**Quantum Machine Learning**

**Quantum Machine Learning**

**Quantum computing has come a long way since the discovery of Shor’s factoring (1995) and Grover’s search (1996) algorithms. We now know a quantum computer can solve an enormously large set of linear equations, can simulate a wide range of Hamiltonians representing chemical and biological systems, can perform various linear transformations including Fourier transforms, and can efficiently evaluate inner products and distances in super high dimensional vector space, the last of which is particularly useful in machine learning. In this project, we will explore applications in data processing, machine learning, and classification, taking advantage of intrinsic quantum correlations and quantum parallelism. In particular, we will examine which parts of classical machine learning schemes can be sped up in the quantum setting with deterministic queries.**

**Quantum walk-based algorithms**

**Quantum Combinatorial optimization**

**Combinatorial optimization is to find an optimal solution over an ordering of a discrete set of objects. For many such problems, exhaustive search is not feasible due to the exponentially large number of possible orderings. A well-known combinatorial optimization problem is the traveling salesperson problem, which is NP-hard. The intrinsic parallelism offered by quantum computing provides a simultaneous evaluation of all possible combinations and permutations, which may lead to quantum algorithms capable of solving classically intractable problems. The quantum approximate optimization algorithm (QAOA) is one powerful quantum approach to finding high-quality solutions to combinatorial problems. Below is an illustration of a hybrid quantum-classical variational method for finding the optimal QAOA parameters β and γ, where the dashed region is the quantum component.**

**Nonlinear quantum computing**

**Analyzing Quantum Algorithms via Tensor Networks**

**Quantum computing holds the promise of solving classically intractable problems, which would lead to ground-breaking advances in science and technology. However, there is currently a setback in the development of quantum algorithms, because we don’t have access to a full-scale quantum computer yet. Instead, we use classical computers to analyze the proposed quantum algorithms in order to establish their effectiveness. The Tensor Network formalism, or Tensor Network Notation (TNN), is a mathematical tool used to turn the classically intractable problem of analyzing quantum algorithms, specifically those requiring 50 or more qubits, into a classically tractable problem by closely approximating the behavior of the algorithm rather than solving it exactly. TNN offers us the necessary insight into the dynamics of these quantum algorithms and ultimately, it allows us to check whether the proposed quantum algorithms will work! In this project, we would like to do exactly that: (1) select a quantum algorithm suitable for some classically intractable purpose; (2) with the use of TNN and the Pawsey supercomputer, demonstrate the application of TNN to analyze the algorithm both with and without noise, and (3) check that the algorithm really works how we intend it to.**