## Physics

### A master equation for strongly interacting dipoles. (arXiv:1709.05875v2 [quant-ph] UPDATED)

arXiv.org: Quantum Physics - Tue, 2018-04-17 05:33

We consider a pair of dipoles for which direct electrostatic dipole-dipole interactions may be significantly larger than the coupling to transverse radiation. We derive a master equation using the Coulomb gauge, which naturally enables us to include the inter-dipole Coulomb energy within the system Hamiltonian rather than the interaction. In contrast, the standard master equation for a two- dipole system, which depends entirely on well-known gauge-invariant S-matrix elements, is usually derived using the multipolar gauge, wherein there is no explicit inter-dipole Coulomb interaction. We show using a generalised arbitrary-gauge light-matter Hamiltonian that this master equation is obtained in other gauges only if the inter-dipole Coulomb interaction is kept within the interaction Hamiltonian rather than the unperturbed part as in our derivation. Thus, our master equation, while still gauge-invariant, depends on different S-matrix elements, which give separation-dependent corrections to the standard matrix elements describing resonant energy transfer and collective decay. The two master equations coincide in the large separation limit where static couplings are negligible. We provide an application of our master equation by finding separation-dependent corrections to the natural emission spectrum of the two-dipole system.

Categories: Journals, Physics

### Deutsch, Toffoli, and CNOT Gates via Rydberg Blockade of Neutral Atoms. (arXiv:1710.01859v2 [quant-ph] UPDATED)

arXiv.org: Quantum Physics - Tue, 2018-04-17 05:33

Universal quantum gates and quantum error correction~(QEC) lie in the heart of quantum information science. Large-scale quantum computing depends on a universal set of quantum gates, in which some gates may be easily carried out, while others are hard with a certain physical system. There is a unique three-qubit quantum gate called the Deutsch gate~[$\mathbb{D}(\theta)$], from which alone a circuit can be constructed so that any feasible quantum computing is attainable. As far as we know, however, $\mathbb{D}(\theta)$ has not been demonstrated. Here we design an easily realizable $\mathbb{D}(\theta)$ by using Rydberg blockade of neutral atoms, where $\theta$ can be tuned to any value in $[0,\pi]$ by adjusting the strengths of external control fields. Using similar protocols, we further show that both the Toffoli and CNOT gates can be achieved with only three laser pulses. The Toffoli gate, being universal for classical reversible computing, is also useful for QEC that plays an important role in quantum communication and fault-tolerant quantum computation. The possibility and briefness to realize these gates shed new light on the study of quantum information with neutral atoms.

Categories: Journals, Physics

### Quantum SDP Solvers: Large Speed-ups, Optimality, and Applications to Quantum Learning. (arXiv:1710.02581v2 [quant-ph] UPDATED)

arXiv.org: Quantum Physics - Tue, 2018-04-17 05:33

We give two new quantum algorithms for solving semidefinite programs (SDPs) providing quantum speed-ups. We consider SDP instances with $m$ constraint matrices, each of dimension $n$, rank $r$, and sparsity $s$. The first algorithm assumes an input model where one is given access to entries of the matrices at unit cost. We show that it has run time $\tilde{O}(s^2(\sqrt{m}\epsilon^{-10}+\sqrt{n}\epsilon^{-12}))$, where $\epsilon$ is the error. This gives an optimal dependence in terms of $m, n$ and quadratic improvement over previous quantum algorithms when $m\approx n$. The second algorithm assumes a fully quantum input model in which the matrices are given as quantum states. We show that its run time is $\tilde{O}(\sqrt{m}+\text{poly}(r))\cdot\text{poly}(\log m,\log n,B,\epsilon^{-1})$, with $B$ an upper bound on the trace-norm of all input matrices. In particular the complexity depends only poly-logarithmically in $n$ and polynomially in $r$.

We apply the second SDP solver to the problem of learning a good description of a quantum state with respect to a set of measurements: Given $m$ measurements and copies of an unknown state $\rho$, we show we can find in time $\sqrt{m}\cdot\text{poly}(\log m,\log n,r,\epsilon^{-1})$ a description of the state as a quantum circuit preparing a density matrix which has the same expectation values as $\rho$ on the $m$ measurements, up to error $\epsilon$. The density matrix obtained is an approximation to the maximum entropy state consistent with the measurement data considered in Jaynes' principle from statistical mechanics.

