Related papers: Singular value transformation for unknown quantum …
World-wide efforts aim at the realization of advanced quantum simulators and processors. However, despite the development of intricate hardware and pulse control systems, it may still not be generally known which effective quantum dynamics,…
Entanglement is a defining property of quantum systems. For a subsystem of a larger quantum system, one can formally define an operator known as the modular Hamiltonian, which is closely linked to the entanglement properties of that…
Quantum superdense coding protocols enhance channel capacity by using shared quantum entanglement between two users. The channel capacity can be as high as 2 when one uses entangled qubits. However, this limit can be surpassed by using…
Quantum error correction (QEC) is essential for reliable quantum information processing. Targeting a particular error channel, both the encoding and the recovery channel can be optimized through a biconvex optimization to give a…
We study the general framework of quantum channel simulation, that is, the ability of a quantum channel to simulate another one using different classes of codes. First, we show that the minimum error of simulation and the one-shot quantum…
Symmetry inherent in quantum states has been widely used to reduce the effect of noise in quantum error correction and a quantum error mitigation technique known as symmetry verification. However, these symmetry-based techniques exploit…
Simulating quantum physical processes has been one of the major motivations for quantum information science. Quantum channels, which are completely positive and trace preserving processes, are the standard mathematical language to describe…
The computational problem of distinguishing two quantum channels is central to quantum computing. It is a generalization of the well-known satisfiability problem from classical to quantum computation. This problem is shown to be…
In convolutional neural networks, the linear transformation of multi-channel two-dimensional convolutional layers with linear convolution is a block matrix with doubly Toeplitz blocks. Although a "wrapping around" operation can transform…
We study private quantum channels on a single qubit, which encrypt given set of plaintext states $P$. Specifically, we determine all achievable states $\rho^{(0)}$ (average output of encryption) and for each particular set $P$ we determine…
Quasi-degenerate eigenvalue problems are central to quantum chemistry and condensed-matter physics, where low-energy spectra often form manifolds of nearly degenerate states that determine physical properties. Standard quantum algorithms,…
From telecommunication to computing architectures, the realm of classical information hinges on converter technology to enable the exchange of data between digital and analog formats, a process now routinely performed across a variety of…
In this work, we present a method to exponentiate non-sparse indefinite low-rank matrices on a quantum computer. Given an operation for accessing the elements of the matrix, our method allows singular values and associated singular vectors…
Quantum signal processing is a powerful framework in quantum algorithms, playing a central role in Hamiltonian simulation and related applications. The sequence of polynomials implemented at each step of this protocol provides a polynomial…
Quantum process tomography, the standard procedure to characterize any quantum channel in nature, is affected by a circular argument: in order to characterize the channel, the tomographic preparation and measurement need in turn to be…
Quantum algorithms for estimating the eigenvalues of matrices, including the phase estimation algorithm, serve as core subroutines in a wide range of quantum algorithms, including those in quantum chemistry and quantum machine learning. The…
Given a list of n complex numbers, when can it be the spectrum of a quantum channel, i.e., a completely positive trace preserving map? We provide an explicit solution for the n=4 case and show that in general the characterization of the…
In high dimensional quantum communication networks, quantum frequency convertor (QFC) is indispensable as an interface in the frequency domain. For example, many QFCs have been built to link atomic memories and fiber channels. However,…
Quantum key distribution (QKD) allows for communication with security guaranteed by quantum theory. The main theoretical problem in QKD is to calculate the secret key rate for a given protocol. Analytical formulas are known for protocols…
We establish a connection between quantum mechanics and computation, revealing fundamental limitations for algorithms computing spectra, especially in non-Hermitian settings. Introducing the concept of locally trivial pseudospectra (LTP),…