Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userConnector tensor networks: a renormalization-type approach to quantum certification
113
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
As quantum technologies develop, we acquire control of an ever-growing number of quantum systems. Unfortunately, current tools to detect relevant quantum properties of quantum states, such as entanglement and Bell nonlocality, suffer from severe scalability issues and can only be computed for systems of a very modest size, of around $6$ sites. In order to address large many-body systems, we propose a renormalisation-type approach based on a class of local linear transformations, called connectors, which can be used to coarse-grain the system in a way that preserves the property under investigation. Repeated coarse-graining produces a system of manageable size, whose properties can then be explored by means of usual techniques for small systems. In case of a successful detection of the desired property, the method outputs a linear witness which admits an exact tensor network representation, composed of connectors. We demonstrate the power of our method by certifying using a normal desktop computer entanglement, Bell nonlocality and supra-quantum Bell nonlocality in systems with hundreds of sites.
rate research
Read More
Tensor network methods are a conceptually elegant framework for encoding complicated datasets, where high-order tensors are approximated as networks of low-order tensors. In practice, however, the numeric implementation of tensor network algorithms is often a labor-intensive and error-prone task, even for experienced researchers in this area. emph{TensorTrace} is application designed to alleviate the burden of contracting tensor networks: it provides a graphic drawing interface specifically tailored for the construction of tensor network diagrams, from which the code for their optimal contraction can then be automatically generated (in the users choice of the MATLAB, Python or Julia languages). emph{TensorTrace} is freely available at url{https://www.tensortrace.com} wi
We characterize the variational power of quantum circuit tensor networks in the representation of physical many-body ground-states. Such tensor networks are formed by replacing the dense block unitaries and isometries in standard tensor networks by local quantum circuits. We explore both quantum circuit matrix product states and the quantum circuit multi-scale entanglement renormalization ansatz, and introduce an adaptive method to optimize the resulting circuits to high fidelity with more than $10^4$ parameters. We benchmark their expressiveness against standard tensor networks, as well as other common circuit architectures, for both the energy and correlation functions of the 1D Heisenberg and Fermi-Hubbard models in the gapless regime. We find quantum circuit tensor networks to be substantially more expressive than other quantum circuits for these problems, and that they can even be more compact than standard tensor networks. Extrapolating to circuit depths which can no longer be emulated classically, this suggests a region of quantum advantage with respect to expressiveness in the representation of physical ground-states.
Cluster expansions for the exponential of local operators are constructed using tensor networks. In contrast to other approaches, the cluster expansion does not break any spatial or internal symmetries and exhibits a very favourable prefactor to the error scaling versus bond dimension. This is illustrated by time evolving a matrix product state using very large time steps, and by constructing a novel robust algorithm for finding ground states of 2-dimensional Hamiltonians using projected entangled pair states as fixed points of 2-dimensional transfer matrices.
We present in this work an exact renormalization group (RG) treatment of a one-dimensional $p$-wave superconductor. The model proposed by Kitaev consists of a chain of spinless fermions with a $p$-wave gap. It is a paradigmatic model of great actual interest since it presents a weak pairing superconducting phase that has Majorana fermions at the ends of the chain. Those are predicted to be useful for quantum computation. The RG allows to obtain the phase diagram of the model and to study the quantum phase transition from the weak to the strong pairing phase. It yields the attractors of these phases and the critical exponents of the weak to strong pairing transition. We show that the weak pairing phase of the model is governed by a chaotic attractor being non-trivial from both its topological and RG properties. In the strong pairing phase the RG flow is towards a conventional strong coupling fixed point. Finally, we propose an alternative way for obtaining $p$-wave superconductivity in a one-dimensional system without spin-orbit interaction.
We investigate the potential of tensor network based machine learning methods to scale to large image and text data sets. For that, we study how the mutual information between a subregion and its complement scales with the subsystem size $L$, similarly to how it is done in quantum many-body physics. We find that for text, the mutual information scales as a power law $L^ u$ with a close to volume law exponent, indicating that text cannot be efficiently described by 1D tensor networks. For images, the scaling is close to an area law, hinting at 2D tensor networks such as PEPS could have an adequate expressibility. For the numerical analysis, we introduce a mutual information estimator based on autoregressive networks, and we also use convolutional neural networks in a neural estimator method.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
