## Journals

### Spectral lower bounds for the quantum chromatic number of a graph. (arXiv:1805.08334v2 [math.CO] UPDATED)

arXiv.org: Quantum Physics - Sat, 2018-07-14 00:33

The quantum chromatic number, $\chi_q(G)$, of a graph $G$ was originally defined as the minimal number of colors necessary in a quantum protocol in which two provers that cannot communicate with each other but share an entangled state can convince an interrogator with certainty that they have a coloring of the graph. We use an equivalent purely combinatorial definition of $\chi_q(G)$ to prove that many spectral lower bounds for the chromatic number, $\chi(G)$, are also lower bounds for $\chi_q(G)$. This is achieved using techniques from linear algebra called pinching and twirling. We illustrate our results with some examples.

Categories: Journals, Physics

### Robust Hadamard matrices, unistochastic rays in Birkhoff polytope and equi-entangled bases in composite spaces. (arXiv:1804.10715v2 [math.CO] UPDATED)

arXiv.org: Quantum Physics - Sat, 2018-07-14 00:33

We study a special class of (real or complex) robust Hadamard matrices, distinguished by the property that their projection onto a $2$-dimensional subspace forms a Hadamard matrix. It is shown that such a matrix of order $n$ exists, if there exists a skew Hadamard matrix of this size. This is the case for any even dimension $n\le 20$, and for these dimensions we demonstrate that a bistochastic matrix $B$ located at any ray of the Birkhoff polytope, (which joins the center of this body with any permutation matrix), is unistochastic. An explicit form of the corresponding unitary matrix $U$, such that $B_{ij}=|U_{ij}|^2$, is determined by a robust Hadamard matrix. These unitary matrices allow us to construct a family of orthogonal bases in the composed Hilbert space of order $n \times n$. Each basis consists of vectors with the same degree of entanglement and the constructed family interpolates between the product basis and the maximally entangled basis.

Categories: Journals, Physics

### Complexity Growth with Lifshitz Scaling and Hyperscaling Violation. (arXiv:1802.06740v4 [hep-th] UPDATED)

arXiv.org: Quantum Physics - Sat, 2018-07-14 00:33

Using complexity=action proposal we study the growth rate of holographic complexity for Lifshitz and hyperscaling violating geometries. We will consider both one and two sided black branes in an Einstein-Maxwell-Dilaton gravitational theory. We find that in either case Lloyd's bound is violated and the rate of growth of complexity saturates to a value which is greater than twice the mass of the corresponding black brane. This value reduces to the mass of the black brane in the isotropic case. We show that in two sided black brane the saturation happens from above while for one sided black brane it happens from below.

Categories: Journals, Physics

### Variational principle for quantum impurity systems in and out of equilibrium: application to Kondo problems. (arXiv:1802.03861v3 [cond-mat.str-el] UPDATED)

arXiv.org: Quantum Physics - Sat, 2018-07-14 00:33

We provide a detailed formulation of the recently proposed variational approach [Y. Ashida et al., Phys. Rev. Lett. 121, 026805 (2018)] to study ground-state properties and out-of-equilibrium dynamics for generic quantum spin-impurity systems. Motivated by the original ideas by Tomonaga, Lee, Low, and Pines, we construct a canonical transformation that completely decouples the impurity from the bath degrees of freedom. By combining this transformation with a Gaussian ansatz for the fermionic bath, we obtain a family of variational many-body states that can efficiently encode the strong entanglement between the impurity and fermions of the bath. We give a detailed derivation of equations of motions in the imaginary- and real-time evolutions on the variational manifold. We benchmark our approach by applying it to investigate ground-state and dynamical properties of the anisotropic Kondo model and compare results with those obtained using matrix-product state (MPS) ansatz. We show that our approach can achieve an accuracy comparable to MPS-based methods with several orders of magnitude fewer variational parameters than the corresponding MPS ansatz. Comparisons to the Yosida ansatz and the exact solution from the Bethe ansatz are also discussed. We use our approach to investigate the two-lead Kondo model and analyze its long-time spatiotemporal behavior and the conductance behavior at finite bias and magnetic fields. The obtained results are consistent with the previous findings in the Anderson model and the exact solutions at the Toulouse point.

Categories: Journals, Physics

### Excitation and propagation of surface polaritonic rogue waves and breathers

Excitation and propagation of the surface polaritonic rogue waves and breathers are investigated by proposing a coupler free optical waveguide that consists of a transparent layer, middle negative index metamaterial layer, and bottom layer of the cold four level atomic medium. In this planar optical...

