finally highlighted.Boyu Ning, Zhongbao Tian, Zhi Chen, Chong Han, Shaoqian Li, Jinhong Yuan, Rui Zhangwork_o7hbhjtehreaxjimtjzrkygghyFri, 14 Oct 2022 00:00:00 GMTMeasurement-induced phases of matter require adaptive dynamics
https://scholar.archive.org/work/lgtoh32bjfblfnnx2r42pdyrsy
We investigate quantum dynamics with projective measurements using the Stinespring formalism, which affords significant technical advantages and conceptual insight into hybrid dynamics. We consider spectral properties as well as commonly used and experimentally tractable probes of phase structure and universality, finding that all of these probes are blind to the effects of measurement in nonadaptive hybrid protocols. Essentially, if the outcomes of measurements are not utilized, their effect is no different than chaotic time evolution, on average, precluding measurement-induced phases of matter. We therefore consider adaptive circuits, in which gates depend on the outcomes of prior measurements via active feedback, finding nontrivial examples of order related to symmetry and topology with connections to quantum computing. However, transitions as a function of measurement rate do not appear possible with maximally chaotic time evolution; we identify nonrandom adaptive hybrid protocols as the leading candidate for genuine, measurement-induced transitions between distinct phases of matter.Aaron J. Friedman, Oliver Hart, Rahul Nandkishorework_lgtoh32bjfblfnnx2r42pdyrsyThu, 13 Oct 2022 00:00:00 GMTOn the Emerging Potential of Quantum Annealing Hardware for Combinatorial Optimization
https://scholar.archive.org/work/qim6thaegvbklcegix44yq4him
Over the past decade, the usefulness of quantum annealing hardware for combinatorial optimization has been the subject of much debate. Thus far, experimental benchmarking studies have indicated that quantum annealing hardware does not provide an irrefutable performance gain over state-of-the-art optimization methods. However, as this hardware continues to evolve, each new iteration brings improved performance and warrants further benchmarking. To that end, this work conducts an optimization performance assessment of D-Wave Systems' most recent Advantage Performance Update computer, which can natively solve sparse unconstrained quadratic optimization problems with over 5,000 binary decision variables and 40,000 quadratic terms. We demonstrate that classes of contrived problems exist where this quantum annealer can provide run time benefits over a collection of established classical solution methods that represent the current state-of-the-art for benchmarking quantum annealing hardware. Although this work does not present strong evidence of an irrefutable performance benefit for this emerging optimization technology, it does exhibit encouraging progress, signaling the potential impacts on practical optimization tasks in the future.Byron Tasseff, Tameem Albash, Zachary Morrell, Marc Vuffray, Andrey Y. Lokhov, Sidhant Misra, Carleton Coffrinwork_qim6thaegvbklcegix44yq4himSun, 09 Oct 2022 00:00:00 GMTTopological States of Matter in Frustrated Quantum Magnetism
https://scholar.archive.org/work/datu4mbgdngjfje66z6ii4fvcy
Frustrated quantum magnets may exhibit fascinating collective phenomena. The main goal of this dissertation is to provide conclusive evidence for the emergence of novel phases of matter like quantum spin liquids in local quantum spin models. We develop novel algorithms for large-scale Exact Diagonalization computations. Sublattice coding methods for efficient use of lattice symmetries in the procedure of diagonalizing the Hamiltonian matrix are proposed and suggest a randomized distributed memory parallelization strategy. Benchmarks of computations on various supercomputers with system size up to 50 spin-1/2 particles have been performed. Results concerning the emergence of a chiral spin liquid in a frustrated kagome Heisenberg antiferromagnet are presented. The stability and extent of this phase are discussed. In an extended Heisenberg model on the triangular lattice, we establish another chiral spin liquid phase. We discuss the special case of the Heisenberg J_1-J_2 model and present a scenario where the critical point of phase transition from the 120-degree Néel to a putative 𝐙_2 spin liquid is described by a Dirac spin liquid. A generalization of the SU(2) Heisenberg model with SU(N) degrees of freedom on the triangular lattice with an additional ring-exchange term is discussed. We present our contribution to the project and the final results that suggest a series of chiral spin liquid phases in an extended parameter range. Finally, we present preliminary data from a Quantum Monte Carlo study of an SU(N) version of the J-Q model on a square lattice for N=2,...,10, and multi-column representations. We establish the phase boundary between the Néel ordered phase and the disordered phases. The disordered phase in the four-column representation is expected to be a two-dimensional analog of the Haldane phase for the spin-1 Heisenberg chain.Alexander Wietekwork_datu4mbgdngjfje66z6ii4fvcyFri, 07 Oct 2022 00:00:00 GMTCalibration: A Simple Trick for Wide-table Delta Analytics
