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Concept# Quantum entanglement

Summary

Quantum entanglement is the phenomenon that occurs when a group of particles are generated, interact, or share spatial proximity in a way such that the quantum state of each particle of the group cannot be described independently of the state of the others, including when the particles are separated by a large distance. The topic of quantum entanglement is at the heart of the disparity between classical and quantum physics: entanglement is a primary feature of quantum mechanics not present in classical mechanics.
Measurements of physical properties such as position, momentum, spin, and polarization performed on entangled particles can, in some cases, be found to be perfectly correlated. For example, if a pair of entangled particles is generated such that their total spin is known to be zero, and one particle is found to have clockwise spin on a first axis, then the spin of the other particle, measured on the same axis, is found to be anticlockwise. However, this behavior gives rise

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We study many-body localization (MBL) in a pair-hopping model exhibiting strong fragmentation of the Hilbert space. We show that several Krylov subspaces have both ergodic statistics in the thermodynamic limit and a dimension that scales much slower than the full Hilbert space but still exponentially. Such a property allows us to study the MBL phase transition in systems including up to 64 spins. The different Krylov spaces that we consider show clear signatures of a many-body localization transition, both in the Kullback-Leibler divergence of the distribution of their level spacing ratio and their entanglement properties. However, they also present distinct scalings with the system size. Depending on the subspace, the critical disorder strength can be nearly independent of the system size or conversely show an approximately linear increase with the number of spins.

2021Quantum computing is one of the great scientific challenges of the 21st century. Small-scalesystems today promise to surpass classical computers in the coming years and to enable thesolution of classically intractable computational tasks in the fields of quantum chemistry,optimization, cryptography and more.In contrast to classical computers, quantum computers based on superconducting quantumbits (qubits) can to date not be linked over long distance in a network to improve their computingcapacity, since devices, which preserve the quantumstate when it is transferred from onemachine to another, are not available. Several approaches are being pursued to realize such acomponent, one of themost promising to date makes use of an intermediary, micromechanicalelement that enables quantum coherent conversion between the information presentin the quantum computer and an optical fiber, without compromising the quantum natureof the information, via optomechanical interaction. This approach could allow fiber-opticquantum networks between separate quantum computers based on superconducting qubitsin the future.In this work a platformfor such a microwave-to-optic link was developed based on the piezoelectricmaterial gallium phosphide. This III-V semiconductor offers not only a piezoelectriccoupling between the electric field of a microwave circuit and a mechanicalmode, but also awide optical bandgap E_g = 2.26eV which reduces nonlinear optical absorption in the deviceand a large refractive index n(1550nm) = 3.01 which allows strong optical confinement atnear-infrared wavelengths.Importantly and in contrast to other approaches with gallium phosphide, an epitaxiallygrown, single crystal thin film of the material is integrated directly on a silicon wafer withpre-structured niobium electrodes by direct wafer-bonding. This opens up the possibility ofintegrating the device design presented here directly with superconducting qubits fabricatedwith this material system.A microwave-to-optical transducer design was simulated and fabricated in the galliumphosphideon-silicon platform. The device was found to exhibit large vacuum optomechanical couplingrates g0/2 pi ~ 290kHz and a high intrinsic optical quality factor Q >10^5 while at the same timepermitting electromechanical coupling to a microwave electrode. Coherent microwave-toopticaltransductionwas shown at room temperature for this device and the electromechanicalcoupling rate could be extracted from a model derived by input-output theory.The electromechanical coupling between the electro-optomechanical device and a superconductingqubit was estimated to be g/2 pi = O(200kHz) which indicates that strong couplingbetween the here presented device and a superconducting transmon qubit is achievable.In addition, superconducting microwave cavities with high quality factor at single photonenergy Q ~ 5x10^5 were fabricated and measured to verify that fabrication process of themicrowave-to-optical transducer is compatible with high-quality superconducting microwavecircuits.

Quantum many-body dynamics generically result in increasing entanglement that eventually leads to thermalization of local observables. This makes the exact description of the dynamics complex despite the apparent simplicity of (high-temperature) thermal states. For accurate but approximate simulations one needs a way to keep track of essential (quantum) information while discarding inessential one. To this end, we first introduce the concept of the information lattice, which supplements the physical spatial lattice with an additional dimension and where a local Hamiltonian gives rise to well-defined locally conserved von Neumann information current. This provides a convenient and insightful way of capturing the flow, through time and space, of information during quantum time-evolution, and gives a distinct signature of when local degrees of freedom decouple from long-range entanglement. As an example, we describe such de-coupling of local degrees of freedom for the mixed-field transverse Ising model. Building on this, we secondly construct algorithms to time-evolve sets of local density matrices without any reference to a global state. With the notion of information currents, we motivate algorithms based on the intuition that information for statistical reasons flows from small to large scales. Using this guiding principle, we construct an algorithm that, at worst, shows two-digit convergence in time-evolutions up to very late times for diffusion process governed by the mixed-field transverse Ising Hamiltonian. While we focus on dynamics in 1D with nearest-neighbor Hamiltonians, the algorithms do not essentially rely on these assumptions and can in principle be generalized to higher dimensions and more complicated Hamiltonians.