- 1. Presented by Dr. Alexander Perry May 23, 2024 Hybrid Quantum Machine Learning Utilizing Limited-Scale Quantum Computing
- 2. Agenda Bill Gibbs, Host 1. About Capitol Technology University 2. Session Pointers 3. About the Presenter 4. Presentation 5. Q and A 6. Upcoming Webinars 7. Recording, Slides, Certificate
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- 6. Session Pointers • We will answer questions at the conclusion of the presentation. At any time, you can post a question in the text chat and we will answer as many as we can. • Microphones and webcams are not activated for participants. • A link to the recording and to the slides will be sent to all registrants and available on our webinar web page. • A participation certificate is available by request for both Live Session and On Demand viewers.
- 7. Dr. Alexander Perry • Adjunct Professor at Capitol • Data Scientist: Hybrid Quantum-Classical Machine Learning (HQML) • Experience: Cyber, Data Science, AI/ML, Quantum Computing • 30-year career as software engineer, system administrator, data scientist, technical director • Doctor of Science (DSc) in Cybersecurity from Capitol Technology University
- 8. Presented by Dr. Alexander Perry May 23, 2024 Hybrid Quantum Machine Learning Utilizing Limited-Scale Quantum Computing
- 9. Hybrid Quantum Machine Learning Utilizing Limited-Scale Quantum Computing Dr. Alexander Perry CapitolTechnology University May 23, 2024
- 10. Modified Heilmeier Catechism • What is HQML via Limited-Scale Quantum Computing? • Who cares? If you are successful, what difference will it make? • What are you trying to do? • How is it done today, and what are the limits of current practice? • What is new in your approach and why do you think it will be successful? • What are the risks? • How much will it cost? • How long will it take? • What are the mid-term and final “exams” to check for success?
- 11. Quantum Computing • The goal of quantum computation is not a single output but rather to create a sampling device of a probability distribution. • A qubit is the computational unit in quantum computers. • Quantum Superposition:The notion that tiny objects can exist in multiple places or states simultaneously—is a cornerstone of quantum physics. • Knowing the quantum state of the system allows us to predict the outcomes of experiments. • The Two Golden Rules of Quantum Mechanics: 1. A particle can be in quantum superposition where it behaves as though it is in multiple states at once. 2. When measured, the particle will be found in a single state.
- 12. Quantum Computing Implementation • There are multiple ways to implement a quantum computer:81,84
- 13. Quantum Machine Learning (QML) • Quantum Machine Learning (QML) explores how to devise and implement quantum software that could enable machine learning on quantum computers (including noisy intermediate-scale quantum, or NISQ) that is faster than classical computers. • Hybrid quantum machine learning (HQML) explores how to implement QML using quantum computers (including noisy intermediate-scale quantum, or NISQ) in conjunction with classical computers to solve ML problems faster than classical computers.
- 14. Modified Heilmeier Catechism • What is HQML via Limited-ScaleQuantum Computing? • Who cares? If you are successful, what difference will it make? • What are you trying to do? • How is it done today, and what are the limits of current practice? • What is new in your approach and why do you think it will be successful? • What are the risks? • How much will it cost? • How long will it take? • What are the mid-term and final “exams” to check for success?
- 15. The Big Picture
- 16. Strategic Goal
- 17. Government and Industry Investments • May 09, 2024: DOE Announces $60-70M Quantum Information Science Funding Opportunity • Aug 30, 2023: DOE Announces $24M for Research on Quantum Networks • Aug 24, 2023: "The administration has requested $75 million for a new account focused on near-term applications of quantum information science.“ • Aug 17, 2023: NIST Issues Congressionally Mandated Report on EmergingTech Areas • Aug 16, 2023: NSF Invests $38M to Advance Quantum Information Science and Engineering • Aug 15, 2023: AFRL opens Extreme Computing centre for quantum computing research • Jul 27, 2023: DOE Announces $11.7 Million for Research on Quantum Computing • Jul 12, 2023:Truist and IBM Collaborate on EmergingTechnology Innovation and Quantum Computing • Jun 22, 2023: Expansion of National Quantum Initiative Pitched to Science Committee
- 18. Quantum Potential • Quantum computing makes use of intrinsically quantum properties such as entanglement and superposition to design algorithms that are faster than classical ones for some class of problems. • They offer computational speed-up, that provably no classical system could ever exhibit. • Some approaches are based on a parameterized quantum circuit (PQC, discussed in detail later), using neural network-inspired algorithms to train them.
