Related papers: On multivariate polynomials achievable with quantu…
Black-box quantum-state preparation is a variant of quantum-state preparation where we want to construct an $n$-qubit state $|\psi_c\rangle \propto \sum_x c(x) |x\rangle$ with the amplitudes $c(x)$ given as a (quantum) oracle. This variant…
The concurrent rise of artificial intelligence and quantum information poses opportunity for creating interdisciplinary technologies like quantum neural networks. Quantum reservoir processing, introduced here, is a platform for quantum…
Symmetric quantum signal processing provides a parameterized representation of a real polynomial, which can be translated into an efficient quantum circuit for performing a wide range of computational tasks on quantum computers. For a given…
The $q$-th order spectrum is a polynomial of degree $q$ in the entries of a signal $x\in\mathbb{C}^N$, which is invariant under circular shifts of the signal. For $q\geq 3$, this polynomial determines the signal uniquely, up to a circular…
Quantum phase estimation is a central primitive in quantum algorithms and sensing, where performance is governed by the sensitivity of measurement signals to the target parameter. While existing methods have developed increasingly…
Spectroscopy underpins modern scientific discovery across diverse disciplines. While experimental spectroscopy probes material properties through scattering or radiation measurements, computational spectroscopy combines theoretical models…
The application of quantum computation to accelerate machine learning algorithms is one of the most promising areas of research in quantum algorithms. In this paper, we explore the power of quantum learning algorithms in solving an…
Quantum signal processing allows for quantum eigenvalue transformation with Hermitian matrices, in which each eigenspace component of an input vector gets transformed according to its eigenvalue. In this work, we introduce the multivariate…
Predicting and analyzing global behaviour of complex systems is challenging due to the intricate nature of their component interactions. Recent work has started modelling complex systems using networks endowed with multiway interactions…
Quantum computing can provide speedups in solving many problems as the evolution of a quantum system is described by a unitary operator in an exponentially large Hilbert space. Such unitary operators change the phase of their eigenstates…
Quantum algorithm is an algorithm for solving mathematical problems using quantum systems encoded as information, which is found to outperform classical algorithms in some specific cases. The objective of this study is to develop a quantum…
We introduce the Hidden Polynomial Function Graph Problem as a natural generalization of an abelian Hidden Subgroup Problem (HSP) where the subgroups and their cosets correspond to graphs of linear functions over the finite field F_p. For…
Entangled quantum probes can achieve Heisenberg-limited measurement precision, but this advantage is typically destroyed by noise. We address this issue by introducing a framework that we call encoded quantum signal processing, which…
We present two new algorithms for the computation of the q-integer linear decomposition of a multivariate polynomial. Such a decomposition is essential for the treatment of q-hypergeometric symbolic summation via creative telescoping and…
A novel family of Cosine series Quantum Sampling (QCoSamp) operators appropriate for quantum computing is described. The development of quantum algorithms, analogous to classical algorithms, we apply to the harmonic analysis of signals. We…
We prove that quantum computation is polynomially equivalent to classical probabilistic computation with an oracle for estimating the value of simple sums, quadratically signed weight enumerators. The problem of estimating these sums can be…
Quantum process tomography (QPT), used to estimate the linear map that best describes a quantum operation, is usually performed using a priori assumptions about state preparation and measurement (SPAM), which yield a biased and inconsistent…
In recent years there has been an increasing interest on the theoretical and experimental investigation of space-time dual quantum circuits. They exhibit unique properties and have applications to diverse fields. Periodic space-time dual…
Quantum linear system solvers typically realize the inverse map as a polynomial transformation of the spectrum, so their practical cost hinges on implementing this transformation at a low polynomial degree. We introduce constrained optimal…
Symbolic Mathematical tasks such as integration often require multiple well-defined steps and understanding of sub-tasks to reach a solution. To understand Transformers' abilities in such tasks in a fine-grained manner, we deviate from…