Related papers: Unitary designs from statistical mechanics in rand…
We study the scrambling of quantum information in local random unitary circuits by focusing on the tripartite information proposed by Hosur et al. We provide exact results for the averaged R\'enyi-$2$ tripartite information in two cases:…
Given a persistence diagram with $n$ points, we give an algorithm that produces a sequence of $n$ persistence diagrams converging in bottleneck distance to the input diagram, the $i$th of which has $i$ distinct (weighted) points and is a…
Graphical models are useful tools for describing structured high-dimensional probability distributions. Development of efficient algorithms for generating unbiased and independent samples from graphical models remains an active research…
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 prove that random 1D Clifford brickwork circuits form (in expectation) good approximate quantum error correction codes in logarithmic depth. Our proof makes use of the statistical mechanics techniques for random circuits developed by…
Lattice gauge theories in varying dimensions, lattice volumes, and truncations offer a rich family of targets for Hamiltonian simulation on quantum devices. In return, formulating quantum simulations can provide new ways of thinking about…
Combinatorial problems are formulated to find optimal designs within a fixed set of constraints. They are commonly found across diverse engineering and scientific domains. Understanding how to best use quantum computers for combinatorial…
The concept of quantum complexity has far-reaching implications spanning theoretical computer science, quantum many-body physics, and high energy physics. The quantum complexity of a unitary transformation or quantum state is defined as the…
Pseudo-random operators consist of sets of operators that exhibit many of the important statistical features of uniformly distributed random operators. Such pseudo-random sets of operators are most useful whey they may be parameterized and…
Quantum mechanics predicts the existence of intrinsically random processes. Contrary to classical randomness, this lack of predictability can not be attributed to ignorance or lack of control. Here we find the optimal method to quantify the…
Correlations and measures of entanglement in ground state wavefunctions of relativistic quantum field theories are spatially localized over length scales set by the mass of the lightest particle. We utilize this localization to design…
We compute the number of circuits and of loops with multiple crossings in random regular graphs. We discuss the importance of this issue for the validity of the cavity approach. On the one side we obtain analytic results for the infinite…
The study of the boundary between classically simulable and computationally complex quantum dynamics is fundamental to understanding which physical resources may enable enhanced information-processing capabilities. We investigate this…
Quantum computing is a hotspot technology for its potential to accelerate specific applications by exploiting quantum parallelism. However, current physical quantum computers are limited to a relatively small scale, simulators based on…
Quantum circuits generating probability distributions has applications in several areas. Areas like finance require quantum circuits that can generate distributions that mimic some given data pattern. Hamiltonian simulations require…
A central problem in quantum computation is to understand which quantum circuits are useful for exponential speed-ups over classical computation. We address this question in the setting of query complexity and show that for almost any…
We provide a generalization of the idea of unitary designs to cover finite averaging over much more general operations on quantum states. Namely, we construct finite averaging sets for averaging quantum states over arbitrary reductive Lie…
Near term quantum computers with a high quantity (around 50) and quality (around 0.995 fidelity for two-qubit gates) of qubits will approximately sample from certain probability distributions beyond the capabilities of known classical…
Quantum expanders are a quantum analogue of expanders, and k-tensor product expanders are a generalisation to graphs that randomise k correlated walkers. Here we give an efficient construction of constant-degree, constant-gap quantum…
Quantum circuit optimization - the process of transforming a quantum circuit into an equivalent one with reduced time and space requirements - is crucial for maximizing the utility of current and near-future quantum devices. While most…