Related papers: Optimal Scaling Quantum Interior Point Method for …
Classical optimization algorithms in machine learning often take a long time to compute when applied to a multi-dimensional problem and require a huge amount of CPU and GPU resource. Quantum parallelism has a potential to speed up machine…
The demand for classical-quantum hybrid algorithms to solve large-scale combinatorial optimization problems using quantum annealing (QA) has increased. One approach involves obtaining an approximate solution using classical algorithms and…
Constrained combinatorial optimization problems, which are ubiquitous in industry, can be solved by quantum algorithms such as quantum annealing (QA) and the quantum approximate optimization algorithm (QAOA). In these quantum algorithms,…
For typical quantum subroutines in the gate-based model of quantum computing, explicit decompositions of circuits in terms of single-qubit and two-qubit entangling gates may exist. However, they often lead to large-depth circuits that are…
Mission planning often involves optimising the use of ISR (Intelligence, Surveillance and Reconnaissance) assets in order to achieve a set of mission objectives within allowed parameters subject to constraints. The missions of interest…
We present a quantum interior point method with worst case running time $\widetilde{O}(\frac{n^{2.5}}{\xi^{2}} \mu \kappa^3 \log (1/\epsilon))$ for SDPs and $\widetilde{O}(\frac{n^{1.5}}{\xi^{2}} \mu \kappa^3 \log (1/\epsilon))$ for LPs,…
Quantum neural networks (QNNs) provide expressive probabilistic models by leveraging quantum superposition and entanglement, yet their practical training remains challenging due to highly oscillatory loss landscapes and noise inherent to…
Linear equations play a pivotal role in many areas of science and engineering, making efficient solutions to linear systems highly desirable. The development of quantum algorithms for solving linear systems has been a significant…
We present a quantum algorithm to solve systems of linear equations of the form $A\mathbf{x}=\mathbf{b}$, where $A$ is a tridiagonal Toeplitz matrix and $\mathbf{b}$ results from discretizing an analytic function, with a circuit complexity…
Integer linear programming (ILP) remains computationally challenging due to its NP-complete nature despite its central role in scheduling, logistics, and design optimization. We introduce a fully quantum Metropolis-Hastings algorithm for…
Hard combinatorial optimization problems, often mapped to Ising models, promise potential solutions with quantum advantage but are constrained by limited qubit counts in near-term devices. We present an innovative quantum-inspired framework…
The Quantum Approximate Optimization Algorithm (QAOA) is a promising approach for programming a near-term gate-based hybrid quantum computer to find good approximate solutions of hard combinatorial problems. However, little is currently…
The ADMM-based interior point (ABIP, Lin et al. 2021) method is a hybrid algorithm that effectively combines interior point method (IPM) and first-order methods to achieve a performance boost in large-scale linear optimization. Different…
Quantum machine learning for classical data is currently perceived to have a scalability problem due to (i) a bottleneck at the point of loading data into quantum states, (ii) the lack of clarity around good optimization strategies, and…
Quantum annealing offers a promising paradigm for solving NP-hard combinatorial optimization problems, but its practical application is severely hindered by two challenges: the complex, manual process of translating problem descriptions…
Learning the closest matrix product state (MPS) representation of a quantum state enables useful tools for quantum machine learning and analysis of complex quantum systems. In this work, we study the problem of learning MPS in the following…
Engineering design processes involve iterative design evaluations requiring numerous computationally intensive numerical simulations. Quantum algorithms promise substantial speedups for specific tasks relevant to engineering simulations.…
Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of…
The Quantum Approximate Optimization Algorithm (QAOA) is a leading approach for solving combinatorial optimization problems on near-term quantum processors. However, finding good variational parameters remains a significant challenge due to…
This thesis focuses on the intersection of mathematical and computational optimization and quantum information. Main contributions are open-source software code: A hybrid approach mixing "traditional" nonconvex and convex methods can make…