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 ORNL – OLCF
 Project Information
 Project Name: (12 words max) True Thermal Annealing Continuous-Variable Quantum Quadratic Optimization Simulations
 Research Area: Computer Science? Machine learning? (Probably both, but choose one)
 Abstract/Project Summary (1-2 Paragraphs)
 True thermal annealing will provide an order of magnitude or more improvement in solutions to quantum quadratic optimization (QQO) problems. Existing QQO problems are binary, while our true thermal annealing QQO (tQQO) is capable of solving continuous-variable optimization problems. By establishing the quadratic optimization problem on the quantum computers with appropriately entangled qubits and allowing the high energy solutions to decohere through annealing by interaction with the thermal bath, our solution leaves behind the low-energy, optimized solutions. Unlike traditional systems, we do not avoid decoherence. We embrace it.
 The present project proposes systems software development of the simulations required to baseline the technology proposed above and begin establishment of the hardware requirements needed for construction, commissioning, and testing of the systems in question.
 Previous Computational Proposals
 None.
 Overview and Significance of Research
 RequisiteQ’s patent pending technology utilizes true thermal annealing to conduct continuous-variable quantum quadratic optimization. Previous quantum computing optimization systems did not utilize actual thermal annealing and were limited to binary systems. By utilizing true thermal annealing, the entangled qubits established in the problem definition step are allowed to decohere by interaction with a thermal fluid. The highest-energy solutions decohere first, leaving low-energy solutions behind. By proper setup of the problems, these minima become the solution to some of the most complex problems ever attempted. Further, as continuous-variable optimization is enabled, an entire branch of questions never attempted in quantum computing will be opened.
 Research Objectives and Milestones
 Initial research objectives include finalization of simulations of the thermal bath with the quantum hardware. The first milestone is completion of a suite of simulations, both algorithmic and physical, that provide direction for construction of hardware. The second stage research objectives are to build and commission the hardware systems. Baseline testing will be conducted to show the hardware’s speed compared to existing solutions on binary quantum computers. The last stage of research is development of consumer options for the hardware.
 Justification for Leadership Computing Resources
-I have no idea, but here’s me winging it: While RequisiteQ has the foundations of the initial simulations, the true costs of simulation of a truly revolutionary quantum system on slow classical personal computers add up with more than money. Better resources and the chance to dedicate our programmers to the task full-time are needed.
+While RequisiteQ has the foundations of the initial simulations, the true costs of simulation of a truly revolutionary quantum system on slow classical personal computers add up with more than money. Better resources and the chance to dedicate our programmers to the task full-time are needed.
 State-of-the-Art and Parallel Performance
-George: Review and revise this, too.
 The current state-of-the-art in the quantum computing field is binary, simulated annealing quantum quadratic optimization. In papers describing the D-Wave system, for example, the system is disclosed as only simulating thermal annealing, not actually using real-world thermal annealing. Our patent pending technology will utilize true thermal annealing and thereby move from binary to continuous-variable optimization. [Geordie – I need this to be tweaked to be 100% accurate, as I don’t want them suing us for defamation or something.]
-[Provide direct evidence? Supporting quantitative data? I do not have this. Tabular or graphical form?]
 Proposed Approach
 Mathematical Formulation:
 Equations defining the problem:
 The core optimization task is the task of finding a vector u (made up of n flux qubits, u1 to un) which minimizes
 	H^ =∑_(j=1)^n H_j^0 u_j+∑_(j,k=1)^n H_jk^I u_j u_k	(1)
 for the pair of matrices H0 and HI which are used to define the specific problem in this task.
 Quantum annealing solves this Ising Hamiltonian of the problem by finding the vector u for the continuous variables in the problem.  Annealing leverages quantum noise to move the Hamiltonian to the lowest energy state, and hence the optimal solution u of the problem.
 This is a very simple approach mathematically, which we believe is elegant and universal to solving a large number of problems due to its simplicity.