As in previous work, we obtain our algorithm by "quantizing" classical SDP solvers based on the matrix multiplicative weight method. One of our main technical contributions is a quantum Gibbs state sampler for low-rank Hamiltonians with a poly-logarithmic dependence on its dimension, which could be of independent interest.

Categories: Journals, Physics

### Quantum criticality and state engineering in the simulated anisotropic quantum Rabi model. (arXiv:1710.08862v2 [quant-ph] UPDATED)

arXiv.org: Quantum Physics - Tue, 2018-04-17 05:33

Promising applications of the anisotropic quantum Rabi model (AQRM) in broad parameter ranges are explored, which is realized with superconducting flux qubits simultaneously driven by two-tone time-dependent magnetic fields. Regarding the quantum phase transitions (QPTs), with assistant of fidelity susceptibility, we extract the scaling functions and the critical exponents, with which the universal scaling of the cumulant ratio is captured with rescaling of the parameters due to the anisotropy. Moreover, a fixed point of the cumulant ratio is predicted at the critical point of the AQRM. In respect to quantum information tasks, the generation of the macroscopic Schr\"{o}dinger cat states and quantum controlled phase gates are investigated in the degenerate case of the AQRM, whose performance is also investigated by numerical calculation with practical parameters. Therefore, our results pave a way to explore distinct features of the AQRM in circuit QED systems for QPTs, quantum simulations and quantum information processings.

Categories: Journals, Physics

### Semiconducting double-dot exchange-only qubit dynamics in presence of magnetic and charge noises. (arXiv:1710.10032v2 [quant-ph] UPDATED)

arXiv.org: Quantum Physics - Tue, 2018-04-17 05:33

The effects of magnetic and charge noises on the dynamical evolution of the double-dot exchange-only qubit (DEOQ) is theoretically investigated. The DEOQ consisting of three electrons arranged in an electrostatically defined double quantum dot deserves special interest in quantum computation applications due to its advantages in terms of fabrication, control and manipulation in view of implementation of fast single and two qubit operations through only electrical tuning. The presence of the environmental noise due to nuclear spins and charge traps, in addition to fluctuations in the applied magnetic field and charge fluctuations on the electrostatic gates adopted to confine the electrons, is taken into account including random magnetic field and random coupling terms in the Hamiltonian. The behavior of the return probability as a function of time for initial conditions of interest is presented. Moreover, through an envelope-fitting procedure on the return probabilities, coherence times are extracted when model parameters take values achievable experimentally in semiconducting devices.

Categories: Journals, Physics

### From Near to Eternity: Spin-glass planting, tiling puzzles, and constraint satisfaction problems. (arXiv:1711.04083v2 [cond-mat.dis-nn] UPDATED)

arXiv.org: Quantum Physics - Tue, 2018-04-17 05:33

We present a methodology for generating Ising Hamiltonians of tunable complexity and with a priori known ground states based on a decomposition of the model graph into edge-disjoint subgraphs. The idea is illustrated with a spin-glass model defined on a cubic lattice, where subproblems, whose couplers are restricted to the two values {-1,+1}, are specified on unit cubes and are parametrized by their local degeneracy. The construction is shown to be equivalent to a type of three-dimensional constraint satisfaction problem known as the tiling puzzle. By varying the proportions of subproblem types, the Hamiltonian can span a dramatic range of typical computational complexity, from fairly easy to many orders of magnitude more difficult than prototypical bimodal and Gaussian spin glasses in three space dimensions. We corroborate this behavior via experiments with different algorithms and discuss generalizations and extensions to different types of graphs.

Categories: Journals, Physics

### Cavity quantum electrodynamics in the non-perturbative regime. (arXiv:1712.00015v2 [quant-ph] UPDATED)

arXiv.org: Quantum Physics - Tue, 2018-04-17 05:33

We study a generic cavity-QED system where a set of (artificial) two-level dipoles is coupled to the electric field of a single-mode LC resonator. This setup is used to derive a minimal quantum mechanical model for cavity QED, which accounts for both dipole-field and direct dipole-dipole interactions. The model is applicable for arbitrary coupling strengths and allows us to extend the usual Dicke model into the non-perturbative regime of QED, where the dipole-field interaction can be associated with an effective finestructure constant of order unity. In this regime, we identify three distinct classes of normal, superradiant and subradiant vacuum states and discuss their characteristic properties and the transitions between them. Our findings reconcile many of the previous, often contradictory predictions in this field and establish a common theoretical framework to describe ultrastrong coupling phenomena in a diverse range of cavity-QED platforms.