https://scholar.archive.org/work/clg2ms7b3vcjzllz2ptaoq23w4
Data analytics over normalized databases typically requires computing and materializing expensive joins (wide-tables). Factorized query execution models execution as message passing between relations in the join graph and pushes aggregations through joins to reduce intermediate result sizes. Although this accelerates query execution, it only optimizes a single wide-table query. In contrast, wide-table analytics is usually interactive and users want to apply delta to the initial query structure. For instance, users want to slice, dice and drill-down dimensions, update part of the tables and join with new tables for enrichment. Such Wide-table Delta Analytics offers novel work-sharing opportunities. This work shows that carefully materializing messages during query execution can accelerate Wide-table Delta Analytics by >10^5x as compared to factorized execution, and only incurs a constant factor overhead. The key challenge is that messages are sensitive to the message passing ordering. To address this challenge, we borrow the concept of calibration in probabilistic graphical models to materialize sufficient messages to support any ordering. We manifest these ideas in the novel Calibrated Junction Hypertree (CJT) data structure, which is fast to build, aggressively re-uses messages to accelerate future queries, and is incrementally maintainable under updates. We further show how CJTs benefit applications such as OLAP, query explanation, streaming data, and data augmentation for ML. Our experiments evaluate three versions of the CJT that run in a single-threaded custom engine, on cloud DBs, and in Pandas, and show 30x - 10^5x improvements over state-of-the-art factorized execution algorithms on the above applications.Zezhou Huang, Eugene Wuwork_clg2ms7b3vcjzllz2ptaoq23w4Fri, 07 Oct 2022 00:00:00 GMTQuantum Simulation on Noisy Superconducting Quantum Computers
https://scholar.archive.org/work/w7vujkry5jbkjavlz6iismti2i
Quantum simulation is a potentially powerful application of quantum computing, holding the promise to be able to emulate interesting quantum systems beyond the reach of classical computing methods. Despite such promising applications, and the increase in active research, there is little introductory literature or demonstrations of the topic at a graduate or undergraduate student level. This artificially raises the barrier to entry into the field which already has a limited workforce, both in academia and industry. Here we present an introduction to simulating quantum systems, starting with a chosen Hamiltonian, overviewing state preparation and evolution, and discussing measurement methods. We provide an example simulation by measuring the state dynamics of a tight-binding model with disorder by time evolution using the Suzuki-Trotter decomposition. Furthermore, error mitigation and noise reduction are essential to executing quantum algorithms on currently available noisy quantum computers. We discuss and demonstrate various error mitigation and circuit optimization techniques that significantly improve performance. All source code is freely available, and we encourage the reader to build upon it.Kaelyn J. Ferris, A. J. Rasmusson, Nicholas T. Bronn, Olivia Laneswork_w7vujkry5jbkjavlz6iismti2iThu, 06 Oct 2022 00:00:00 GMTQuantum Computation for Periodic Solids in Second Quantization
https://scholar.archive.org/work/ee3vx6ogcnei7fkmoch76medw4
In this work, we present a quantum algorithm for ground-state energy calculations of periodic solids on error-corrected quantum computers. The algorithm is based on the sparse qubitization approach in second quantization and developed for Bloch and Wannier basis sets. We show that Wannier functions require less computational resources with respect to Bloch functions because: (i) the L_1 norm of the Hamiltonian is considerably lower and (ii) the translational symmetry of Wannier functions can be exploited in order to reduce the amount of classical data that must be loaded into the quantum computer. The resource requirements of the quantum algorithm are estimated for periodic solids such as NiO and PdO. These transition metal oxides are industrially relevant for their catalytic properties. We find that ground-state energy estimation of Hamiltonians approximated using 200–900 spin orbitals requires ca. 10^10–10^12 T gates and up to 3·10^8 physical qubits for a physical error rate of 0.1%.Aleksei V. Ivanov, Christoph Sünderhauf, Nicole Holzmann, Tom Ellaby, Rachel N. Kerber, Glenn Jones, Joan Campswork_ee3vx6ogcnei7fkmoch76medw4Wed, 05 Oct 2022 00:00:00 GMT