Related papers: Decomposing large unitaries into multimode devices…
Dimension reduction techniques for multivariate time series decompose the observed series into a few useful independent/orthogonal univariate components. We develop a spectral domain method for multivariate second-order stationary time…
We present a data-driven method for separating complex, multiscale systems into their constituent time-scale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed…
A recurrence scheme is presented to decompose an $n$-qubit unitary gate to the product of no more than $N(N-1)/2$ single qubit gates with small number of controls, where $N = 2^n$. Detailed description of the recurrence steps and formulas…
With applications ranging from metabolomics to histopathology, quantitative phase microscopy (QPM) is a powerful label-free imaging modality. Despite significant advances in fast multiplexed imaging sensors and deep-learning-based inverse…
Multi-port beamsplitters are cornerstone devices for high-dimensional quantum information tasks, which can outperform the two-dimensional ones. Nonetheless, the fabrication of such devices has been proven to be challenging with progress…
We propose a variational scheme to represent composite quantum systems using multiple parameterized functions of varying accuracies on both classical and quantum hardware. The approach follows the variational principle over the entire…
We show that any unitary operator on the $d_A\times d_B$ system ($d_A\ge 2$) can be decomposed into the product of at most $4d_A-5$ controlled unitary operators. The number can be reduced to $2d_A-1$ when $d_A$ is a power of two. We also…
A key task in quantum computation is the application of a sequence of gates implementing a specific unitary operation. However, the decomposition of an arbitrary unitary operation into simpler quantum gates is a nontrivial problem. Here we…
On-chip mode-division multiplexing (MDM) has been emerging as a promising technology to further enhance the link capacity and bandwidth of data communications with multiple mode channels. Both mode converters and mode exchangers are…
Denoising is a fundamental imaging problem. Versatile but fast filtering has been demanded for mobile camera systems. We present an approach to multiscale filtering which allows real-time applications on low-powered devices. The key idea is…
Unknown unitary inversion is a fundamental primitive in quantum computing and physics. Although recent work has demonstrated that quantum algorithms can invert arbitrary unknown unitaries without accessing their classical descriptions,…
Electron transport in realistic physical and chemical systems often involves the non-trivial exchange of energy with a large environment, requiring the definition and treatment of open quantum systems. Because the time evolution of an open…
Although only two quantum states of a physical system are often used to encode quantum information in the form of qubits, many levels can in principle be used to obtain qudits and increase the information capacity of the system. To take…
One of the fundamental steps toward understanding a complex system is identifying variation at the scale of the system's components that is most relevant to behavior on a macroscopic scale. Mutual information provides a natural means of…
We propose an iterative algorithm to simulate the dynamics generated by any $n$-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator $U$ (unitary) into a product of different time-step unitaries. The…
Interferences in multi-path systems for single and multiple particles are theoretically analyzed. A holistic method is presented, which allows to construct the unitary transition matrix describing interferometers for any port number d and…
Positive time varying frequency representation for transient signals has been a hearty desire of signal analysts due to its theoretical and practical importance. During approximately the last two decades there has formulated a signal…
Linear combination of unitaries (LCU) decompositions have appeared as one of the main tools for encoding operators on quantum computers, allowing efficient implementations of arbitrary operators. In particular, LCU approaches present a way…
The problem of decomposing non-manifold object has already been studied in solid modeling. However, the few proposed solutions are limited to the problem of decomposing solids described through their boundaries. In this thesis we study the…
Composite quantum systems can be decomposed into subsystems in many different inequivalent ways. We call a particular decomposition a meronomic reference frame for the system. We apply the ideas of quantum reference frames to characterize…