Related papers: On multivariate polynomials achievable with quantu…
This research extends quantum singular value transformation (QSVT) for general bounded operators embedded in unitary operators on possibly infinite-dimensional Hilbert spaces. Through in-depth mathematical exploration, we have achieved a…
We study separable plus quadratic (SPQ) polynomials, i.e., polynomials that are the sum of univariate polynomials in different variables and a quadratic polynomial. Motivated by the fact that nonnegative separable and nonnegative quadratic…
A quantum processor is a device with a data register and a program register. The input to the program register determines the operation, which is a completely positive linear map, that will be performed on the state in the data register. We…
Complex processes often arise from sequences of simpler interactions involving a few particles at a time. These interactions, however, may not be directly accessible to experiments. Here we develop the first efficient method for unravelling…
A fundamental task in photonics is to characterise an unknown optical process, defined by properties such as birefringence, spectral response, thickness and flatness. Amongst many ways to achieve this, single-photon probes can be used in a…
An estimation method is presented for polynomial phase signals, i.e., those adopting the form of a complex exponential whose phase is polynomial in its indices. Transcending the scope of existing techniques, the proposed estimator can…
A generalization of quantum broadcasting protocol is presented. Here the goal is to copy an unknown input state into two subsystems which partially overlap. We show that the possibility of implementing these protocols strongly depends upon…
Frequency-bin qubits possess unique synergies with wavelength-multiplexed lightwave communications, suggesting valuable opportunities for quantum networking with the existing fiber-optic infrastructure. Although the coherent manipulation of…
Equivariant quantum neural networks (QNNs) are promising variational models that exploit symmetries to improve machine learning capabilities. Despite theoretical developments in equivariant QNNs, their implementation on near-term quantum…
Quantum signal processing (QSP) studies quantum circuits interleaving known unitaries (the phases) and unknown unitaries encoding a hidden scalar (the signal). For a wide class of functions one can quickly compute the phases applying a…
Let $s_{ij}$ represent a tranposition in $S_n$. A polynomial $P$ in $\mathbb{Q}[X_n]$ is said to be $m$-quasiinvariant with respect to $S_n$ if $(x_i-x_j)^{2m+1}$ divides $(1-s_{ij})P$ for all $1 \leq i, j \leq n$. We call the ring…
Quantum mechanics contains some strange unphysical concepts. Among these are complex numbers, Hilbert spaces with their unitary and self-adjoint operators, states represented by complex vectors, superpositions of states, collapse of wave…
The paradigm behind digital quantum computing inherits the idea of using binary information processing. Nature in fact gives much more rich structures of physical objects that can be used for encoding information, which is especially…
We define a $q$-deformation of the classical ring of integer-valued polynomials which we call the ring of quantum integer-valued polynomials. We show that this ring has a remarkable combinatorial structure and enjoys many positivity…
We advocate a new approach of addressing hidden structure problems and finding efficient quantum algorithms. We introduce and investigate the Hidden Symmetry Subgroup Problem (HSSP), which is a generalization of the well-studied Hidden…
Theoretical development and applications of graph signal processing (GSP) have attracted much attention. In classical GSP, the underlying structures are restricted in terms of dimensionality. A graph is a combinatorial object that models…
Statistically interpretable axioms are formulated that define a quantum stochastic process (QSP) as a causally ordered operator field in an arbitrary space-time region T of an open quantum system under a sequential observation at a discrete…
Numerous quantum algorithms operate under the assumption that classical data has already been converted into quantum states, a process termed Quantum State Preparation (QSP). However, achieving precise QSP requires a circuit depth that…
A fundamental step of any quantum algorithm is the preparation of qubit registers in a suitable initial state. Often qubit registers represent a discretization of continuous variables and the initial state is defined by a multivariate…
Multivariate quantum signal processing (M-QSP) has recently been shown to be applicable for non-Hermitian Hamiltonian simulation, opening several problems regarding the optimization landscape, angle-finding, and constant-factor analysis. We…