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Non-autonomous dynamical systems appear in a very wide range of interesting applications, both in classical and quantum dynamics, where in the latter case it corresponds to having a time-dependent Hamiltonian. However, the quantum…
Quantum information science explores the frontier of highly complex quantum states, the "entanglement frontier." This study is motivated by the observation (widely believed but unproven) that classical systems cannot simulate highly…
State-of-the-art noisy intermediate-scale quantum devices (NISQ), although imperfect, enable computational tasks that are manifestly beyond the capabilities of modern classical supercomputers. However, present quantum computations are…
Quantum computers are believed to have the ability to process huge data sizes which can be seen in machine learning applications. In these applications, the data in general is classical. Therefore, to process them on a quantum computer,…
Quantum computing holds great promise to accelerate scientific computations in fluid dynamics and other classical physical systems. While various quantum algorithms have been proposed for linear flows, developing quantum algorithms for…
The nonlinear supersymmetry of one-dimensional systems is investigated in the context of the quantum anomaly problem. Any classical supersymmetric system characterized by the nonlinear in the Hamiltonian superalgebra is symplectomorphic to…
We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially…
This work outlines a consistent method of identifying subsystems in finite-dimensional Hilbert spaces, independent of the underlying inner-product structure. Such Hilbert spaces arise in $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics,…
We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the…
Superconducting quantum circuits are promising candidate for building scalable quantum computers. Here, we use a four-qubit superconducting quantum processor to solve a two-dimensional system of linear equations based on a quantum algorithm…
Computational fluid dynamics lies at the heart of many issues in science and engineering, but solving the associated partial differential equations remains computationally demanding. With the rise of quantum computing, new approaches have…
Attempts to find new quantum algorithms that outperform classical computation have focused primarily on the nonabelian hidden subgroup problem, which generalizes the central problem solved by Shor's factoring algorithm. We suggest an…
As with many tasks in engineering, structural design frequently involves navigating complex and computationally expensive problems. A prime example is the weight optimization of laminated composite materials, which to this day remains a…
Discovering a suitable coordinate transformation for nonlinear systems enables the construction of simpler models, facilitating prediction, control, and optimization for complex nonlinear systems. To that end, Koopman operator theory offers…
It is well-known that the controllability of finite-dimensional nonlinear systems can be established by showing the controllability of the linearized system. However, this classical result does not generalize to infinite-dimensional…
Quantum algorithms have been developed for efficiently solving linear algebra tasks. However, they generally require deep circuits and hence universal fault-tolerant quantum computers. In this work, we propose variational algorithms for…
An algorithm for quantum computing Hamiltonian cycles of simple, cubic, bipartite graphs is discussed. It is shown that it is possible to evolve a quantum computer into an entanglement of states which map onto the set of all possible paths…
Many promising quantum applications depend on the efficient quantum simulation of an exponentially large sparse Hamiltonian, a task known as sparse Hamiltonian simulation, which is fundamentally important in quantum computation. Although…
We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves…
We propose a scheme for data-driven parameterization of unresolved dimensions of dynamical systems based on the mathematical framework of quantum mechanics and Koopman operator theory. Given a system in which some components of the state…