相关论文: Hardness of recognizing phases of matter
Characterizing the entanglement structure of ground states of local Hamiltonians is a fundamental problem in quantum information. In this work we study the computational complexity of this problem, given the Hamiltonian as input. Our main…
It is shown that determining whether a quantum computation has a non-zero probability of accepting is at least as hard as the polynomial time hierarchy. This hardness result also applies to determining in general whether a given quantum…
The application of quantum computation to accelerate machine learning algorithms is one of the most promising areas of research in quantum algorithms. In this paper, we explore the power of quantum learning algorithms in solving an…
In recent years, the entanglement spectra of quantum states have been identified to be highly valuable for improving our understanding on many problems in quantum physics, such as classification of topological phases, symmetry-breaking…
Drawing the quantum phase diagram of a many-body system in the parameter space of its Hamiltonian can be seen as a learning problem, which implies labelling the corresponding ground states according to some classification criterium that…
Quantum process tomography is an experimental technique to fully characterize an unknown quantum process. Standard quantum process tomography suffers from exponentially scaling of the number of measurements with the increasing system size.…
We study the identification of quantum phases of matter, at zero temperature, when only part of the phase diagram is known in advance. Following a supervised learning approach, we show how to use our previous knowledge to construct an…
The phase diagram of a material is of central importance to describe the properties and behaviour of a condensed matter system. We prove that the general task of determining the quantum phase diagram of a many-body Hamiltonian is…
The classification of quantum phases of matter remains a fundamental challenge in condensed matter physics. We present a novel framework that combines shadow tomography with modern time-series machine learning models to enable efficient and…
Given a local Hamiltonian, how difficult is it to determine the entanglement structure of its ground state? We show that this problem is computationally intractable even if one is only trying to decide if the ground state is volume-law vs…
We give a polynomial time algorithm that, given copies of an unknown quantum state $\vert\psi\rangle=U\vert 0^n\rangle$ that is prepared by an unknown constant depth circuit $U$ on a finite-dimensional lattice, learns a constant depth…
Quantum complexity measures the difficulty of obtaining a given state starting from a typically unentangled state. In this work, we show that complexity, when defined through the minimization of a Riemannian cost functional over the…
We provide a general framework for the identification of open quantum systems. By looking at the input-output behavior, we try to identify the system inside a black box in which some Markovian time-evolution takes place. Due to the…
Quantifying the complexity of quantum states is a longstanding key problem in various subfields of science, ranging from quantum computing to the black-hole theory. The lower bound on quantum pure state complexity has been shown to grow…
The usual way to reveal properties of an unknown quantum state, given many copies of a system in that state, is to perform measurements of different observables and to analyze the measurement results statistically. Here we show that the…
We establish connections between state tomography, pseudorandomness, quantum state synthesis, and circuit lower bounds. In particular, let $\mathfrak{C}$ be a family of non-uniform quantum circuits of polynomial size and suppose that there…
Relativistic quantum field theory imposes additional fundamental restrictions on the distinguishability of quantum states. Because of the unavoidable delocalization of the quantum field states in the Minkowski space-time, the reliable (with…
Matrix permanents are hard to compute or even estimate in general. It had been previously suggested that the permanents of Positive Semidefinite (PSD) matrices may have efficient approximations. By relating PSD permanents to a task in…
The creation complexity of a quantum state is the minimum number of elementary gates required to create it from a basic initial state. The creation complexity of quantum states is closely related to the complexity of quantum circuits, which…
Phase estimation, due to Kitaev [arXiv'95], is one of the most fundamental subroutines in quantum computing. In the basic scenario, one is given black-box access to a unitary $U$, and an eigenstate $\lvert \psi \rangle$ of $U$ with unknown…