Related papers: Fourier Analysis of Variational Quantum Circuits f…
Algorithms to compute the quantum Fourier transform over a cyclic group are fundamental to many quantum algorithms. This paper describes such an algorithm and gives a proof of its correctness, tightening some claimed performance bounds…
Quantum signal processing is a framework for implementing polynomial functions on quantum computers. To implement a given polynomial $P$, one must first construct a corresponding complementary polynomial $Q$. Existing approaches to this…
Distributed quantum computing (DQC) provides a way to scale quantum computers using multiple quantum processing units (QPU) connected through quantum communication links. In this paper, we have built a distributed quantum computing…
In this paper, we strengthen the connection between qubit-based quantum circuits and photonic quantum computation. Within the framework of circuit-based quantum computation, the sum-over-paths interpretation of quantum probability…
One of the major promises of quantum computing is the realization of SIMD (single instruction - multiple data) operations using the phenomenon of superposition. Since the dimension of the state space grows exponentially with the number of…
In the current noisy intermediate-scale quantum (NISQ) era, quantum machine learning is emerging as a dominant paradigm to program gate-based quantum computers. In quantum machine learning, the gates of a quantum circuit are parametrized,…
Quantum machine learning, focusing on quantum neural networks (QNNs), remains a vastly uncharted field of study. Current QNN models primarily employ variational circuits on an ansatz or a quantum feature map, often requiring multiple…
In this note we compare two measures of the complexity of a class $\mathcal F$ of Boolean functions studied in (unconditional) pseudorandomness: $\mathcal F$'s ability to distinguish between biased and uniform coins (the coin problem), and…
We present the first computationally-efficient algorithm for average-case learning of shallow quantum circuits with many-qubit gates. Specifically, we provide a quasi-polynomial time and sample complexity algorithm for learning unknown…
Quantum computers promise improving machine learning. We investigated the performance of new quantum neural network designs. Quantum neural networks currently employed rely on a feature map to encode the input into a quantum state. This…
Quantum programs today are written at a low level of abstraction - quantum circuits akin to assembly languages - and the unitary parts of even advanced quantum programming languages essentially function as circuit description languages.…
Parameterized quantum circuits (PQCs) have emerged as a promising approach for quantum neural networks. However, understanding their expressive power in accomplishing machine learning tasks remains a crucial question. This paper…
Quantum Variational Circuits (QVCs) are often claimed as one of the most potent uses of both near term and long term quantum hardware. The standard approaches to optimizing these circuits rely on a classical system to compute the new…
In this work we present a novel strategy to evaluate multi-variable integrals with quantum circuits. The procedure first encodes the integration variables into a parametric circuit. The obtained circuit is then derived with respect to the…
Quantum computing has the potential to solve many complex algorithms in the domains of optimization, arithmetics, structural search, financial risk analysis, machine learning, image processing, and others. Quantum circuits built to…
Quantum systems can be dynamically controlled using time-periodic external fields, leading to the concept of Floquet engineering, with promising technological applications. Computing Floquet energy spectra is harder than only computing…
Quantum compiling aims to construct a quantum circuit V by quantum gates drawn from a native gate alphabet, which is functionally equivalent to the target unitary U. It is a crucial stage for the running of quantum algorithms on noisy…
The integration of Fourier transform and deep learning opens new avenues for time series forecasting. We reconsider the Fourier transform from a basis functions perspective. Specifically, the real and imaginary parts of the frequency…
For a real sequence of length of m = nl, we may deduce its congruence derivative sequence with length of l. The discrete Fourier transform of original sequence can be calculated by the discrete Fourier transform of the congruence derivative…
Parameterized quantum circuits (PQCs) are fundamental to quantum machine learning (QML), quantum optimization, and variational quantum algorithms (VQAs). The expressibility of PQCs is a measure that determines their capability to harness…