相关论文: Simple constructions of linear-depth t-designs and…

Randomized iterative algorithms have attracted much attention in recent years because they can approximately solve large-scale linear systems of equations without accessing the entire coefficient matrix. In this paper, we propose two novel…

Physical Unclonable Functions (PUFs) provide hardware-level security by exploiting intrinsic randomness to produce device-unique responses. However, machine learning and side-channel attacks increasingly undermine their classical…

We prove a new concentration result for non-catalytic decoupling by showing that, for suitably large $t$, applying a unitary chosen uniformly at random from an approximate $t$-design on a quantum system followed by a fixed quantum operation…

A well-known class of non-stationary self-similar time series is the fractional Brownian motion (fBm) considered to model ubiquitous stochastic processes in nature. In this paper, we study the homology groups of high-dimensional point cloud…

Consistency models have recently been introduced to accelerate sampling from diffusion models by directly predicting the solution (i.e., data) of the probability flow ODE (PF ODE) from initial noise. However, the training of consistency…

Pseudorandom states (PRSs) are state ensembles that cannot be efficiently distinguished from Haar random states. However, the definition of PRSs has been limited to pure states and lacks robustness against noise. Here, we introduce…

$k$-Uniform states are fundamental to quantum information and computing, with applications in multipartite entanglement and quantum error-correcting codes (QECCs). Prior work has primarily focused on constructing exact $k$-uniform states or…

Over-parameterization is commonly used to increase the expressivity of variational quantum circuits (VQCs), yet deeper and more highly parameterized circuits often exhibit poor trainability and limited generalization. In this work, we…

Quantum computational pseudorandomness has emerged as a fundamental notion that spans connections to complexity theory, cryptography and fundamental physics. However, all known constructions of efficient quantum-secure pseudorandom objects…

The intrinsic conformality is a general property of the renormalizable gauge theory, which ensures the scale-invariance of a fixed-order series at each perturbative order. Following the idea of intrinsic conformality, we suggest a novel…

We develop the concept of a unitary t-design as a means of expressing operationally useful subsets of the stochastic properties of the uniform (Haar) measure on the unitary group U(2^n) on n qubits. In particular, sets of unitaries forming…

Unitary Designs have become a vital tool for investigating pseudorandomness since they approximate the statistics of the uniform Haar ensemble. Despite their central role in quantum information, their relation to quantum chaotic evolution…

Unitary $k$-designs are finite ensembles of unitary matrices that approximate the Haar distribution over unitary matrices. Several ensembles are known to be 2-designs, including the uniform distribution over the Clifford group, but no…

A unitary t-design is a set of unitaries that is "evenly distributed" in the sense that the average of any t-th order polynomial over the design equals the average over the entire unitary group. In various fields -- e.g. quantum information…

This paper introduces a sparse projection matrix composed of discrete (digital) periodic lines that create a pseudo-random (p.frac) sampling scheme. Our approach enables random Cartesian sampling whilst employing deterministic and…

Recent active studies have demonstrated that cryptography without one-way functions (OWFs) could be possible in the quantum world. Many fundamental primitives that are natural quantum analogs of OWFs or pseudorandom generators (PRGs) have…

Principal Components Regression (PCR) is a traditional tool for dimension reduction in linear regression that has been both criticized and defended. One concern about PCR is that obtaining the leading principal components tends to be…

Given a universal gate set on two qubits, it is well known that applying random gates from the set to random pairs of qubits will eventually yield an approximately Haar-distributed unitary. However, this requires exponential time. We show…

This work is directed to uncertainty quantification of homogenized effective properties for composite materials with complex, three dimensional microstructure. The uncertainties arise in the material parameters of the single constituents as…

Unitary $t$-designs are `good' finite subsets of the unitary group $U(d)$ that approximate the whole unitary group $U(d)$ well. Unitary $t$-designs have been applied in randomized benchmarking, tomography, quantum cryptography and many…