Related papers: Quantum signal processing and nonlinear Fourier an…
The results of quantum process tomography on a three-qubit nuclear magnetic resonance quantum information processor are presented, and shown to be consistent with a detailed model of the system-plus-apparatus used for the experiments. The…
We consider the quantum computational process as viewed by an insider observer: this is equivalent to an isomorphism between the quantum computer and a quantum space, namely the fuzzy sphere. The result is the formulation of a reversible…
Quantum Mechanics and Signal Processing in the line R, are strictly related to Fourier Transform and Weyl-Heisenberg algebra. We discuss here the addition of a new discrete variable that measures the degree of the Hermite functions and…
It is shown how it is possible to reconstruct the initial state of a one-dimensional system by measuring sequentially two conjugate variables. The procedure relies on the quasi-characteristic function, the Fourier-transform of the Wigner…
Accurate and robust estimation of quantum process properties is crucial for quantum information processing and quantum many-body physics. Combining classical shadow tomography and randomized benchmarking, Helsen et al. introduced a method…
While quantum computers are naturally well-suited to implementing linear operations, it is less clear how to implement nonlinear operations on quantum computers. However, nonlinear subroutines may prove key to a range of applications of…
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…
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…
The characterization of a quantum device is a crucial step in the development of quantum experiments. This is accomplished via Quantum Process Tomography, which combines the outcomes of different projective measurements to deliver a…
One approach to quantum information processing is to use photons as quantum bits and rely on linear optical elements for most operations. However, some optical nonlinearity is necessary to enable universal quantum computing. Here, we…
This paper provides necessary and sufficient conditions for constructing a universal quantum computer over continuous variables. As an example, it is shown how a universal quantum computer for the amplitudes of the electromagnetic field…
Recent experimental advances have inspired the development of theoretical tools to describe the non-equilibrium dynamics of quantum systems. Among them an exact representation of quantum spin systems in terms of classical stochastic…
Accurately predicting response properties of molecules such as the dynamic polarizability and hyperpolarizability using quantum mechanics has been a long-standing challenge with widespread applications in material and drug design. Classical…
The summatory function of a $q$-regular sequence in the sense of Allouche and Shallit is analysed asymptotically. The result is a sum of periodic fluctuations for eigenvalues of absolute value larger than the joint spectral radius of the…
Several quantities of interest in quantum information, including entanglement and purity, are nonlinear functions of the density matrix and cannot, even in principle, correspond to proper quantum observables. Any method aimed to determine…
Shor's algorithms for factorization and discrete logarithms on a quantum computer employ Fourier transforms preceding a final measurement. It is shown that such a Fourier transform can be carried out in a semi-classical way in which a…
Quantum signal processing (QSP) is a framework for implementing certain polynomial functions via quantum circuits. To construct a QSP circuit, one needs (i) a target polynomial $P(z)$, which must satisfy $\lvert P(z)\rvert\leq 1$ on the…
We experimentally show that the response of a quantum-chaotic system can display resonance lines sharper than the inverse of the excitation duration. This allows us to discriminate two neighboring frequencies with a resolution nearly 40…
Incorporating nonlinearity into quantum machine learning is essential for learning a complicated input-output mapping. We here propose quantum algorithms for nonlinear regression, where nonlinearity is introduced with feature maps when…
We present a recursive algorithm for multi-coefficient inversion in nonlinear Helmholtz equations with polynomial-type nonlinearities, utilizing the linearized Dirichlet-to-Neumann map as measurement data. To achieve effective recursive…