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The optimization of the power consumption of antenna networks is a problem with a potential impact in the field of telecommunications. In this work, we investigate the application of the quantum approximate optimization algorithm (QAOA) and…
In the circuit model of quantum computing, amplitude amplification techniques can be used to find solutions to NP-hard problems defined on $n$-bits in time $\text{poly}(n) 2^{n/2}$. In this work, we investigate whether such general…
We give an approximation algorithm for Quantum Max-Cut which works by rounding an SDP relaxation to an entangled quantum state. The SDP is used to choose the parameters of a variational quantum circuit. The entangled state is then…
Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum…
The emergence of huge-scale, data-intensive linear optimization (LO) problems in applications such as machine learning has driven the need for more computationally efficient interior point methods (IPMs). While conventional IPMs are…
In this work, we consider two-stage quadratic optimization problems under ellipsoidal uncertainty. In the first stage, one needs to decide upon the values of a subset of optimization variables (control variables). In the second stage, the…
An enhanced framework of quantum approximate optimization algorithm (QAOA) is introduced and the parameter setting strategies are analyzed. The enhanced QAOA is as effective as the QAOA but exhibits greater computing power and flexibility,…
We introduce a framework for mapping NP-Hard problems to adiabatic quantum computing (AQC) architectures that are heavily restricted in both connectivity and dynamic range of couplings, for which minor-embedding -- the standard problem…
We consider the task of simulating time evolution under a Hamiltonian $H$ within its low-energy subspace. Assuming access to a block-encoding of $H'=(H-E)/\lambda$ for some $E \in \mathbb R$, the goal is to implement an…
Recent advances in quantum technology have led to the development and manufacturing of experimental programmable quantum annealers that promise to solve certain combinatorial optimization problems of practical relevance faster than their…
We develop an energy calculation algorithm leveraging quantum phase difference estimation (QPDE) scheme and a tensor-network-based unitary compression method in the preparation of superposition states and time-evolution gates. Alongside its…
In this work we develop theoretical techniques for analysing the performance of the quantum approximate optimization algorithm (QAOA) when applied to random boolean constraint satisfaction problems (CSPs), and use these techniques to…
We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…
In this paper, we study optimal experimental design problems with a broad class of smooth convex optimality criteria, including the classical A-, D- and p th mean criterion. In particular, we propose an interior point (IP) method for them…
Ising Machines are emerging hardware architectures that efficiently solve NP-Hard combinatorial optimization problems. Generally, combinatorial problems are transformed into quadratic unconstrained binary optimization (QUBO) form, but this…
The quantum approximate optimization algorithm (QAOA) is a leading iterative variational quantum algorithm for heuristically solving combinatorial optimization problems. A large portion of the computational effort in QAOA is spent by the…
We consider the problem of computing the value and an optimal strategy for minimizing the expected termination time in one-counter Markov decision processes. Since the value may be irrational and an optimal strategy may be rather…
Combinatorial optimization is a promising application for near-term quantum computers, however, identifying performant algorithms suited to noisy quantum hardware remains as an important goal to potentially realizing quantum computational…
Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems…
We consider the hardness of approximation of optimization problems from the point of view of definability. For many NP-hard optimization problems it is known that, unless P = NP, no polynomial-time algorithm can give an approximate solution…