Experimental certification of millions of genuinely entangled atoms in a solid

Nature Communications, Published online: 13 October 2017; doi:10.1038/s41467-017-00898-6

The presence of entanglement in macroscopic systems is notoriously difficult to observe. Here, the authors develop a witness which allow them to demonstrate entanglement between millions of atoms in a solid-state quantum memory prepared by the heralded absorption of a single photon.

Authors: Leonardo Modesto, Yun Soo Myung, Sang-Heon Yi

In this paper we prove the universal nature of the Unruh effect in a general class of weakly non-local field theories.

At the same time we solve the tension between two conflicting claims published in literature.

Our universality statement is based on two independent computations based on the canonical formulation as well as path integral formulation of the quantum theory.

Authors: Giuseppe Castagnoli

A bare description of the seminal quantum algorithm devised by Deutsch could mean more than an introduction to quantum computing. It could contribute to opening the field to interdisciplinary research.

One-dimensional topological superconductors host Majorana zero modes (MZMs), the non-local property of which could be exploited for quantum computing applications. We use spin-polarized scanning tunneling microscopy to show that MZMs realized in self-assembled Fe chains on the surface of Pb have a spin polarization that exceeds that stemming from the magnetism of these chains. This feature, captured by our model calculations, is a direct consequence of the nonlocality of the Hilbert space of MZMs emerging from a topological band structure. Our study establishes spin polarization measurements as a diagnostic tool to distinguish topological MZMs from trivial in-gap states of a superconductor.

Authors: Sanjib Dey, Anha Bhat, Davood Momeni, Mir Faizal, Ahmed Farag Ali, Tarun Kumar Dey, Atikur Rehman

One of the major difficulties of modern science underlies at the unification of general relativity and quantum mechanics. Different approaches towards such theory have been proposed. Noncommutative theories serve as the root of almost all such approaches. However, the identification of the appropriate passage to quantum gravity is suffering from the inadequacy of experimental techniques. It is beyond our ability to test the effects of quantum gravity thorough the available scattering experiments, as it is unattainable to probe such high energy scale at which the effects of quantum gravity appear. Here we propose an elegant alternative scheme to test such theories by detecting the deformations emerging from the noncommutative structures. Our protocol relies on the novelty of an opto-mechanical experimental setup where the information of the noncommutative oscillator is exchanged via the interaction with an optical pulse inside an optical cavity. We also demonstrate that our proposal is within the reach of current technology and, thus, it could uncover a feasible route towards the realization of quantum gravitational phenomena thorough a simple table-top experiment.

Authors: Ivan Glasser, Nicola Pancotti, Moritz August, Ivan D. Rodriguez, J. Ignacio Cirac

Neural Networks Quantum States have been recently introduced as an Ansatz for describing the wave function of quantum many-body systems. We show that there are strong connections between Neural Networks Quantum States in the form of Restricted Boltzmann Machines and some classes of Tensor Network states in arbitrary dimension. In particular we demonstrate that short-range Restricted Boltzmann Machines are Entangled Plaquette States, while fully connected Restricted Boltzmann Machines are String-Bond States with a non-local geometry and low bond dimension. These results shed light on the underlying architecture of Restricted Boltzmann Machines and their efficiency at representing many-body quantum states. String-Bond States also provide a generic way of enhancing the power of Neural Networks Quantum States and a natural generalization to systems with larger local Hilbert space. We compare the advantages and drawbacks of these different classes of states and present a method to combine them together. This allows us to benefit from both the entanglement structure of Tensor Networks and the efficiency of Neural Network Quantum States into a single Ansatz capable of targeting the wave function of strongly correlated systems. While it remains a challenge to describe states with chiral topological order using traditional Tensor Networks, we show that Neural Networks Quantum States and their String-Bond States extension can describe a lattice Fractional Quantum Hall state exactly. In addition, we provide numerical evidence that Neural Networks Quantum States can approximate a chiral spin liquid with better accuracy than Entangled Plaquette States and local String-Bond States. Our results demonstrate the efficiency of neural networks to describe complex quantum wave functions and pave the way towards the use of String-Bond States as a tool in more traditional machine learning applications.

Authors: W. David Wick

In the first paper of this series, I introduced a non-linear, Hamiltonian, generalization of Schroedinger’s theory that blocks formation of macroscopic dispersion (“cats”). But that theory was entirely deterministic, and so the origin of random outcomes in experiments such as Stern-Gerlach or EPRB was left open. Here I propose that Schroedinger’s wavefunction has a random component and demonstrate that such an improvised stochastic theory can violate Bell’s inequality. Repeated measurements and the back-reaction on the microsystem are discussed in a toy example. Experiments that might falsify the theory are described.

