Related papers: Infinite quantum signal processing
A quantum processor (QuP) can be used to exploit quantum mechanics to find the prime factors of composite numbers[1]. Compiled versions of Shor's algorithm have been demonstrated on ensemble quantum systems[2] and photonic systems[3-5],…
We provide a complete solution to the problem of infinite quantum signal processing for the class of Szeg\H{o} functions, which are functions that satisfy a logarithmic integrability condition and include almost any function that allows for…
A universal programmable quantum processor uses program quantum states to apply an arbitrary quantum channel to an input state. We generalize the concept of a finite-dimensional programmable quantum processor to infinite dimension assuming…
The phase estimation algorithm, which is at the heart of a variety of quantum algorithms, including Shor's factoring algorithm, allows a quantum computer to accurately determine an eigenvalue of an unitary operator. Quantum nondemolition…
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…
As a signal recovery algorithm, compressed sensing is particularly useful when the data has low-complexity and samples are rare, which matches perfectly with the task of quantum phase estimation (QPE). In this work we present a new…
Quantum effects like entanglement and coherent amplification can be used to drastically enhance the accuracy of quantum parameter estimation beyond classical limits. However, challenges such as decoherence and time-dependent errors hinder…
Quantum-mechanical phenomena are playing an increasing role in information processing, as transistor sizes approach the nanometer level, and quantum circuits and data encoding methods appear in the securest forms of communication.…
Although linear quantum amplification has proven essential to the processing of weak quantum signals, extracting higher-order quantum features such as correlations in principle demands nonlinear operations. However, nonlinear processing of…
Pricing financial derivatives on quantum computers typically includes quantum arithmetic components which contribute heavily to the quantum resources required by the corresponding circuits. In this manuscript, we introduce a method based on…
In the era of quantum computing, the emergence of quantum computers and subsequent advancements have led to the development of various quantum algorithms capable of solving linear equations and eigenvalues, surpassing the pace of classical…
Two-stage stochastic programming is a problem formulation for decision-making under uncertainty. In the first stage, the actor makes a best "here and now" decision in the presence of uncertain quantities that will be resolved in the future,…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
We study the approximation capabilities of two families of univariate polynomials that arise in applications of quantum signal processing. Although approximation only in the domain $[0,1]$ is physically desired, these polynomial families…
Efficient estimation of nonlinear functions of quantum states is crucial for various key tasks in quantum computing, such as entanglement spectroscopy, fidelity estimation, and feature analysis of quantum data. Conventional methods using…
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…
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 develop a comprehensive theory of phase for finite-dimensional quantum systems. The only physical requirement we impose is that phase is complementary to amplitude. To implement this complementarity we use the notion of mutually unbiased…
Significant developments made in quantum hardware and error correction recently have been driving quantum computing towards practical utility. However, gaps remain between abstract quantum algorithmic development and practical applications…
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…