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Quantum gates built out of braid group elements form the building blocks of topological quantum computation. They have been extensively studied in $SU(2)_k$ quantum group theories, a rich source of examples of non-Abelian anyons such as the…
One of the challenging scientific computing problems is topology optimization, where searching through the combinatorially complex configurations and solving the constraints of partial differential equations need to be done simultaneously.…
Combinatorial problems are formulated to find optimal designs within a fixed set of constraints. They are commonly found across diverse engineering and scientific domains. Understanding how to best use quantum computers for combinatorial…
A foundational assumption of quantum error correction theory is that quantum gates can be scaled to large processors without exceeding the error-threshold for fault tolerance. Two major challenges that could become fundamental roadblocks…
Scalability is currently one of the most sought-after objectives in the field of quantum computing. Distributing a quantum circuit across a quantum network is one way to facilitate large computations using current quantum computers. In this…
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…
A limited number of qubits, high error rates, and limited qubit connectivity are major challenges for effective near-term quantum computations. Quantum circuit partitioning divides a quantum computation into a set of computations that…
Quasi branch and bound is a recently introduced generalization of branch and bound, where lower bounds are replaced by a relaxed notion of quasi-lower bounds, required to be lower bounds only for sub-cubes containing a minimizer. This paper…
We propose a complete quantum-classical hybrid branch-and-bound algorithm (QCBB) to solve binary linear programs with equality constraints. That includes bound calculation, convergence metrics and optimality guarantee to the quantum…
We consider a group of computation units trying to cooperatively solve a distributed optimization problem with shared linear equality and inequality constraints. Assuming that the computation units are communicating over a network whose…
We study the problem of probability distribution matching and sampling on near-term quantum computers, aiming to construct parameterized circuits that generate samples from a target distribution while minimizing resource overhead. This task…
A fundamental model of quantum computation is the programmable quantum gate array. This is a quantum processor that is fed by a program state that induces a corresponding quantum operation on input states. While being programmable, any…
In a topological quantum computer, universal quantum computation is performed by dragging quasiparticle excitations of certain two dimensional systems around each other to form braids of their world lines in 2+1 dimensional space-time. In…
Bayesian network structure learning is an NP-hard problem that has been faced by a number of traditional approaches in recent decades. Currently, quantum technologies offer a wide range of advantages that can be exploited to solve…
Variational quantum algorithms, such as the Recursive Quantum Approximate Optimization Algorithm (RQAOA), have become increasingly popular, offering promising avenues for employing Noisy Intermediate-Scale Quantum devices to address…
We propose a Riemannian limited-memory BFGS method for optimization problems with Euclidean bounds. The method combines a limited-memory quasi-Newton update in the tangent space with a Riemannian adaptation of the generalized Cauchy point…
Huffman coding finds a prefix code that minimizes mean codeword length for a given probability distribution over a finite number of items. Campbell generalized the Huffman problem to a family of problems in which the goal is to minimize not…
Present quantum computers are constrained by limited qubit capacity and restricted physical connectivity, leading to challenges in large-scale quantum computations. Distributing quantum computations across a network of quantum computers is…
Probabilistic verification problems of neural networks are concerned with formally analysing the output distribution of a neural network under a probability distribution of the inputs. Examples of probabilistic verification problems include…
One of the main limitations of variational quantum algorithms is the classical optimization of the highly dimensional non-convex variational parameter landscape. To simplify this optimization, we can reduce the search space using problem…