We review aspects of twistor theory, its aims and achievements spanning the last five decades. In the twistor approach, space–time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex threefold—the twistor space. After giving an elementary construction of this space, we demonstrate how solutions to linear and nonlinear equations of mathematical physics—anti-self-duality equations on Yang–Mills or conformal curvature—can be encoded into twistor cohomology. These twistor correspondences yield explicit examples of Yang–Mills and gravitational instantons, which we review. They also underlie the twistor approach to integrability: the solitonic systems arise as symmetry reductions of anti-self-dual (ASD) Yang–Mills equations, and Einstein–Weyl dispersionless systems are reductions of ASD conformal equations. We then review the holomorphic string theories in twistor and ambitwistor spaces, and explain how these theories give rise to remarkable new formulae for the computation of quantum scattering amplitudes. Finally, we discuss the Newtonian limit of twistor theory and its possible role in Penrose’s proposal for a role of gravity in quantum collapse of a wave function.

Abstract

Multi-time wave functions are wave functions for multi-particle quantum systems that involve several time variables (one per particle). In this paper we contrast them with solutions of wave equations on a space–time with multiple timelike dimensions, i.e., on a pseudo-Riemannian manifold whose metric has signature such as\({+}{+}{-}{-}\) or \({+}{+}{-}{-}{-}{-}{-}{-}\) , instead of \({+}{-}{-}{-}\) . Despite the superficial similarity, the two behave very differently: whereas wave equations in multiple timelike dimensions are typically mathematically ill-posed and presumably unphysical, relevant Schrödinger equations for multi-time wave functions possess for every initial datum a unique solution on the spacelike configurations and form a natural covariant representation of quantum states.

Authors: Mario Hubert, Davide Romano

It is generally argued that if the wave-function in the de Broglie–Bohm theory is a physical field, it must be a field in configuration space. Nevertheless, it is possible to interpret the wave-function as a multi-field in three-dimensional space. This approach hasn’t received the attention yet it really deserves. The aim of this paper is threefold: first, we show that the wave-function is naturally and straightforwardly construed as a multi-field; second, we show why this interpretation is superior to other field interpretations; third, we clarify common misconceptions.

Authors: Manaka Okuyama, Masayuki Ohzeki

The quantum speed limit (QSL), or the energy-time uncertainty relation, describes the fundamental maximum rate for quantum time evolution and has been regarded as being unique in quantum mechanics. In this study, we obtain a classical speed limit corresponding to the QSL using the Hilbert space for the classical Liouville equation. Thus, classical mechanics has a fundamental speed limit, and QSL is not a purely quantum phenomenon but a universal dynamical property of the Hilbert space. Furthermore, we obtain similar speed limits for the imaginary-time Schroedinger equations such as the master equation.

Authors: Patrick Rebentrost, Thomas R. Bromley, Christian Weedbrook, Seth Lloyd

Quantum computing allows for the potential of significant advancements in both the speed and the capacity of widely-used machine learning algorithms. In this paper, we introduce quantum algorithms for a recurrent neural network, the Hopfield network, which can be used for pattern recognition, reconstruction, and optimization as a realization of a content addressable memory system. We show that an exponentially large network can be stored in a polynomial number of quantum bits by encoding the network into the amplitudes of quantum states. By introducing a new classical technique for operating such a network, we can leverage quantum techniques to obtain a quantum computational complexity that is logarithmic in the dimension of the data. This potentially yields an exponential speed-up in comparison to classical approaches. We present an application of our method as a genetic sequence recognizer.

Authors: W. David Wick

Working entirely within the Schroedinger paradigm, meaning wavefunction only, I present a modification of his theory that prevents formation of macroscopic dispersion (MD; “cats”). The proposal is to modify the Hamiltonian based on a method introduced by Steven Weinberg in 1989, as part of a program to test quantum mechanics at the atomic or nuclear level. By contrast, the intent here is to eliminate MD without affecting the predictions of quantum mechanics at the microscopic scale. This restores classical physics at the macro level. Possible experimental tests are indicated and the differences from previous theories discussed. In a second paper, I will address the other difficulty of wavefunction physics without the statistical (Copenhagen) interpretation: how to explain random outcomes in experiments such as Stern-Gerlach, and whether a Schroedingerist theory with a random component can violate Bell’s inequality.

Author(s): F. Duncan M. Haldane

The 2016 Nobel Prize for Physics was shared by David J. Thouless, F. Duncan M. Haldane, and John Michael Kosterlitz. These papers are the text of the address given in conjunction with the award.

[Rev. Mod. Phys. 89, 040502] Published Mon Oct 09, 2017