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Due to the limited connectivity of gate model quantum devices, logical quantum circuits must be compiled to target hardware before they can be executed. Often, this process involves the insertion of SWAP gates into the logical circuit,…
This paper investigates the experimental performance of a discrete portfolio optimization problem relevant to the financial services industry on the gate-model of quantum computing. We implement and evaluate a portfolio rebalancing use case…
The Quantum Approximate Optimization Algorithm (QAOA) is a promising variational algorithm for solving combinatorial optimization problems on near-term devices. However, as the number of layers in a QAOA circuit increases, which is…
Quantum computing provides powerful algorithmic tools that have been shown to outperform established classical solvers in specific optimization tasks. A core step in solving optimization problems with known quantum algorithms such as the…
Universal fault-tolerant quantum computers will require error-free execution of long sequences of quantum gate operations, which is expected to involve millions of physical qubits. Before the full power of such machines will be available,…
A quantum circuit must be preprocessed before implementing on NISQ devices due to the connectivity constraint. Quantum circuit mapping (QCM) transforms the circuit into an equivalent one that is compliant with the NISQ device's architecture…
Quantum computing can provide speedups in solving many problems as the evolution of a quantum system is described by a unitary operator in an exponentially large Hilbert space. Such unitary operators change the phase of their eigenstates…
This paper studies quantum optimization baselines for the Generalized Traveling Salesman Problem (GTSP), a clustered routing problem that naturally models variant selection and sequencing problems under discrete alternatives. We propose a…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
The recent progress in the physical realization of quantum computers (the first publicly available ones--IBM's QX architectures--have been launched in 2017) has motivated research on automatic methods that aid users in running quantum…
Portfolio optimization is a primary component of the decision-making process in finance, aiming to tactfully allocate assets to achieve optimal returns while considering various constraints. Herein, we proposed a method that uses the…
Quantum Variational Circuits (QVCs) are often claimed as one of the most potent uses of both near term and long term quantum hardware. The standard approaches to optimizing these circuits rely on a classical system to compute the new…
Solving linear systems and quadratic programming (QP) problems are both ubiquitous tasks in the engineering and computing fields. Direct methods for solving systems, such as Cholesky, LU, and QR factorizations, exhibit data-independent time…
In typical black-box optimization applications, the available computational budget is often allocated to a single algorithm, typically chosen based on user preference with limited knowledge about the problem at hand or according to some…
Quantum computing is a rapidly expanding field with applications ranging from optimization all the way to complex machine learning tasks. Quantum memories, while lacking in practical quantum computers, have the potential to bring quantum…
The quantum approximate optimization algorithm (QAOA) is known for its capability and universality in solving combinatorial optimization problems on near-term quantum devices. The results yielded by QAOA depend strongly on its initial…
In this paper, we give quantum algorithms for two fundamental computation problems: solving polynomial systems over finite fields and optimization where the arguments of the objective function and constraints take values from a finite field…
This paper studies the worst case iteration complexity of an infeasible interior point method (IPM) for seconder order cone programming (SOCP), which is more convenient for warmstarting compared with feasible IPMs. The method studied bases…
Abstraction layers are of paramount importance in software architecture, as they shield the higher-level formulation of payload computations from lower-level details. Since quantum computing (QC) introduces many such details that are often…
We introduce a quantum algorithm that produces approximate solutions for combinatorial optimization problems. The algorithm depends on a positive integer p and the quality of the approximation improves as p is increased. The quantum circuit…