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We consider a composite open quantum system consisting of a fast subsystem coupled to a slow one. Using the time-scale separation, we develop an adiabatic elimination technique to derive at any order the reduced model describing the slow…
Adiabatic quantum computation employs a slow change of a time-dependent control function (or functions) to interpolate between an initial and final Hamiltonian, which helps to keep the system in the instantaneous ground state. When the…
Quantum adiabatic evolution algorithm suggested by Farhi et al. was effective in solving instances of NP-complete problems. The algorithm is governed by the adiabatic theorem. Therefore, in order to reduce the running time, it is essential…
We propose a numerical approach to design highly efficient adiabatic schedules for analog quantum computing, focusing on the maximum-independent-set problem and neutral atom platforms. On the basis of a representative dataset of small…
Quantum computers can solve semidefinite programs (SDPs) using resources that scale better than state-of-the-art classical methods as a function of the problem dimension. At the same time, the known quantum algorithms scale very unfavorably…
The task of finding optimal protocols that minimize the energetic cost of thermodynamic processes of long yet finite duration $\tau$ is a pressing one. We approach this problem here in a rigorous and systematic fashion by means of the…
In a previous publication we proposed discrete global optimization as a method to train a strong binary classifier constructed as a thresholded sum over weak classifiers. Our motivation was to cast the training of a classifier into a format…
While quantum computing provides an exponential advantage in solving linear differential equations, there are relatively few quantum algorithms for solving nonlinear differential equations. In our work, based on the homotopy perturbation…
The quantum approximate optimization algorithm (QAOA) is an approach for near-term quantum computers to potentially demonstrate computational advantage in solving combinatorial optimization problems. However, the viability of the QAOA…
Quantum computation has revolutionary potential for speeding algorithms and for simulating quantum systems such as molecules. We report here a quantum computer design that performs universal quantum computation within a single…
The ability to efficiently prepare ground states of quantum Hamiltonians via adiabatic protocols is typically limited by the smallest energy gap encountered during the quantum evolution. This presents a key obstacle for quantum simulation…
It has been recently argued that adiabatic quantum optimization would fail in solving NP-complete problems because of the occurrence of exponentially small gaps due to crossing of local minima of the final Hamiltonian with its global…
We present an analog version of the quantum approximate optimization algorithm suitable for current quantum annealers. The central idea of this algorithm is to optimize the schedule function, which defines the adiabatic evolution. It is…
Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a $d$-dimensional system…
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…
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…
The demand for classical-quantum hybrid algorithms to solve large-scale combinatorial optimization problems using quantum annealing (QA) has increased. One approach involves obtaining an approximate solution using classical algorithms and…
We present a new quantum adiabatic theorem that allows one to rigorously bound the adiabatic timescale for a variety of systems, including those described by unbounded Hamiltonians. Our bound is geared towards the qubit approximation of…
According to the adiabatic theorem of quantum mechanics, a system initially in the ground state of a Hamiltonian remains in the ground state if one slowly changes the Hamiltonian. This can be used in principle to solve hard problems on…
Big Data is characterized by Volume, Velocity, Veracity and Complexity. The interaction between this huge data is complex with an associated free will having dynamic and non linear nature. We reduced big data based on its characteristics,…