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Register a new userChimera states in quantum mechanics
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Victor Manuel Bastidas Valencia
Publication date
2018
fields
Physics
and research's language is
English
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Classical chimera states are paradigmatic examples of partial synchronization patterns emerging in nonlinear dynamics. These states are characterized by the spatial coexistence of two dramatically different dynamical behaviors, i.e., synchronized and desynchronized dynamics. Our aim in this contribution is to discuss signatures of chimera states in quantum mechanics. We study a network with a ring topology consisting of N coupled quantum Van der Pol oscillators. We describe the emergence of chimera-like quantum correlations in the covariance matrix. Further, we establish the connection of chimera states to quantum information theory by describing the quantum mutual information for a bipartite state of the network.
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We study stabilizer quantum error correcting codes (QECC) generated under hybrid dynamics of local Clifford unitaries and local Pauli measurements in one dimension. Building upon 1) a general formula relating the error-susceptibility of a subregion to its entanglement properties, and 2) a previously established mapping between entanglement entropies and domain wall free energies of an underlying spin model, we propose a statistical mechanical description of the QECC in terms of entanglement domain walls. Free energies of such domain walls generically feature a leading volume law term coming from its surface energy, and a sub-volume law correction coming from thermodynamic entropies of its transverse fluctuations. These are most easily accounted for by capillary-wave theory of liquid-gas interfaces, which we use as an illustrative tool. We show that the information-theoretic decoupling criterion corresponds to a geometric decoupling of domain walls, which further leads to the identification of the contiguous code distance of the QECC as the crossover length scale at which the energy and entropy of the domain wall are comparable. The contiguous code distance thus diverges with the system size as the subleading entropic term of the free energy, protecting a finite code rate against local undetectable errors. We support these correspondences with numerical evidence, where we find capillary-wave theory describes many qualitative features of the QECC; we also discuss when and why it fails to do so.
Symmetries are well known to have had a profound role in our understanding of nature and are a critical design concept for the realization of advanced technologies. In fact, many symmetry-broken states associated with different phases of matter appear in a variety of quantum technology applications. Such symmetries are normally broken in spatial dimension, however they can also be broken temporally leading to the concept of discrete time symmetries and their associated crystals. Discrete time crystals (DTCs) are a novel state of matter emerging in periodically-driven quantum systems. Typically, they have been investigated assuming individual control operations with uniform rotation errors across the entire system. In this work we explore a new paradigm arising from non-uniform rotation errors, where two dramatically different phases of matter coexist in well defined regions of space. We consider a quantum spin network possessing long-range interactions where different driving operations act on different regions of that network. What results from its inherent symmetries is a system where one region is a DTC, while the second is ferromagnetic. We envision our work to open a new avenue of research on Chimera-like phases of matter where two different phases coexist in space.
The task of classifying the entanglement properties of a multipartite quantum state poses a remarkable challenge due to the exponentially increasing number of ways in which quantum systems can share quantum correlations. Tackling such challenge requires a combination of sophisticated theoretical and computational techniques. In this paper we combine machine-learning tools and the theory of quantum entanglement to perform entanglement classification for multipartite qubit systems in pure states. We use a parameterisation of quantum systems using artificial neural networks in a restricted Boltzmann machine (RBM) architecture, known as Neural Network Quantum States (NNS), whose entanglement properties can be deduced via a constrained, reinforcement learning procedure. In this way, Separable Neural Network States (SNNS) can be used to build entanglement witnesses for any target state.
The rapid development of quantum computing technologies already made it possible to manipulate a collective state of several dozen of qubits. This success poses a strong demand on efficient and reliable methods for characterization and verification of large-scale many-body quantum states. Traditional methods, such as quantum tomography, which require storing and operating wave functions on classical computers, become problematic to use in the regime of large number of degrees of freedom. In this paper, we propose a numerically cheap procedure to describe and distinguish quantum states which is based on a limited number of simple projective measurements in at least two different bases and computing inter-scale dissimilarities of the resulting bit-string patterns via coarse-graining. The information one obtains through this procedure can be viewed as a hash function of quantum state -- a simple set of numbers which is specific for a concrete many-body wave function and can be used for certification. By studying a number of archetypal examples, we show that it is enough to characterize quantum states with different structure of entanglement, including the chaotic quantum states. The connection of the dissimilarity to standard measures of quantum correlations such as von Neumann entropy is discussed. We also demonstrate that our approach can be employed to detect phase transitions of different nature in many-body quantum magnetic systems.
Mana is a measure of the amount of non-Clifford resources required to create a state; the mana of a mixed state on $ell$ qudits bounded by $le frac 1 2 (ell ln d - S_2)$; $S_2$ the states second Renyi entropy. We compute the mana of Haar-random pure and mixed states and find that the mana is nearly logarithmic in Hilbert space dimension: that is, extensive in number of qudits and logarithmic in qudit dimension. In particular, the average mana of states with less-than-maximal entropy falls short of that maximum by $ln pi/2$. We then connect this result to recent work on near-Clifford approximate $t$-designs; in doing so we point out that mana is a useful measure of non-Clifford resources precisely because it is not differentiable.
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