- 19. Modified Heilmeier Catechism • What is HQML via Limited-ScaleQuantum Computing? • Who cares? If you are successful, what difference will it make? • What are you trying to do? • How is it done today, and what are the limits of current practice? • What is new in your approach and why do you think it will be successful? • What are the risks? • How much will it cost? • How long will it take? • What are the mid-term and final “exams” to check for success?
- 20. Hybrid Quantum Machine Learning (HQML) High-level depiction of hybrid algorithms used for machine learning. Explore implementing a hybrid quantum machine learning (HQML) prototype using noisy intermediate scale quantum (NISQ) computers (a type of LSQC) in conjunction with classical computers to solve machine learning problems faster than classical computers.
- 21. Outcome, NotTechnology, Focused • Goal: Use Data Classification via Machine Learning as a way to learn quantum thinking. • Method: • Variational Quantum Kernel-Based Classification (VQC): • Operates through using a variational quantum circuit to classify a training set in direct analogy to conventional SVMs.119 • NISQ (a type of LSQC) computers via Parameterized Quantum Circuits (PQCs): • PQCs offer a concrete way to implement algorithms in the NISQ era.2,102 • IBM’s Qiskit will be the quantum simulator of choice for prototyping. • Currently a de-facto community standard. • Offers a rich set of quantum computing examples. • Offers backends that can run simulator code multiple NISQ devices.
- 22. Parameterized Quantum Circuit • A parameterized quantum circuit (PQC) is a type of ansatz (educated guess or starting point). The core idea is basedVariational Quantum Eigensolver (VQE). • The goal of aVQE is to find the ground state (expected value of a quantum measurement in this case) of a Hamiltonian H by minimizing the parameters 𝜃 of a PQC given by 𝑈(𝜃) with regards to an objective function that represents the energy of a given Hamiltonian (classification of data in this case).
- 23. HQML Parameterized Quantum Circuit
- 24. Modified Heilmeier Catechism • What is HQML via Limited-ScaleQuantum Computing? • Who cares? If you are successful, what difference will it make? • What are you trying to do? • How is it done today, and what are the limits of current practice? • What is new in your approach and why do you think it will be successful? • What are the risks? • How much will it cost? • How long will it take? • What are the mid-term and final “exams” to check for success?
- 25. Classical ML ClassificationToday • Done via: • Linear regression (univariate and multivariate) • Support vector machine (SVM) for support vector classification (SVC). • Deep Neural Networks (Deep Learning) • Others… • Limitations: • Speed of processing the data at scale • Certain categories problems are intractable for classical computers in: • Encryption and Cybersecurity • Financial Services • Drug Research and Development
- 26. Modified Heilmeier Catechism • What is HQML via Limited-ScaleQuantum Computing? • Who cares? If you are successful, what difference will it make? • What are you trying to do? • How is it done today, and what are the limits of current practice? • What is new in your approach and why do you think it will be successful? • What are the risks? • How much will it cost? • How long will it take? • What are the mid-term and final “exams” to check for success?
- 27. What’s New This diagram gives a brief overview of theVariational Quantum Classification protocol.
- 28. Why it will work: HQML in Feature Hilbert spaces • The basic idea of quantum computing is surprisingly similar to that of kernel methods in machine learning, namely to efficiently perform computations in an intractably large Hilbert space. • We interpret the process of encoding inputs in a quantum state as a nonlinear feature map that maps data to quantum Hilbert space. • PQCs can form Gaussian Kernels that can be used to derive adaptive learning rates for gradient ascent. • Even at low circuit depth, some classes of PQCs can generate highly non-trivial outputs. • PQCs may offer a concrete way to implement QML algorithms on NISQ devices.
- 29. Kernel Functions • The “kernel trick” maps input data into a higher dimensional space, making it easier to solve non-linearly separable problems. • Mathematically, a kernel function can be defined as: 𝑘 𝑥𝑖, 𝑥𝑗 = ⟨𝑓 𝑥𝑖 , 𝑓 𝑥𝑗 ⟩ where 𝑘 is the kernel function, 𝑥𝑖 and 𝑥𝑗 are 𝑛-dimensional inputs, 𝑓 is a map from n-dimension to 𝑚-dimension space and ⟨𝑎, 𝑏⟩ denotes the inner product.When considering finite data, a kernel function can be represented as a matrix: 𝐾𝑖𝑗 = 𝑘 𝑥𝑖, 𝑥𝑗
- 30. Kernel Methods for Machine Learning
- 31. Modified Heilmeier Catechism • What is HQML via Limited-ScaleQuantum Computing? • Who cares? If you are successful, what difference will it make? • What are you trying to do? • How is it done today, and what are the limits of current practice? • What is new in your approach and why do you think it will be successful? • What are the risks? • How much will it cost? • How long will it take? • What are the mid-term and final “exams” to check for success?
