Increasing the dimension of linear systems solved by classical or quantum binary optimization: A new method to solve large linear equation systems

Recently, binary optimization has become an attractive research topic due to the development of quantum computing and specialized classical systems inspired by quantum computing. These hardware systems promise to speed up the computation significantly. In this work, we propose a new method to solve linear systems written as a binary optimization problem. The procedure solves the problem efficiently and allows it to handle large linear systems. Our approach is founded on the geometry of the original linear problem and resembles the gradient conjugate method. The conjugated directions used can significantly improve the algorithm's convergence rate. We also show that a partial knowledge of the intrinsic geometry of the problem can divide the original problem into independent sub-problems of smaller dimensions. These sub-problems can then be solved using quantum or classical solvers. Although determining the geometry of the problem has an additional computational cost, it can substantially improve the performance of our method compared to previous implementations.Comment: 12 pages, 10 figure

Experimental realization of the Yang-Baxter Equation via NMR interferometry

The Yang-Baxter equation is an important tool in theoretical physics, with many applications in different domains that span from condensed matter to string theory. Recently, the interest on the equation has increased due to its connection to quantum information processing. It has been shown that the Yang-Baxter equation is closely related to quantum entanglement and quantum computation. Therefore, owing to the broad relevance of this equation, besides theoretical studies, it also became significant to pursue its experimental implementation. Here, we show an experimental realization of the Yang-Baxter equation and verify its validity through a Nuclear Magnetic Resonance (NMR) interferometric setup. Our experiment was performed on a liquid state Iodotrifluoroethylene sample which contains molecules with three qubits. We use Controlled-transfer gates that allow us to build a pseudo-pure state from which we are able to apply a quantum information protocol that implements the Yang-Baxter equation

Experimental Implementation of a Two-Stroke Quantum Heat Engine

We put forth an experimental simulation of a stroboscopic two-stroke thermal engine in the IBMQ processor. The system consists of a quantum spin chain connected to two baths at their boundaries, prepared at different temperatures using the variational quantum thermalizer algorithm. The dynamics alternates between heat and work strokes, which can be separately designed using independent quantum circuits. The results show good agreement with theoretical predictions, showcasing IBMQ as a powerful tool to study thermodynamics in the quantum regime, as well as the implementation of variational quantum algorithms in real-world quantum computers. It also opens the possibility of simulating quantum heat transport across a broad range of chains geometries and interactions

Experimental validation of fully quantum fluctuation theorems

Fluctuation theorems are fundamental extensions of the second law of thermodynamics for small systems. Their general validity arbitrarily far from equilibrium makes them invaluable in nonequilibrium physics. So far, experimental studies of quantum fluctuation relations do not account for quantum correlations and quantum coherence, two essential quantum properties. We here experimentally verify detailed and integral fully quantum fluctuation theorems for heat exchange using two quantum-correlated thermal spins-1/2 in a nuclear magnetic resonance setup. We confirm, in particular, individual integral fluctuation relations for quantum correlations and quantum coherence, as well as for the sum of all quantum contributions. These refined formulations of the second law are important for the investigation of fully quantum features in nonequilibrium thermodynamics

Quantum discord determines the interferometric power of quantum states

Quantum metrology exploits quantum mechanical laws to improve the precision in estimating technologically relevant parameters such as phase, frequency, or magnetic fields. Probe states are usually tailored to the particular dynamics whose parameters are being estimated. Here we consider a novel framework where quantum estimation is performed in an interferometric configuration, using bipartite probe states prepared when only the spectrum of the generating Hamiltonian is known. We introduce a figure of merit for the scheme, given by the worst-case precision over all suitable Hamiltonians, and prove that it amounts exactly to a computable measure of discord-type quantum correlations for the input probe. We complement our theoretical results with a metrology experiment, realized in a highly controllable room-temperature nuclear magnetic resonance setup, which provides a proof-of-concept demonstration for the usefulness of discord in sensing applications. Discordant probes are shown to guarantee a nonzero phase sensitivity for all the chosen generating Hamiltonians, while classically correlated probes are unable to accomplish the estimation in a worst-case setting. This work establishes a rigorous and direct operational interpretation for general quantum correlations, shedding light on their potential for quantum technology