Related papers: Fourier Analysis of Parameterized Quantum Circuits…
Parameterized complexity theory was developed in the 1990s to enrich the complexity-theoretic analysis of problems that depend on a range of parameters. In this paper we establish a quantum equivalent of classical parameterized complexity…
Pusey, Barrett and Rudolph (PBR) have recently given a completely novel argument that restricts the class of possible models for quantum phenomena (arXiv:1111.3328). In these notes the assumptions used by PBR are considerably weakened, to…
The parameter-shift rule is an approach to measuring gradients of quantum circuits with respect to their parameters, which does not require ancilla qubits or controlled operations. Here, I discuss applying this approach to a wider range of…
Quantum generative models exploit quantum superposition and entanglement to enhance learning efficiency for both classical and quantum data. Recently, inspired by classical diffusion frameworks, the quantum denoising diffusion probabilistic…
Many promising quantum algorithms in economics, medical science, and material science rely on circuits that are parameterized by a large number of angles. To ensure that these algorithms are efficient, these parameterized circuits must be…
Quantum theory has evolved from a set of provisional rules to an indispensable framework that underlies much of modern technology and infrastructure. Yet, after a century, Born's probability postulate remains at odds with the theory's…
A factor-graph representation of quantum-mechanical probabilities (involving any number of measurements) is proposed. Unlike standard statistical models, the proposed representation uses auxiliary variables (state variables) that are not…
Hybrid quantum-classical systems make it possible to utilize existing quantum computers to their fullest extent. Within this framework, parameterized quantum circuits can be regarded as machine learning models with remarkable expressive…
The Fourier expansion of the loss function in variational quantum algorithms (VQA) contains a wealth of information, yet is generally hard to access. We focus on the class of variational circuits, where constant gates are Clifford gates and…
We show that several quantum circuit families can be simulated efficiently classically if it is promised that their output distribution is approximately sparse i.e. the distribution is close to one where only a polynomially small, a priori…
Variational Quantum Algorithms (VQAs) have received considerable attention due to their potential for achieving near-term quantum advantage. However, more work is needed to understand their scalability. One known scaling result for VQAs is…
Symmetries are crucial for tailoring parametrized quantum circuits to applications, due to their capability to capture the essence of physical systems. In this work, we shift the focus away from incorporating symmetries in the circuit…
Variational quantum algorithms (VQAs), which classically optimize a parametrized quantum circuit to solve a computational task, promise to advance our understanding of quantum many-body systems and improve machine learning algorithms using…
We analyze the notion of quantum coherence in an interference experiment. We let the phase shifts fluctuate according to a given statistical distribution and introduce a decoherence parameter, defined in terms of a generalized visibility of…
The entanglement-induced barren plateau is an exponential vanishing of the parameter gradients with system size that limits the practical application of variational quantum algorithms(VQA). A landscape transition from barren plateau to…
We define \emph{laziness} to describe a large suppression of variational parameter updates for neural networks, classical or quantum. In the quantum case, the suppression is exponential in the number of qubits for randomized variational…
Variational quantum algorithms are promising algorithms for achieving quantum advantage on near-term devices. The quantum hardware is used to implement a variational wave function and measure observables, whereas the classical computer is…
In the domain of variational quantum algorithms, quantum Fourier models (QFMs) provide a mathematically well defined structure for quantum machine learning (QML). There has been a substantial amount of work on the scalability and…
The variational quantum eigensolver is a prominent hybrid quantum-classical algorithm expected to impact near-term quantum devices. They are usually based on a circuit ansatz consisting of parameterized single-qubit gates and fixed…
The Schrodinger equation for a charged particle constrained to a curved surface in the presence of a vector potential is derived using the method of forms. In the limit that the particle is brought infinitesimally close to the surface, a…