Categories: Journals, Physics

### Quantum optical realization of arbitrary linear transformations allowing for loss and gain. (arXiv:1712.01413v2 [quant-ph] UPDATED)

arXiv.org: Quantum Physics - Tue, 2018-04-17 05:33

Unitary transformations are routinely modeled and implemented in the field of quantum optics. In contrast, nonunitary transformations that can involve loss and gain require a different approach. In this theory work, we present a universal method to deal with nonunitary networks. An input to the method is an arbitrary linear transformation matrix of optical modes that does not need to adhere to bosonic commutation relations. The method constructs a transformation that includes the network of interest and accounts for full quantum optical effects related to loss and gain. Furthermore, through a decomposition in terms of simple building blocks it provides a step-by-step implementation recipe, in a manner similar to the decomposition by Reck et al. [Reck et al., Phys. Rev. Lett. 73, 58 (1994)] but applicable to nonunitary transformations. Applications of the method include the implementation of positive-operator-valued measures and the design of probabilistic optical quantum information protocols.

Categories: Journals, Physics

### Non-Gaussianity of multiple photon subtracted thermal states in terms of compound-Poisson photon number distribution parameters: theory and experiment. (arXiv:1712.04174v2 [quant-ph] UPDATED)

arXiv.org: Quantum Physics - Tue, 2018-04-17 05:33

The multiphoton-subtracted thermal states are an interesting example of quantum states of light which are both classical and non-Gaussian. All the properties of such states can be described by just two parameters of compound-Poisson photon number distribution. The non-Gaussianity dependency on these parameters has been calculated numerically and analytically. The loss of non-Gaussianity during the optical damping has been also studied experimentally.

Categories: Journals, Physics

### A unified treatment of polynomial sectors and constraint polynomials of the Rabi models. (arXiv:1712.09371v2 [quant-ph] UPDATED)

arXiv.org: Quantum Physics - Tue, 2018-04-17 05:33

General concept of a gradation slicing is used to analyze polynomial solutions of ordinary differential equations (ODE) with polynomial coefficients, ${\cal L}\psi=0$, where ${\cal L}=\sum_l p_l(z) d_z^l$, $p_l(z)$ are polynomials, $z$ is a one-dimensional coordinate, and $d_z=d/dz$. It is not required that ODE is either (i) Fuchsian or (ii) leads to a usual Sturm-Liouville eigenvalue problem. General necessary and sufficient conditions for the existence of a polynomial solution are formulated involving constraint relations. The necessary condition for a polynomial solution of $n$th degree to exist forces energy to a $n$th baseline. Once the constraint relations on the $n$th baseline can be solved, a polynomial solution is in principle possible even in the absence of any underlying algebraic structure. The usefulness of theory is demonstrated on the examples of various Rabi models. For those models, a baseline is known as a Juddian baseline (e.g. in the case of the Rabi model the curve described by the $n$th energy level of a displaced harmonic oscillator with varying coupling $g$). The corresponding constraint relations are shown to (i) reproduce known constraint polynomials for the usual and driven Rabi models and (ii) generate hitherto unknown constraint polynomials for the two-mode, two-photon, and generalized Rabi models, implying that the eigenvalues of corresponding polynomial eigenfunctions can be determined algebraically. Interestingly, the ODE of the above Rabi models are shown to be characterized, at least for some parameter range, by the same unique set of grading parameters.

Categories: Journals, Physics

### Relativistic quantum mechanics of a Proca particle in Riemannian spacetimes. (arXiv:1712.08625v3 [gr-qc] UPDATED)

arXiv.org: Quantum Physics - Tue, 2018-04-17 05:33

Relativistic quantum mechanics of a Proca (spin-1) particle in Riemannian spacetimes is constructed. Covariant equations defining electromagnetic interactions of a Proca particle with the anomalous magnetic moment and the electric dipole moment in Riemannian spacetimes are formulated. The relativistic Foldy-Wouthuysen transformation with allowance for terms proportional to the zero power of the Planck constant is performed as an example. The Hamiltonian obtained agrees with the corresponding Foldy-Wouthuysen Hamiltonians derived for scalar and Dirac particles and with their classical counterpart. The unification of relativistic quantum mechanics in the Foldy-Wouthuysen representation is discussed.