- 32. Risks: Potentially Expensive Failure • Hardware challenges: • Quantum Decoherence: In quantum information processing, the term decoherence is often used loosely to describe any kind of noise that can affect/collapse quantum particles to a classical state, as if it’s being measured, and eliminate the quantum behavior of particles. • Algorithmic Challenges: • Supervised HQML training often requires extensive amounts of time. • HQML suffers from the barren plateau problem.
- 33. Modified Heilmeier Catechism • What is HQML via Limited-ScaleQuantum Computing? • Who cares? If you are successful, what difference will it make? • What are you trying to do? • How is it done today, and what are the limits of current practice? • What is new in your approach and why do you think it will be successful? • What are the risks? • How much will it cost? • How long will it take? • What are the mid-term and final “exams” to check for success?
- 34. Extremely Expensive • Commercial usage of existing NISQ systems can easily reach into the $100,000 to +$1,000,000 range. • Vendors offer researchers credits and/or free usage of their smaller NISQ systems (often with time limits).
- 35. Modified Heilmeier Catechism • What is HQML via Limited-ScaleQuantum Computing? • Who cares? If you are successful, what difference will it make? • What are you trying to do? • How is it done today, and what are the limits of current practice? • What is new in your approach and why do you think it will be successful? • What are the risks? • How much will it cost? • How long will it take? • What are the mid-term and final “exams” to check for success?
- 36. Timeframes • General Purpose Quantum Computers with millions of logical qubits are 10- 15 years away (at best). • NISQ systems with up to 1000 raw qubits and 48 logical qubits exist: • Dec 4, 2023: IBM releases first-ever 1,000-qubit quantum chip • Dec 7, 2023: Logical quantum processor based on reconfigurable atom arrays
- 37. Modified Heilmeier Catechism • What is HQML via Limited-ScaleQuantum Computing? • Who cares? If you are successful, what difference will it make? • What are you trying to do? • How is it done today, and what are the limits of current practice? • What is new in your approach and why do you think it will be successful? • What are the risks? • How much will it cost? • How long will it take? • What are the mid-term and final “exams” to check for success?
- 38. Success Checkpoints • If HQML is going to work, we should see successful prototypes in the next 3- 5 years. • In 5-10 years, we should see productions applications of HQMLs if the technology is successful.
- 40. Upcoming webinar www.captechu.edu/webinar-series Defining the DoD Roadmap to Digital Supremacy by Effectively Adopting Digital Transformation June 20 Dr. Donovan Wright
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- 43. Thanks for Joining Us! Thank You! This concludes today’s webinar Watch for a follow up email that contains: 1. How to get a Participation Certificate (Available by request for both Live Session and On Demand viewers) 2. Link to the webinar recording and slides

- General Purpose Quantum Computers with millions of logical (fault-tolerant) qubits are 10-15 years away (at best). Anyone who tells you they have quantum computer that will solve your problems should be met with the GREATEST of skepticism. This topic, HQML, is merely research in preparation for the future. Think of it as beginning to train learners of today to think in a “quantum way”.
- Depending on the quantum computing platform, different approaches can be divided in two groups: digital approaches using gate-based quantum computers and analog approaches using analog quantum computing platforms.
- NISQ (Noisy Intermediate Scale Quantum) devices contain a limited number of qubits that are stable for a concise period.25
- This work takes a science-first approach that aligns with the NQIAC efforts under the National Quantum Initiative (NQI) in alignment with the NQIAC.
- The strategic goal of this work is to help accelerate technology development toward mission applications of Limited-Scale Quantum Computer(s) (LSQC). As of December 16, 2022: https://www.quantum.gov/wp-content/uploads/2023/01/NQIAC-Slides-2022-12-16.pdf
- High-level depiction of hybrid algorithms used for machine learning:2,25 The role of the human is to set up the model using prior information, assess the learning process, and exploit the forecasts (Quantum State Preparation). Within the hybrid system, the quantum computer prepares quantum states according to a set of parameters (Quantum State Processing). The outcomes of the quantum states are measured (Quantum State Measurement). Using the measurement outcomes, the classical learning algorithm adjusts the parameters in order to minimize an objective function (Quantum State Preparation). The updated parameters, now defining a new quantum circuit, are fed back to the quantum hardware in a closed loop.
