Quantum Preprints

We consider the problem of optimizing the state average of a polynomial of non-commuting variables, over all states and operators satisfying a number of polynomial constraints, and over all Hilbert spaces where such states and operators are defined. Such non-commutative polynomial optimization (NPO) problems are routinely solved through hierarchies of... Read more

Quantum kernel methods leverage a kernel function computed by embedding input information into the Hilbert space of a quantum system. However, large Hilbert spaces can hinder generalization capability, and the scalability of quantum kernels becomes an issue. To overcome these challenges, various strategies under the concept of inductive bias have... Read more

This paper presents a comprehensive comparative analysis of the performance of Equivariant Quantum Neural Networks (EQNN) and Quantum Neural Networks (QNN), juxtaposed against their classical counterparts: Equivariant Neural Networks (ENN) and Deep Neural Networks (DNN). We evaluate the performance of each network with two toy examples for a binary classification... Read more

The perturbative consistency of coherent states within interacting quantum field theory requires them to be altered beyond the simple non-squeezed form. Building on this point, we perform explicit construction of consistent squeezed coherent states, required by the finiteness of physical quantities at the one-loop order. Extending this analysis to two-loops,... Read more

Machine learning algorithms are heavily relied on to understand the vast amounts of data from high-energy particle collisions at the CERN Large Hadron Collider (LHC). The data from such collision events can naturally be represented with graph structures. Therefore, deep geometric methods, such as graph neural networks (GNNs), have been... Read more

We design algorithms for computing expectation values of observables in the equilibrium states of local quantum Hamiltonians, both at zero and positive temperature. The algorithms are based on hierarchies of convex relaxations over the positive semidefinite cone and the matrix relative entropy cone, and give certified and converging upper and... Read more

By connecting multiple quantum computers (QCs) through classical and quantum channels, a quantum communication network can be formed. This gives rise to new applications such as blind quantum computing, distributed quantum computing and quantum key distribution. In distributed quantum computing, QCs collectively perform a quantum computation. As each device only... Read more

We show the following unconditional results on quantum commitments in two related yet different models: 1. We revisit the notion of quantum auxiliary-input commitments introduced by Chailloux, Kerenidis, and Rosgen (Comput. Complex. 2016) where both the committer and receiver take the same quantum state, which is determined by the security... Read more

We demonstrate how to build computationally secure commitment schemes with the aid of quantum auxiliary inputs without unproven complexity assumptions. Furthermore, the quantum auxiliary input can be prepared either (1) efficiently through a trusted setup similar to the classical common random string model, or (2) strictly between the two involved... Read more

ZX-diagrams are a powerful graphical language for the description of quantum processes with applications in fundamental quantum mechanics, quantum circuit optimization, tensor network simulation, and many more. The utility of ZX-diagrams relies on a set of local transformation rules that can be applied to them without changing the underlying quantum... Read more

In recent years, tensor network renormalization (TNR) has emerged as an efficient and accurate method for studying (1+1)D quantum systems or 2D classical systems using real-space renormalization group (RG) techniques. One notable application of TNR is its ability to extract central charge and conformal scaling dimensions for critical systems. In... Read more

The nonlinear Schr"odinger-Newton equation, a prospective semiclassical alternative to a quantized theory of gravity, predicts a gravitational self-force between the two trajectories corresponding to the two z-spin eigenvalues for a particle in a Stern-Gerlach interferometer. To leading order, this force results in a relative phase between the trajectories. For the... Read more

Bell scenarios involve space-like separated measurements made by multiple parties. The standard no-signalling constraints ensure that such parties cannot signal superluminally by choosing their measurement settings. In tripartite Bell scenarios, relaxed non-signalling constraints have been proposed, which permit a class of post-quantum theories known as jamming non-local theories. To analyse... Read more

It is remarkable that Heisenberg's position-momentum uncertainty relation leads to the existence of a maximal acceleration for a physical particle in the context of a geometric reformulation of quantum mechanics. It is also known that the maximal acceleration of a quantum particle is related to the magnitude of the speed... Read more

The emergence of quantum computing has introduced unprecedented security challenges to conventional cryptographic systems, particularly in the domain of optical communications. This research addresses these challenges by innovatively combining quantum key distribution (QKD), specifically the E91 protocol, with logistic chaotic maps to establish a secure image transmission scheme. Our approach... Read more

Realizing nonabelian topological orders and their anyon excitations is an esteemed objective. In this work, we propose a novel approach towards this goal: quantum simulating topological orders in the doubled Hilbert space - the space of density matrices. We show that ground states of all quantum double models (toric code... Read more

It is known that the Frenet-Serret apparatus of a space curve in three-dimensional Euclidean space determines the local geometry of curves. In particular, the Frenet-Serret apparatus specifies important geometric invariants, including the curvature and the torsion of a curve. It is also acknowledged in quantum information science that low complexity... Read more

We present a geometric perspective on how to quantify the bending and the twisting of quantum curves traced by state vectors evolving under nonstationary Hamiltonians. Specifically, relying on the existing geometric viewpoint for stationary Hamiltonians, we discuss the generalization of our theoretical construct to time-dependent quantum-mechanical scenarios where both time-varying... Read more

Non-Gaussian quantum states, described by negative valued Wigner functions, are important both for fundamental tests of quantum physics and for emerging quantum information technologies. One of the promising ways of generation of the non-Gaussian states is the use of the cubic (Kerr) optical non-linearity, which produces the characteristic banana-like shape... Read more

Krylov complexity and Nielsen complexity are successful approaches to quantifying quantum evolution complexity that have been actively pursued without much contact between the two lines of research. The two quantities are motivated by quantum chaos and quantum computation, respectively, while the relevant mathematics is as different as matrix diagonalization algorithms... Read more