Categories: Journals, Physics

### Irreversibility at zero temperature from the perspective of the environemnt. (arXiv:1804.02970v2 [quant-ph] UPDATED)

arXiv.org: Quantum Physics - Tue, 2018-04-17 05:33

We address the emergence of entropy production in the non-equilibrium process of an open quantum system from the viewpoint of the environment. By making use of a dilation-based approach akin to Stinespring theorem, we derive an expression for the entropy production that comprises two fundamental contributions. The first is linked to the rate of creation of correlations between system and environment whereas the second highlights the possibility for the environment to modify its state in light of its coupling to the system. Both terms are shown to be associated with irreversible currents within the system and the environment, which pinpoint the emergence of irreversibility in the Markovian limit. Finally, we discuss how such a change of perspective in the study of entropy production has fecund implications for the study of non-Markovian open-system dynamics.

Categories: Journals, Physics

### Quantizations of the classical time of arrival and their dynamics. (arXiv:1804.03344v2 [quant-ph] UPDATED)

arXiv.org: Quantum Physics - Tue, 2018-04-17 05:33

The classical time of arrival in the interacting case is quantized by way of quantizing its expansion about the free time of arrival. The quantization is formulated in coordinate representation which represents ordering rules in terms of two variable polynomial functions. This leads to representations of the quantized time of arrival operators as integral operators whose kernels are determined by the chosen ordering rule. The formulation lends itself to generalization which allows construction of time of arrival operators that cannot be obtained by direct quantization using particular ordering rules. Wey, symmetric and Born-Jordan quantizations are specifically studied. The dynamics of the eigenfunctions of the different time of arrival operators are investigated. The eigenfunctions exhibit unitary arrival at the intended arrival point at their respective eigenvalues.

Categories: Journals, Physics

### Normal projected entangled pair states generating the same state. (arXiv:1804.04964v1 [cond-mat.str-el] CROSS LISTED)

arXiv.org: Quantum Physics - Tue, 2018-04-17 05:33

Tensor networks are generated by a set of small rank tensors and define many-body quantum states in a succinct form. The corresponding map is not one-to-one: different sets of tensors may generate the very same state. A fundamental question in the study of tensor networks naturally arises: what is then the relation between those sets? The answer to this question in one dimensional setups has found several applications, like the characterization of local and global symmetries, the classification of phases of matter and unitary evolutions, or the determination of the fixed points of renormalization procedures. Here we answer this question for projected entangled-pair states (PEPS) in any dimension and lattice geometry, as long as the tensors generating the states are normal, which constitute an important and generic class.

Categories: Journals, Physics

### Efficient algorithms for tensor scaling, quantum marginals and moment polytopes. (arXiv:1804.04739v2 [cs.DS] UPDATED)

arXiv.org: Quantum Physics - Tue, 2018-04-17 05:33

We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our algorithm provides an efficient weak membership oracle for the associated moment polytopes, an important family of implicitly-defined convex polytopes with exponentially many facets and a wide range of applications. These include the entanglement polytopes from quantum information theory (in particular, we obtain an efficient solution to the notorious one-body quantum marginal problem) and the Kronecker polytopes from representation theory (which capture the asymptotic support of Kronecker coefficients). Our algorithm can be applied to succinct descriptions of the input tensor whenever the marginals can be efficiently computed, as in the important case of matrix product states or tensor-train decompositions, widely used in computational physics and numerical mathematics.

We strengthen and generalize the alternating minimization approach of previous papers by introducing the theory of highest weight vectors from representation theory into the numerical optimization framework. We show that highest weight vectors are natural potential functions for scaling algorithms and prove new bounds on their evaluations to obtain polynomial-time convergence. Our techniques are general and we believe that they will be instrumental to obtain efficient algorithms for moment polytopes beyond the ones consider here, and more broadly, for other optimization problems possessing natural symmetries.

Categories: Journals, Physics

### Quantum Supremacy Circuit Simulation on Sunway TaihuLight. (arXiv:1804.04797v2 [quant-ph] UPDATED)

arXiv.org: Quantum Physics - Tue, 2018-04-17 05:33

With the rapid progress made by industry and academia, quantum computers with dozens of qubits or even larger size are coming true. However, the fidelity of existing quantum computers often sharply decreases as the circuit depth increases. Thus, an ideal quantum circuit simulator on classical computers, especially on high-performance computers, is needed for benchmarking and validation. We design a novel simulator of universal random quantum circuits, often called 'quantum supremacy circuits', and implement it on Sunway TaihuLight. The simulator can be used to accomplish the following two tasks: 1) Computing a complete output state-vector; 2) Calculating one or a few amplitudes.We target the simulation of 49-qubit circuits. For task 1), we successfully simulate such a circuit of depth 39, and for task 2) we reach the 55-depth level. To the best of our knowledge, both of the results are the state-of-the-art, which in return raises the bar of 'quantum supremacy'.