[Phys. Rev. A 98, 013825] Published Fri Jul 13, 2018

Categories: Journals, Physics

### Composable security analysis of continuous-variable measurement-device-independent quantum key distribution with squeezed states for coherent attacks

PRA: Quantum information - Fri, 2018-07-13 12:00

Author(s): Ziyang Chen, Yichen Zhang, Gan Wang, Zhengyu Li, and Hong Guo

Measurement-device-independent quantum key distribution protocol, whose security analysis does not rely on any assumption on the detection system, can immune the attacking against detectors. We give a first composable security analysis for continuous-variable measurement-device-independent quantum k...

[Phys. Rev. A 98, 012314] Published Fri Jul 13, 2018

Categories: Journals, Physics

### From unextendible product bases to genuinely entangled subspaces

PRA: Quantum information - Fri, 2018-07-13 12:00

Author(s): Maciej Demianowicz and Remigiusz Augusiak

Unextendible product bases (UPBs) are interesting mathematical objects arising in composite Hilbert spaces that have found various applications in quantum information theory, for instance in a construction of bound entangled states or Bell inequalities without quantum violation. They are closely rel...

[Phys. Rev. A 98, 012313] Published Fri Jul 13, 2018

Categories: Journals, Physics

### Separability-entanglement classifier via machine learning

PRA: Quantum information - Fri, 2018-07-13 12:00

Author(s): Sirui Lu, Shilin Huang, Keren Li, Jun Li, Jianxin Chen, Dawei Lu, Zhengfeng Ji, Yi Shen, Duanlu Zhou, and Bei Zeng

The problem of determining whether a given quantum state is entangled lies at the heart of quantum information processing. Despite the many methods—such as the positive partial transpose criterion and the k-symmetric extendibility criterion—to tackle this problem, none of them enables a general, pra...

[Phys. Rev. A 98, 012315] Published Fri Jul 13, 2018

Categories: Journals, Physics

### Capacity of a continuously distributed quantum network

PRA: Quantum information - Fri, 2018-07-13 12:00

Author(s): Xiang-Zhen Zhou, Xu-Tao Yu, and Zai-Chen Zhang

This paper investigates the capacity of a continuously distributed quantum network. A mathematical model of a multihop quantum communication process is given for capacity analysis. Our model assumes n nodes in a unit square, and both a capacity upper bound for arbitrarily distributed quantum network...

[Phys. Rev. A 98, 012316] Published Fri Jul 13, 2018

Categories: Journals, Physics

### Position Measurement-Induced Collapse: A Unified Quantum Description of Fraunhofer and Fresnel Diffractions. (arXiv:1807.03800v1 [quant-ph])

arXiv.org: Quantum Physics - Thu, 2018-07-12 23:45

Position measurement-induced collapse states are shown to provide a unified quantum description of diffraction of particles passing through a single slit. These states, which we here call quantum location states', are represented by the conventional rectangular wave function at the initial moment of position measurement. We expand this state in terms of the position eigenstates, which in turn can be represented as a linear combination of energy eigenfunctions of the problem. The time-evolution of these states in the case of free particles is shown to have position probability density patterns closely resembling diffraction patterns in the Fresnel region for small times and the same in Fraunhofer region for large times. Using the quantum trajectory representations in the de Broglie-Bohm, modified de Broglie-Bohm and Floyd-Faraaggi-Matone formalisms, we show that Fresnel and Fraunhofer diffractions can be described using a single expression. We have also plotted the probability density of location states for the case of particles moving in a general potential, detected at some arbitrary point. In the case of the harmonic oscillator potential, we find that they have oscillatory properties similar to coherent states.

Categories: Journals, Physics

### Internal Quantum Dynamics of a Nanoparticle in a Thermal Electromagnetic Field: a Minimal Model. (arXiv:1807.03811v1 [quant-ph])

arXiv.org: Quantum Physics - Thu, 2018-07-12 23:45

We argue that macroscopic electrodynamics is unsuited to describe the process of radiative thermalization between a levitated nanoparticle in high vacuum and the thermal electromagnetic field. Based on physical arguments, we propose a model to describe such systems beyond the quasi-equilibrium approximation. We use path integral techniques to analytically solve the model and exactly calculate the time evolution of the quantum degrees of freedom of the system. Free parameters of the microscopic quantum model are determined by matching analytical results to well-known macroscopic response functions. The time evolution of the internal energy of a levitated nanoparticle in a thermal electromagnetic field, as described by our model, qualitatively differs from macroscopic electrodynamics, a prediction that can be experimentally tested.