- A Variational Quantum Algorithm (VQA) uses both quantum and classical computers to accomplish a task. VQC: A VQA based approach leveraging linear kernels (in this case) VQNN: A VQA that uses qubits to emulate the hidden layers of a classical neural network (NN) to estimate the gradient of a function. This estimate from the measured quantum state is sent to a classical optimizer in epochs like classical NN. VQR: : A VQA quantum reservoir computing where quantum noise can be beneficial to the machine learning.
- A Hamiltonian matrix is a 2𝑛-by-2𝑛 matrix 𝐴 such that 𝐽𝐴 is symmetric, where 𝐽 is the skew-symmetric matrix: 𝑱= 𝑶 𝒏 𝑰 𝒏 −𝑰 𝒏 𝑶 𝒏 𝑬𝒒. and 𝑰 𝒏 is the 𝒏-by-𝒏 identity matrix. In other words, 𝑨 is Hamiltonian if and only if (𝑱𝑨) † = 𝑱𝑨 where () † denotes the transpose in ℝ and the adjoint (complex conjugate) in ℂ.65
- A machine learning model comprised of classical pre/post-processing and parameterized quantum circuit. A data vector is sampled from the dataset distribution, 𝑥~ 𝑃 𝐷 . The pre-processing scheme maps it to the vector 𝜙(𝑥) that parameterizes the encoder circuit 𝑈 𝜙(𝑥) . A variational circuit 𝑈 𝜃 , parameterized by a vector 𝜃, acts on the state prepared by the encoder circuit and possibly on an additional register of ancilla qubits, producing the state 𝑈 𝜃 𝑈 𝜙(𝑥) |0⟩. A set of observable quantities ⟨ 𝑀 𝑘 ⟩ 𝑥,𝜃 𝑘−1 𝐾 is estimated from the measurements. These estimates are then mapped to the output space through classical post-processing function 𝑓. For a supervised model, this output is the forecast associated to input 𝑥. Generative models can be expressed in this framework with small adaptations.
- Due to the strong parallelism of quantum computing in Hilbert space, ordinarily intractable calculation problems could now be solved very efficiently with non-classical means. [https://www.sciencedirect.com/science/article/abs/pii/S0577907321001039]
- Quantum machine learning in feature Hilbert spaces: https://arxiv.org/abs/1803.07128
- Kernel methods use kernel functions to analyze patterns in high-dimensional feature spaces. Support Vector Machines (SVMs) are a popular application for classification tasks in supervised learning, establishing decision boundaries to separate data into distinct classes. Kernels are particularly useful when data spaces are not linearly separable, allowing for the identification of hyperplanes within the space.
- General ML Risks: https://hbr.org/2021/01/when-machine-learning-goes-off-the-rails Technical Risk: The algorithms typically rely on the probability of an event and may be wrong. The operational environment may differ from the development environment. The complexity of the overall systems it’s embedded in (see Agency Risk). Agency Risk: Risks stemming from things that aren’t under the control of a specific business or user. Because machine learning is typically embedded within a complex system, it will often be unclear what led to a breakdown. Moral Risk (Responsible Algorithm Design): Products and services that make decisions autonomously will also need to resolve ethical dilemmas raising and regulatory and product development challenges. This is framed as "responsible algorithm design". Noise: Irregular fluctuations that accompany a transmitted signal that tend to obscure it, attributable to the discrete and probabilistic nature of physical phenomena and their interactions. Quantum Barren Plateaus: The magnitude of the gradients vanishes as the number of qubits increases.1 The gradients of a VQA do not vanish when the fidelity between the initial state and the state to be learned is bounded from below.1 Despite what type of optimization method is used, if the loss landscape is fairly flat, it can be difficult for the method to determine which direction to search. This situation is called a barren plateau. For a wide class of reasonable parameterized quantum circuits, the probability that the gradient along any reasonable direction is non-zero to some fixed precision is exponentially small as a function of the number of qubits.104 One approach to overcome this problem is to use structured initial guesses, such as those adopted in quantum simulation. Another possibility is to consider the full quantum circuit as a sequence of shallow blocks, selecting some parameters randomly and choosing the rest of the parameters such that all shallow blocks implement the identity to restrict the effective depth. This is an area of current investigation.104