Related papers: Near-optimal quantum circuit for Grover's unstruct…
We introduce a novel quantum optimization paradigm: the Fixed-Parameter-Count Quantum Approximate Optimization Algorithm (FPC-QAOA). It is a scalable variational framework that maintains a constant number of trainable parameters regardless…
Traffic optimization on roads is a highly complex problem, with one important aspect being minimization of traffic congestion. By mapping to an Ising formulation of the traffic congestion problem, we benchmark solutions obtained from the…
A quantum computer encodes information in quantum states and runs quantum algorithms to surpass the classical counterparts by exploiting quantum superposition and quantum correlation. Grover's quantum search algorithm is a typical quantum…
Quantum Annealing (QA) and QAOA are promising quantum optimisation algorithms used for finding approximate solutions to combinatorial problems on near-term NISQ systems. Many NP-hard problems can be reformulated as Quadratic Unconstrained…
This paper addresses the problem of finding the densest $k$-vertex subgraph in an arbitrary graph. This problem is NP-hard and has important applications in social network analysis, fraud detection, recommendation systems, and…
The Quantum Approximate Optimization Algorithm (QAOA) is designed to run on a gate model quantum computer and has shallow depth. It takes as input a combinatorial optimization problem and outputs a string that satisfies a high fraction of…
Proposed hybrid algorithms encode a combinatorial cost function into a problem Hamiltonian and optimize its energy by varying over a set of states with low circuit complexity. Classical processing is typically only used for the choice of…
Quantum Approximate Optimization Algorithm (QAOA) and its variants exhibit immense potential in tackling combinatorial optimization challenges. However, their practical realization confronts a dilemma: the requisite circuit depth for…
The variational preparation of complex quantum states using the quantum approximate optimization algorithm (QAOA) is of fundamental interest, and becomes a promising application of quantum computers. Here, we systematically study the…
While the ultimate goal of solving computationally intractable problems is to find a provably optimal solutions, practical constraints of real-world scenarios often necessitate focusing on efficiently obtaining high-quality, near-optimal…
Farhi et al. recently proposed a class of quantum algorithms, the Quantum Approximate Optimization Algorithm (QAOA), for approximately solving combinatorial optimization problems. A level-p QAOA circuit consists of p steps; in each step a…
As combinatorial optimization is one of the main quantum computing applications, many methods based on parameterized quantum circuits are being developed. In general, a set of parameters are being tweaked to optimize a cost function out of…
Quantum Approximate Optimization Algorithm (QAOA) and Quantum Annealing are prominent approaches for solving combinatorial optimization problems, such as those formulated as Quadratic Unconstrained Binary Optimization (QUBO). These…
Quantum variational algorithms have garnered significant interest recently, due to their feasibility of being implemented and tested on noisy intermediate scale quantum (NISQ) devices. We examine the robustness of the quantum approximate…
Quantum Annealing (QA) and the Quantum Approximate Optimization Algorithm (QAOA) are two special cases of the following control problem: apply a combination of two Hamiltonians to minimize the energy of a quantum state. Which is more…
The Quantum Alternating Operator Ansatz (QAOA) is a hybrid classical-quantum algorithm that aims to sample the optimal solution(s) of discrete combinatorial optimization problems. We present optimized QAOA circuit constructions for sampling…
Combinatorial optimization is among the main applications envisioned for near-term and fault-tolerant quantum computers. In this work, we consider a well-studied quantum algorithm for combinatorial optimization: the Quantum Approximate…
Current state-of-the-art quantum optimization algorithms require representing the original problem as a binary optimization problem, which is then converted into an equivalent cost Hamiltonian suitable for the quantum device. Implementing…
The promise of quantum computing to address complex problems requiring high computational resources has long been hindered by the intrinsic and demanding requirements of quantum hardware development. Nonetheless, the current state of…
This article consists of a short introduction to the quantum approximation optimisation algorithm (QAOA). The mathematical structure of the QAOA, as well as its basic properties, are described. The implementation of the QAOA on MaxCut…