Categories: Journals, Physics

### Quantum teleportation in vacuum only via Unruh-DeWitt detectors. (arXiv:1804.01183v2 [gr-qc] UPDATED)

arXiv.org: Quantum Physics - Tue, 2018-04-17 05:33

We consider entanglement extraction into two two-level Unruh-DeWitt detectors from a vacuum of a neutral massless quantum scalar field in a four-dimensional spacetime, where the general monopole coupling to the scalar field is assumed. Based on the reduced density matrix of the two detectors derived within the perturbation theory, we show that the single copy of the entangled pair of the detectors can be utilized in quantum teleportation even when the detectors are separated acausally, while we observe no violation of the Bell-CHSH inequality. In the case of the Minkowski vacuum, in particular, we find that entanglement usable in quantum teleportation is extracted due to the special relativistic effect when the detectors are in a relative inertial motion, while it is not when they are comoving inertially and the switching of the detectors is executed adiabatically at infinite past and future.

Categories: Journals, Physics

### Spin squeezing in symmetric multiqubit states with two distinct Majorana spinors. (arXiv:1803.09143v3 [quant-ph] UPDATED)

arXiv.org: Quantum Physics - Tue, 2018-04-17 05:33

Majorana geometric representation of pure N-qubit states obeying exchange symmetry is em- ployed to explore spin squeezing properties in the family of states with two distinct spinors. Dicke states are characterized by two orthogonal spinors and belong to this family - but they are not spin squeezed. On the otherhand, those constituted by two non-orthogonal spinors exhibit spin squeezing.

Categories: Journals, Physics

### Restoring Heisenberg scaling in noisy quantum metrology by monitoring the environment. (arXiv:1803.05891v2 [quant-ph] UPDATED)

arXiv.org: Quantum Physics - Tue, 2018-04-17 05:33

We study quantum frequency estimation for $N$ qubits subjected to independent Markovian noise, via strategies based on time-continuous monitoring of the environment. Both physical intuition and an extended convexity property of the quantum Fisher information (QFI) suggest that these strategies are more effective than the standard ones based on the measurement of the unconditional state after the noisy evolution. Here we focus on initial GHZ states and on parallel or transverse noise. For parallel noise, i.e. dephasing, we show that perfectly efficient time-continuous photo-detection allows to recover the unitary (noiseless) QFI, and thus to obtain a Heisenberg scaling for every value of the monitoring time. For finite detection efficiency, one falls back to the noisy standard quantum limit scaling, but with a constant enhancement due to an effective reduced dephasing. Also in the transverse noise case we obtain that the Heisenberg scaling is recovered for perfectly efficient detectors, and we find that both homodyne and photo-detection based strategies are optimal. For finite detectors efficiency, our numerical simulations show that, as expected, an enhancement can be observed, but we cannot give any conclusive statement regarding the scaling. We finally describe in detail the stable and compact numerical algorithm that we have developed in order to evaluate the precision of such time-continuous estimation strategies, and that may find application in other quantum metrology schemes.

Categories: Journals, Physics

### Thermoelectric performance of topological boundary modes. (arXiv:1803.03609v2 [cond-mat.stat-mech] UPDATED)

arXiv.org: Quantum Physics - Tue, 2018-04-17 05:33

We investigate quantum transport and thermoelectrical properties of a finite-size Su-Schrieffer-Heeger model, a paradigmatic model for a one-dimensional topological insulator, which displays topologically protected edge states. By coupling the model to two fermionic reservoirs at its ends, we can explore the non-equilibrium dynamics of the system. Investigating the energy-resolved transmission, the current and the noise, we find that these observables can be used to detect the topologically non-trivial phase. With specific parameters, we show that we can dissipatively prepare the edge states as stationary states of a non-equilibrium configuration. We demonstrate that the edge states can be exploited to design a refrigerator driven by chemical work or a heat engine driven by a thermal gradient, respectively. These devices are topologically protected against symmetry-preserving perturbations, and their maximum efficiencies significantly exceed that of a single quantum dot device at comparable coupling strengths.

Categories: Journals, Physics