 In this sense, annealing is massively parallel since the noise inherent in quantum devices provides a continuous driving force across all elements of the solution vector u during a continuous-time annealing process.
 Moreover, this Ising Hamiltonian can be used across a variety of machine learning applications.  A few examples:
 	Accelerate the training of large-scale neural networks (e.g., LLMs) that traditionally use backpropagation to minimize the error term and solve for the optimal network weights
 	Large-scale scheduling/routing
 	Investment portfolio optimization
 	Computationally intensive machine learning using Reinforcement Learning and Adaptive Dynamic Programming (RLADP).
 Annealing equations:
 To accomplish annealing, we will use the Qiskit Lindblad function for evolving a master equation over time. This will simulate the annealing process that drives the Hamiltonian to the lowest energy state.
 The master equation, also called the density matrix, defines the system state over time. It includes dissipator operators that compute the effect of the annealing process.
 The annealing simulation consists of the time evolution of N qubits with dynamics dictated by the problem Hamiltonian.  The environment is simulated as a memory-less (Markovian) bath. The qubits and bath evolve together with a density matrix that evolves in accordance with the Lindblad master equation as follows:
 	∂ρ/∂t=-i/ħ [H,ρ]+Ɗ[ρ]	(2)
 The Hamiltonian is composed of a sum of single-qubit terms and two-qubit interactions, defined for the problem to solve as previously noted:
-	 	(3)
+H = HO + HI	 	(3)
 The two terms on the right side of equation (3), HO and HI, correspond to the two matrices in equation (1).
 For additional details, please see the Lindblad tutorial at https://qiskit-extensions.github.io/qiskit-dynamics/tutorials/Lindblad_dynamics_simulation.html.
 Libraries:
 We plan to use the Lindblad function in the IBM Qiskit library:
 https://qiskit-extensions.github.io/qiskit-dynamics/stubs/qiskit_dynamics.models.LindbladModel.html
 The programming language is Python, with the remote possibility of using C++ in conjunction with Cython for the Python interface.  Use of C++ may be desirable if we need to develop custom modules for performing the annealing process, although this is unlikely.
 Depending upon results from the Qiskit Lindblad model, we may investigate the linbladmpo tool, part of the Qiskit ecosystem for solving dissipative quantum dynamics:
 https://github.com/qiskit-community/lindbladmpo
 The linbladmpo may provide additional functionality for modeling the annealing process since it provides multithreading capability to maximize performance.
 Parallel Programming Model(s):
 We will use MPI with Python and/or C++ for multiprocessing capability.  This will be done to leverage additional computing nodes that enable determination of the speed to problem solution and accuracy of solutions for large problems.
 Workflow:
 We will use an incremental development process.
 The workflow is straightforward in that it begins with quantum simulations of an NP-hard problem with a small number of variables, and then incrementally expands the problem to a large number of variables.
 	Begin with a Quantum Unsigned Integer Problem (QUBO) for an NP-hard problem. We have selected the Traveling Salesman Problem (TSP).
 	Develop simulation software and validate annealing for this problem using a small set of variables.
 	Incrementally expand the size of the simulation to determine the relationship between problem size and speed to convergence on the optimum.
 	Define the points for incrementally increasing problem size - for capturing accuracy and convergence times versus problem size.
 	Revise the simulation software to use more computing nodes by adding multiprocessing code.
 	When problem convergence is reached, record accuracy of solution and convergence time.
 	Repeat steps 2 - 3 for a problem involving continuous variables.
 We may investigate the use of optical quantum platforms depending upon the results using Qiskit (a squid-based platform). If this is done, we anticipate use of the Xanadu simulation tools, although we will address this decision at that time.
 Optional Xanadu tools for optical quantum platforms: https://www.xanadu.ai/products/pennylane
 I/O Requirements:
 The quantum simulations we plan to perform do not make use of massive amounts of data for input.  The input data for the simulation is the Hamiltonian equation defined above.  We do not anticipate this requiring significant I/O.
