Related papers: A Lyapunov Framework for Quantum Algorithm Design …
Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and…
In this paper, we solve a maximization problem where the objective function is quadratic and the constraints set is the reachable values set of a stable discrete-time affine system. This problem is equivalent to solve an infinite number of…
Gate model quantum computers with too many qubits to be simulated by available classical computers are about to arrive. We present a strategy for programming these devices without error correction or compilation. This means that the number…
As industrial models and designs grow increasingly complex, the demand for optimal control of large-scale dynamical systems has significantly increased. However, traditional methods for optimal control incur significant overhead as problem…
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,…
The quantum approximate optimization algorithm (QAOA) is a hybrid variational quantum-classical algorithm that solves combinatorial optimization problems. While there is evidence suggesting that the fixed form of the standard QAOA ansatz is…
A range of quantum algorithms, especially those leveraging variational parameterization and circuit-based optimization, are being studied as alternatives for solving classically intractable combinatorial optimization problems (COPs).…
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…
We propose an anytime online algorithm for the problem of learning a sequence of adversarial convex cost functions while approximately satisfying another sequence of adversarial online convex constraints. A sequential algorithm is called…
In this paper, we propose a systematic approach for extending first-order optimization algorithms, originally designed for unconstrained strongly convex problems, to handle closed and convex set constraints. We show that the resulting…
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 introduce an iterative method to search for time-optimal Hamiltonians that drive a quantum system between two arbitrary, and in general mixed, quantum states. The method is based on the idea of progressively improving the efficiency of…
Approximate combinatorial optimization is a promising use case for quantum computers. The quantum optimization algorithms often employ a fixed ansatz that evolves an unbiased initial state towards states with better values of the optimand,…
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…
It is hoped that quantum computers will offer advantages over classical computers for combinatorial optimization. Here, we introduce a feedback-based strategy for quantum optimization, where the results of qubit measurements are used to…
Recently, feedback-based quantum algorithms have been introduced to calculate the ground states of Hamiltonians, inspired by quantum Lyapunov control theory. This paper aims to generalize these algorithms to the problem of calculating an…
The Quantum Approximate Optimization Algorithm (QAOA) constitutes one of the often mentioned candidates expected to yield a quantum boost in the era of near-term quantum computing. In practice, quantum optimization will have to compete with…
Combinatorial optimization problems that arise in science and industry typically have constraints. Yet the presence of constraints makes them challenging to tackle using both classical and quantum optimization algorithms. We propose a new…
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…
Algorithms based on non-unitary evolution have attracted much interest for ground state preparation on quantum computers. One recently proposed method makes use of ancilla qubits and controlled unitary operators to implement weak…