Related papers: The Quantum Fourier Transform for Continuous Varia…
Moderate-size quantum computers are now publicly accessible over the cloud, opening the exciting possibility of performing dynamical simulations of quantum systems. However, while rapidly improving, these devices have short coherence times,…
Quantum computing hardware is undergoing rapid development from proof-of-principle devices to scalable machines that could eventually challenge classical supercomputers on specific tasks. On platforms with local connectivity, the transition…
Quantum transducers are critical for quantum interconnect, enabling coherent signal transfer across disparate frequency domains. Beyond material and device advances, protocol design has become a powerful means to improve transduction. We…
Dynamical mean-field theory (DMFT) is a useful tool to analyze models of strongly correlated fermions like the Hubbard model. In DMFT, the lattice of the model is replaced by a single impurity site embedded in an effective bath. The…
In the near future, material and drug design may be aided by quantum computer assisted simulations. These have the potential to target chemical systems intractable by the most powerful classical computers. However, the resources offered by…
Discrete transforms such as the discrete Fourier transform (DFT) and the discrete Hartley transform (DHT) are important tools in numerical analysis. The successful application of transform techniques relies on the existence of efficient…
We show how to represent the state and the evolution of a quantum computer (or any system with an $N$--dimensional Hilbert space) in phase space. For this purpose we use a discrete version of the Wigner function which, for arbitrary $N$, is…
The Fast Fourier Transform (FFT) is a computationally intensive digital signal processing (DSP) function widely used in applications such as imaging, software-defined radio, wireless communication, instrumentation. In this paper, a…
Time reversal and spin flip are discrete symmetry operations of substantial import to quantum information and quantum computation. Spin flip arises in the context of separability, quantification of entanglement and the construction of…
In this paper we introduce activation functions that move the entire computation of Convolutional Networks into the frequency domain, where they are actually Hadamard Networks. To achieve this result we employ the properties of Discrete…
We examine the ability of gate-based continuous-variable quantum computers to outperform qubit or discrete-variable quantum computers. Gate-based continuous-variable operations refer to operations constructed using a polynomial sequence of…
Quantum control in large dimensional Hilbert spaces is essential for realizing the power of quantum information processing. For closed quantum systems the relevant input/output maps are unitary transformations, and the fundamental challenge…
A `register' in quantum information processing -- is composition of k quantum systems, `qudits'. The dimensions of Hilbert spaces for one qudit and whole quantum register are d and d^k respectively, but we should have possibility to prepare…
The Fermi-Hubbard model, a fundamental framework for studying strongly correlated phenomena could significantly benefit from quantum simulations when exploring non-trivial settings. However, simulating this problem requires twice as many…
Although quantum computing holds promise to accelerate a wide range of computational tasks, the quantum simulation of quantum dynamics as originally envisaged by Feynman remains the most promising candidate for achieving quantum advantage.…
We study Fourier theory on quantum Euclidean space. A modified version of the general definition of the Fourier transform on a quantum space is used and its inverse is constructed. The Fourier transforms can be defined by their Bochner's…
We present a general methodology to obtain the basis of qudits which are admissible to Quantum Fourier Transform (QFT). We first study this method for qubits to characterize the ensemble that works for the Hadamard transformation (QFT for…
Quantum Fourier transformations are an essential component of many quantum algorithms, from prime factoring to quantum simulation. While the standard abelian QFT is well-studied, important variants corresponding to \emph{nonabelian} groups…
We propose a simpler and more efficient scheme for the implementation of the multi-valued Grover's quantum search. The multi-valued search generalizes the original Grover's search by replacing qubits with qudits --- quantum systems of $d$…
The physical limitations of quantum hardware often require nearest-neighbor qubit structures, in which two-qubit gates are required to construct nearest-neighbor quantum circuits. However, two-qubit gates are considered a major cost of…