Categories: Journals, Physics

### Multiphoton Quantum Logic Gates for Superconducting Resonators with Tunable Nonlinear Interaction. (arXiv:1807.03820v1 [quant-ph])

arXiv.org: Quantum Physics - Thu, 2018-07-12 23:45

We propose a tunable nonlinear interaction for the implementation of quantum logic operations on pairs of superconducting resonators, where the two-resonator interaction is mediated by a transmon quantum bit (qubit). This interaction is characterized by a high on-to-off coupling ratio and allows for fast qubit-type and $d$-level system (qudit)-type operations for quantum information processing with multiphoton cavity states. We present analytical and numerical calculations showing that these operations can be performed with practically unit fidelity in absence of any dissipative phenomena, whereas physical two-photon two-resonator operations can be realized with a fidelity of 99.9% in presence of qubit and resonator decoherence. The resonator-qubit-resonator system proposed in this Letter can be implemented using available planar or three-dimensional microwave technology.

Categories: Journals, Physics

### Strongly inhomogeneous distribution of spectral properties of silicon-vacancy color centers in nanodiamonds. (arXiv:1807.03842v1 [quant-ph])

arXiv.org: Quantum Physics - Thu, 2018-07-12 23:45

The silicon-vacancy (SiV) color center in diamond is a solid-state single photon emitter and spin quantum bit suited as a component in quantum devices. Here, we show that the SiV center in nanodiamond exhibits a strongly inhomogeneous distribution with regard to the center wavelengths and linewidths of the zero-phonon-line (ZPL) emission at room temperature. We find that the SiV centers separate in two clusters: one group exhibits ZPLs with center wavelengths within a narrow range of approximatly 730 nm to 742 nm and broad linewidths between 5 nm and 17 nm, whereas the second group comprises a very broad distribution of center wavelengths between 715 nm and 835 nm, but narrow linewidths from below 1 nm up to 4 nm. Supported by ab initio Kohn-Sham density functional theory calculations we show that the ZPL shifts of the first group are consistently explained by strain in the diamond lattice. Further, we suggest, that the second group showing the strongly inhomogeneous distribution of center wavelengths might be comprised of modified SiV centers. Whereas single photon emission is demonstrated for SiV centers of both clusters, we show that emitters from different clusters show different spectroscopic features such as variations of the phonon sideband spectra and different blinking dynamics.

Categories: Journals, Physics

### Quantum causal models via QBism: the short version. (arXiv:1807.03843v1 [quant-ph])

arXiv.org: Quantum Physics - Thu, 2018-07-12 23:45

This paper is a concise summary of the main ideas presented in the companion paper Quantum causal models via Quantum Bayesianism'[arXiv:1806.00895]. I present the proposed definition of a quantum causal model with minimal background and justification, focusing only on its essential physical properties. The mathematical structure and definitions are provided as an Appendix. I discuss the possible physical significance of the fact that the model is symmetric under causal inversion.

Categories: Journals, Physics

### Quantum computing for finance: overview and prospects. (arXiv:1807.03890v1 [quant-ph])

arXiv.org: Quantum Physics - Thu, 2018-07-12 23:45

We discuss how quantum computation can be applied to financial problems, providing an overview of current approaches and potential prospects. We review quantum optimization algorithms, and expose how quantum annealers can be used to optimize portfolios, find arbitrage opportunities, and perform credit scoring. We also discuss deep-learning in finance, and suggestions to improve these methods through quantum machine learning. Finally, we consider quantum amplitude estimation, and how it can result in a quantum speed-up for Monte Carlo sampling. This has direct applications to many current financial methods, including pricing of derivatives and risk analysis. Perspectives are also discussed.

Categories: Journals, Physics

### Dephasing-insensitive quantum information storage and processing with superconducting qubits. (arXiv:1807.03897v1 [quant-ph])

arXiv.org: Quantum Physics - Thu, 2018-07-12 23:45

A central task towards building a practical quantum computer is to protect individual qubits from decoherence while retaining the ability to perform high-fidelity entangling gates involving arbitrary two qubits. Here we propose and demonstrate a dephasing-insensitive procedure for storing and processing quantum information in an all-to-all connected superconducting circuit involving multiple frequency-tunable qubits, each of which can be controllably coupled to any other through a central bus resonator. Although it is generally believed that the extra frequency tunability enhances the control freedom but induces more dephasing impact for superconducting qubits, our results show that any individual qubit can be dynamically decoupled from dephasing noise by applying a weak continuous and resonant driving field whose phase is reversed in the middle of the pulse. More importantly, we demonstrate a new method for realizing two-qubit phase gate with inherent dynamical decoupling via the combination of continuous driving and qubit-qubit swapping coupling. We find that the weak continuous driving fields not only enable the conditional dynamics essential for quantum information processing, but also protect both qubits from dephasing during the gate operation.

