Related papers: Singular value transformation for unknown quantum …
Estimating the eigenvalues of a unitary transformation U by standard phase estimation requires the implementation of controlled-U-gates which are not available if U is only given as a black box. We show that a simple trick allows to measure…
Quantum Signal Processing (QSP) and Quantum Singular Value Transformation (QSVT) currently stand as the most efficient techniques for implementing functions of block encoded matrices, a central task that lies at the heart of most prominent…
It is known that the unified transform method may be used to solve any well-posed initial-boundary value problem for a linear constant-coefficient evolution equation on the finite interval or the half-line. In contrast, classical methods…
Singularity of the potential function makes quantum tunneling problem mathematically underdetermined. To circumvent the difficulties it introduced in physics, a potential singularity cutoff is often used, followed by a reverse limit…
The impressive pace of advance of quantum technology calls for robust and scalable techniques for the characterization and validation of quantum hardware. Quantum process tomography, the reconstruction of an unknown quantum channel from…
Quantum dynamics for arbitrary system are traditionally realized by time evolutions of wave functions in Hilbert space and/or density operators in Liouville space. However, the traditional simulations may occasionally turn out to be…
Quantum communication holds the potential to revolutionize information transmission by enabling secure data exchange that exceeds the limits of classical systems. One of the key performance metrics in quantum information theory, namely the…
We propose and theoretically study a method for the stochastic realization of arbitrary quantum channels on multimode single-photon qudits. In order for our method to be undemanding in its implementation, we restrict our analysis to…
Block Encoding (BE) is a crucial subroutine in many modern quantum algorithms, including those with near-optimal scaling for simulating quantum many-body systems, which often rely on Quantum Signal Processing (QSP). Currently, the primary…
Quantum simulation is one of the central discipline to demonstrate the power of quantum computing. In recent years, the theoretical framework of quantum superchannels has been developed and applied widely as the extension of quantum…
Geometric quantum machine learning uses the symmetries inherent in data to design tailored machine learning tasks with reduced search space dimension. The field has been well-studied recently in an effort to avoid barren plateau issues…
In this thesis we analyse the type of states and ensembles which achieve the capacity for certain quantum channels carrying classical information. We first concentrate on the product-state capacity of a particular quantum channel, that is,…
We investigate the possibility of performing full quantum tomography based on the homogeneous time evolution of a single expectation value. Remarkably, every non-trivial binary measurement evolved by any quantum channel, except for a null…
In this work, we propose a generally applicable transformation unit for visual recognition with deep convolutional neural networks. This transformation explicitly models channel relationships with explainable control variables. These…
We introduce a new quantum noise deconvolution technique that does not rely on the complete knowledge of noise and does not require partial noise tomography. In this new method, we construct a set of observables with completely correctable…
Block-encoding operators are one of the essential components in quantum algorithms based on Quantum Signal Processing. Their gate complexity largely determines the overall gate complexity of the full algorithm. Using variational methods, we…
We propose a quantum soft-covering problem for a given general quantum channel and one of its output states, which consists in finding the minimum rank of an input state needed to approximate the given channel output. We then prove a…
Quantum signal processing (QSP), which enables systematic polynomial transformations on quantum data through sequences of qubit rotations, has emerged as a fundamental building block for quantum algorithms and data re-uploading quantum…
The spectral statistics of non-Hermitian random matrices are of importance as a diagnostic tool for chaotic behavior in open quantum systems. Here, we investigate the statistical properties of singular values in non-Hermitian random…
As the rapidly evolving field of machine learning continues to produce incredibly useful tools and models, the potential for quantum computing to provide speed up for machine learning algorithms is becoming increasingly desirable. In…