Related papers: Efficient quantum amplitude encoding of polynomial…
Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum…
Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian…
Efficiently characterizing large quantum states and processes is a central yet notoriously challenging task in quantum information science, as conventional tomography methods typically require resources that grow exponentially with system…
Several problems in computer algebra can be efficiently solved by reducing them to calculations over finite fields. In this paper, we describe an algorithm for the reconstruction of multivariate polynomials and rational functions from their…
This paper focuses on the quantum amplitude estimation algorithm, which is a core subroutine in quantum computation for various applications. The conventional approach for amplitude estimation is to use the phase estimation algorithm, which…
A diffusion probabilistic model (DPM) is a generative model renowned for its ability to produce high-quality outputs in tasks such as image and audio generation. However, training DPMs on large, high-dimensional datasets such as…
Gradient-based algorithms, popular strategies to optimization problems, are essential for many modern machine-learning techniques. Theoretically, extreme points of certain cost functions can be found iteratively along the directions of the…
While quantum algorithms for solving large scale systems of linear equations offer potentially exponential speedups, their application has largely been confined to sparse matrices. This work extends the scope of these algorithms to a broad…
Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value…
Quantum block encoding (QBE) is a crucial step in the development of most quantum algorithms, as it provides an embedding of a given matrix into a suitable larger unitary matrix. Historically, the development of efficient techniques for QBE…
The stable operation of quantum computers will rely on error-correction, in which single quantum bits of information are stored redundantly in the Hilbert space of a larger system. Such encoded qubits are commonly based on arrays of many…
A quantum computer directly manipulates information stored in the state of quantum mechanical systems. The available operations have many attractive features but also underly severe restrictions, which complicate the design of quantum…
Here, we study the capacity of a quantum channel, assuming linear optical encoding, as a function of available photons and optical modes. First, we observe that substantial improvement is made possible by not restricting ourselves to a…
Classical information loading is an essential task for many processing quantum algorithms, constituting a cornerstone in the field of quantum machine learning. In particular, the embedding techniques based on Hamiltonian simulation…
We introduce a versatile method for preparing a quantum state whose amplitudes are given by some known function. Unlike existing approaches, our method does not require handcrafted reversible arithmetic circuits, or quantum table reads, to…
Quantum embedding is an appealing route to fragment a large interacting quantum system into several smaller auxiliary `cluster' problems to exploit the locality of the correlated physics. In this work we critically review approaches to…
Quantum tomography is a crucial tool for characterizing quantum states and devices and estimating nonlinear properties of the systems. Performing full quantum state tomography on an $N_\mathrm{q}$ qubit system requires an exponentially…
This paper introduces quantum circuit methodologies for pointwise multiplication and convolution of complex functions, conceptualized as "processing through encoding". Leveraging known techniques, we describe an approach where multiple…
While the preparation of a general quantum state is challenging, realistic problem instances, such as those encountered in quantum chemistry and quantum machine learning-typically exhibit hierarchical amplitude structures, consisting of a…
The Harrow-Hassidim-Lloyd (HHL) quantum algorithm for sampling from the solution of a linear system provides an exponential speed-up over its classical counterpart. The problem of solving a system of linear equations has a wide scope of…