Categories: Journals, Physics

### Neural networks as "hidden" variable models for quantum systems. (arXiv:1807.03910v1 [quant-ph])

arXiv.org: Quantum Physics - Thu, 2018-07-12 23:45

We successfully model the behavior of two-spin systems using neural networks known as conditional Restricted Boltzmann Machines (cRBMs). The result gives local "hidden" variable models for product states and entangled states, including the singlet state used in the EPR-Bohm experiment. Bell's theorem is circumvented because the state of the system is dependent not only on the preparation but also on the measurement setup (the detector settings). Though at first glance counterintuitive, the apparent "retrocausality" in these models has a historical precedent in the absorber theory of Wheeler and Feynman and an intuitive analog in the simple AC circuit of an electric guitar.

Categories: Journals, Physics

### Recurrent neural networks running on quantum spins: memory accuracy and capacity. (arXiv:1807.03947v1 [cond-mat.dis-nn])

arXiv.org: Quantum Physics - Thu, 2018-07-12 23:45

Quantum computing and neural networks show great promise for the future of information processing. In this paper we study a quantum reservoir computer, a framework harnessing quantum dynamics and designed for fast and efficient solving of temporal machine learning tasks such as speech recognition, time series prediction and natural language processing. Specifically, we study memory capacity and accuracy of a quantum reservoir computer based on the fully connected transverse field Ising model by investigating different forms of inter-spin interactions and computing timescales. We show that variation in inter-spin interactions leads to a better memory capacity in general, by engineering the type of interactions the capacity can be greatly enhanced and there exists an optimal timescale at which the capacity is maximized. To connect computational capabilities to physical properties of the underlaying system, we also study the out-of-time-ordered correlator and find that its faster decay implies a more accurate memory.

Categories: Journals, Physics

### Quantum interference enables constant-time quantum information processing. (arXiv:1807.03960v1 [quant-ph])

arXiv.org: Quantum Physics - Thu, 2018-07-12 23:45

Science, medicine and engineering demand efficient information processing. It is a long-standing goal to use quantum mechanics to significantly improve such computations. The processing routinely involves examining data as a function of complementary variables, e.g., time and frequency. This is done by the Fourier transform approximations which accurately compute inputs of $2^n$ samples in $O(n 2^n)$ steps. In the quantum domain, an analogous process exists, namely a Fourier transform of quantum amplitudes, which requires exponentially fewer $O(n \log n)$ quantum gates. Here, we report a quantum fractional Kravchuk-Fourier transform, a related process suited to finite string processing. Unlike previous demonstrations, our architecture involves only one gate, resulting in constant-time processing of quantum information. The gate exploits a generalized Hong--Ou--Mandel effect, the basis for quantum-photonic information applications. We perform a proof-of-concept experiment by creation of large photon number states, interfering them on a beam splitter and using photon-counting detection. Existing quantum technologies may scale it up towards diverse applications.

Categories: Journals, Physics

### Hamiltonian simulation with nearly optimal dependence on spectral norm. (arXiv:1807.03967v1 [quant-ph])

arXiv.org: Quantum Physics - Thu, 2018-07-12 23:45

We present a quantum algorithm for approximating the real time evolution $e^{-iHt}$ of an arbitrary $d$-sparse Hamiltonian to error $\epsilon$, given black-box access to the positions and $b$-bit values of its non-zero matrix entries. The complexity of our algorithm is $\mathcal{O}((t\sqrt{d}\|H\|_{1 \rightarrow 2})^{1+o(1)}/\epsilon^{o(1)})$ queries and a factor $\mathcal{O}(b)$ more gates, which is shown to be optimal up to subpolynomial factors through a matching query lower bound. This provides a polynomial speedup in sparsity for the common case where the spectral norm $\|H\|\ge\|H\|_{1 \rightarrow 2}$ is known, and generalizes previous approaches which achieve optimal scaling, but with respect to more restrictive parameters. By exploiting knowledge of the spectral norm, our algorithm solves the black-box unitary implementation problem -- $\mathcal{O}(d^{1/2+o(1)})$ queries suffice to approximate any $d$-sparse unitary in the black-box setting, which matches the quantum search lower bound of $\Omega(\sqrt{d})$ queries and improves upon prior art [Berry and Childs, QIP 2010] of $\tilde{\mathcal{O}}(d^{2/3})$ queries. Combined with known techniques, we also solve systems of sparse linear equations with condition number $\kappa$ using $\mathcal{O}((\kappa \sqrt{d})^{1+o(1)}/\epsilon^{o(1)})$ queries, which is a quadratic improvement in sparsity.

Categories: Journals, Physics