 The in-memory requirements will be significant since the simulations will likely involve complex computations and in-process data.  But at this time we cannot estimate the bandwidth required or amount of memory.
 Data Storage Requirements:
 The data requirements are small.  We anticipate storing simulation results at the end of each simulation to capture precision and time-to-converge to a solution.
 We will download and retain these data on our own platforms, and perform data analysis there.
-PRIOR NOTES MADE BY NATHAN, DO NOT INCLUDE:
-Keywords to throw in: Massively parallel. Machine learning.
-Need George or someone, as I don’t know many of these words in context.
 Provide a detailed description of your proposed computational approach. The description may mention:
 	The underlying mathematical formulation (e.g., ODE, PDE).
 	Particular libraries required by the simulation and analysis software, algorithms and numerical techniques employed (e.g., finite element, iterative solver), programming languages, and other software used.
 	Parallel programming model(s) used (e.g., MPI, OpenMP, Pthreads, CUDA, OpenACC).
 	Project workflow, including the role of analysis and visualization and the availability of checkpoint and restart files.
 	I/O requirements (e.g., amount, size, bandwidth, etc) for restart, analysis, and workflow. Highlight any exceptional I/O needs.
 	Data storage requirements. Estimate anticipated cumulative size of stored data at the end of the requested project. What do you plan to do with the data at the end of the project? Do you have tools and/or plans to reduce the data? Justify data storage needs that exceed one petabyte.
 References
 	Kubota, T., et al., Quantum Noise-Induced Reservoir Computing. arXiv [quant-ph], 2022.
 	Suzuki, Y., et al., Natural quantum reservoir computing for temporal information processing. Scientific Reports, 2022. 12(1): p. 1353.
 	Fry, D., et al., Optimizing quantum noise-induced reservoir computing for nonlinear and chaotic time series prediction. Scientific Reports, 2023. 13(1).
 	Walls, D.F. and G.J. Milburn, Quantum Optics. 2nd ed. 2008: Springer-Verlang.
 Team Members
 The Team consists of founders of Requisite Q and of The Foundation for Biodefense Research.
 RequisiteQ:
 Dr. Paul Werbos won the IEEE award in 2022 for development of backpropagation and fundamental contributions to reinforcement learning and time series analysis. Dr. Werbos ran research in advanced AI and quantum technology areas at NSF until his retirement in 2015. He is the inventor of the True Quantum Annealing package being studied under this proposal.
 Dr. George Shannon has a PhD in Engineering with emphasis in artificial intelligence. This includes neural networks and adaptive dynamic programming with reinforcement learning. He has extensive practical experience in product development, product commercialization, research, software development, engineering, customer-focused design, healthcare re-engineering, and leading technology startups.
 Geordie Keitt has several decades of experience delivering large-scale software products for enterprise clients such as Intel, Bank of America, Cigna Insurance, and Boeing.
 Nathan Davis is a chemist, chemical engineer, and outer space resources engineer with extensive heavy industrial consulting experience. Mr. Davis is a patent agent and technical language translator, with active patents prosecuted for quantum computing, machine learning, combustion, cryogenics, outer space resource development, nuclear fuels, nuclear rocketry, and many other fields.
 The Foundation for Biodefense Research:
 Dr. Suzanne Sincavage has a background in public health and epidemiology with specialization in biological terrorism preparedness and response, as well as outer space biology.
 Trevor Muehlfelder has a background in criminology, law, and international diplomacy, with work in outer space biology.
 Software Used including website URLs
 Qiskit-based tools:
 https://qiskit-extensions.github.io/qiskit-dynamics/stubs/qiskit_dynamics.models.LindbladModel.html
 Optional: https://github.com/qiskit-community/lindbladmpo
 Xanadu-based tools (optional simulations for optical quantum platform):
 https://www.xanadu.ai/products/pennylane
 We plan to use the PyCharm IDE for Python development, and if C++ development is necessary, use the Clion C++ IDE.
 https://www.jetbrains.com/pycharm/
 https://www.jetbrains.com/clion/