Related papers: Epsilon-nets, unitary designs and random quantum c…

We study quantum circuits consisting of unitary gates, projective measurements, and control operations that steer the system towards a pure absorbing state. Two types of phase transition occur as the rate of these control operations is…

We prove a quantum information-theoretic conjecture due to Ji, Liu and Song (CRYPTO 2018) which suggested that a uniform superposition with random \emph{binary} phase is statistically indistinguishable from a Haar random state. That is, any…

Motivated by recent work of Bukh and Nivasch on one-sided $\varepsilon$-approximants, we introduce the notion of \emph{weighted $\varepsilon$-nets}. It is a geometric notion of approximation for point sets in $\mathbb{R}^d$ similar to…

In this paper, we establish the conditions for some finite abelian groups and the family all the $k$-sets in each of them summing up to an element $x$ to form $t$-designs. We fully characterize the sufficient and necessary conditions for…

This paper demonstrates that random, independently chosen equi-dimensional subspaces with a unitarily invariant distribution in a real Hilbert space provide nearly tight, nearly equiangular fusion frames. The angle between a pair of…

This paper studies numerical integration over the unit sphere $ \mathbb{S}^2 \subset \mathbb{R}^{3} $ by using spherical $t$-design, which is an equal positive weights quadrature rule with polynomial precision $t$. We investigate two kinds…

Distributed inner product estimation (DIPE) is a fundamental task in quantum information, aiming to estimate the inner product between two unknown quantum states prepared on distributed quantum platforms. Existing rigorous sample complexity…

A t-design for quantum states is a finite set of quantum states with the property of simulating the Haar-measure on quantum states, w.r.t. any test that uses at most t copies of a state. We give efficient constructions for approximate…

Unitary designs are widely used in quantum computation, but in many practical settings it suffices to construct a diagonal state design generated with unitary gates diagonal in the computational basis. In this work, we introduce a simple…

We investigate quantum state tomography (QST) for pure states and quantum process tomography (QPT) for unitary channels via $adaptive$ measurements. For a quantum system with a $d$-dimensional Hilbert space, we first propose an adaptive…

We present an algorithm, along with its implementation that finds T-optimal approximations of single-qubit Z-rotations using quantum circuits consisting of Clifford and T gates. Our algorithm is capable of handling errors in approximation…

Quantum circuits with gates (local unitaries) respecting a global symmetry have broad applications in quantum information science and related fields, such as condensed matter theory and quantum thermodynamics. However, despite their…

Quantifying quantum states' complexity is a key problem in various subfields of science, from quantum computing to black-hole physics. We prove a prominent conjecture by Brown and Susskind about how random quantum circuits' complexity…

We analyze the quantum capacity of a unital quantum channel, using ideas from the proof of near-optimality of Petz recovery map [Barnum and Knill 2000] and give an upper bound on the quantum capacity in terms of regularized output $2$-norm…

We show that deep belief networks with binary hidden units can approximate any multivariate probability density under very mild integrability requirements on the parental density of the visible nodes. The approximation is measured in the…

In this work, we consider the problem of learning nonlinear operators that correspond to discrete-time nonlinear dynamical systems with inputs. Given an initial state and a finite input trajectory, such operators yield a finite output…

Random quantum circuits have been utilized in the contexts of quantum supremacy demonstrations, variational quantum algorithms for chemistry and machine learning, and blackhole information. The ability of random circuits to approximate any…

In this paper we construct a new family of sets based on Diophantine approximation in the Euclidean space, and consider their applications in several problems in harmonic analysis. Our first application is on the Hausdorff dimension of our…

We present a quantum algorithm that additively approximates the value of a tensor network to a certain scale. When combined with existing results, this provides a complete problem for quantum computation. The result is a simple new way of…

In this work, we address the question whether a sufficiently deep quantum neural network can approximate a target function as accurate as possible. We start with simple but typical physical situations that the target functions are physical…