Related papers: Quantum Many-body Bootstrap
Estimating physical properties of quantum states from measurements is one of the most fundamental tasks in quantum science. In this work, we identify conditions on states under which it is possible to infer the expectation values of all…
Quantum many-body systems pose a formidable computational challenge due to the exponential growth of their Hilbert space. While machine learning (ML) has shown promise as an alternative paradigm, most applications remain at the…
We consider matrix quantum mechanics with multiple bosonic matrices, including those obtained from dimensional reduction of Yang-Mills theories. Using the matrix bootstrap, we study simple observables like $\langle \mathop{tr} X^2 \rangle$…
The use of a single-qubit parametrized circuit as an Ansatz for the variational wave function in the calculation of the ground state energy of a quantum many-body system is demonstrated using the one-dimensional Bose-Hubbard model.…
We study the effectiveness of the numerical bootstrap techniques recently developed in arXiv:2004.10212 for quantum mechanical systems. We find that for a double well potential the bootstrap method correctly captures non-perturbative…
We propose and analyze a new approach to the coherent control and manipulation of quantum degrees of freedom in disordered, interacting systems in the many-body localized phase. Our approach leverages a number of unique features of…
The range of motion of a particle with certain energy $E$ confined in a potential is determined from the energy conservation law in classical mechanics. The counterpart of this question in quantum mechanics can be regarded as what the…
Many-body localization (MBL) addresses the absence of thermalization in interacting quantum systems, with non-ergodic high-energy eigenstates behaving as ground states, only area-law entangled. However, computing highly excited many-body…
We develop a quantum field theoretical framework to analytically study the three-body constrained Bose-Hubbard model beyond mean field and non-interacting spin wave approximations. It is based on an exact mapping of the constrained model to…
We propose several designs to simulate quantum many-body systems in manifolds with a non-trivial topology. The key idea is to create a synthetic lattice combining real-space and internal degrees of freedom via a suitable use of induced…
We present a statistical mechanics description to study the ground state of quantum systems. In this approach, averages for the complete system are calculated over the non-interacting energy levels. Taking different interaction parameter,…
We show that for a particular model, the quantum mechanical bootstrap is capable of finding exact results. We consider a solvable system with Hamiltonian $H=SZ(1-Z)S$, where $Z$ and $S$ satisfy canonical commutation relations. While this…
Computationally intractable tasks are often encountered in physics and optimization. Such tasks often comprise a cost function to be optimized over a so-called feasible set, which is specified by a set of constraints. This may yield, in…
Solving ground states of quantum many-body systems has been a long-standing problem in condensed matter physics. Here, we propose a new unsupervised machine learning algorithm to find the ground state of a general quantum many-body system…
Efficient characterization of highly entangled multi-particle systems is an outstanding challenge in quantum science. Recent developments have shown that a modest number of randomized measurements suffices to learn many properties of a…
I present a new approach to the many-body ground state of quantum-Hall systems. The method describes the behavior of a two-dimensional electron system at all Landau-level filling factors $\nu$, continuously as a function of magnetic field,…
Ground-state properties are central to our understanding of quantum many-body systems. At first glance, it seems natural and essential to obtain the ground state before analyzing its properties; however, its exponentially large Hilbert…
{Many-body quantum states at thermal equilibrium are ubiquitous in nature. Investigating their dynamical properties is a formidable task due to the complexity of the Hilbert space they live in. Quantum computers may have the potential to…
Variational methods play an important role in the study of quantum many-body problems, both in the flavor of classical variational principles based on tensor networks as well as of quantum variational principles in near-term quantum…
A machine learning technique to obtain the ground states of quantum few-body systems using artificial neural networks is developed. Bosons in continuous space are considered and a neural network is optimized in such a way that when particle…