Using a generalized reciprocity relation between charge and vortex conductivities at complex frequencies in two space dimensions, we identify the capacitance in the insulating phase as a measure of vortex condensate stiffness. We compute the ratio of boson superfluid stiffness to vortex condensate stiffness at mirror points to be 0.21(1) for the relativistic O(2) model. The product of dynamical conductivities at mirror points is used as a quantitative measure of deviations from self-duality between charge and vortex theories. We propose the finite wave vector compressibility as an experimental measure of the vortex condensate stiffness for neutral lattice bosons.

We derive a set of isometric fluctuation relations, which constrain the order parameter fluctuations in finite-size systems at equilibrium and in the presence of a broken symmetry. These relations are exact and should apply generally to many condensed-matter physics systems. Here, we establish these relations for magnetic systems and nematic liquid crystals in a symmetry-breaking external field, and we illustrate them on the Curie-Weiss and the $XY$ models. Our relations also have implications for spontaneous symmetry breaking, which are discussed.

The method for the computation of the conditional probability density function for the nonlinear Schrödinger equation with additive noise is developed. We present in a constructive form the conditional probability density function in the limit of small noise and analytically derive it in a weakly nonlinear case. The general theory results are illustrated using fiber-optic communications as a particular, albeit practically very important, example.

Error-correcting codes protect quantum information and form the basis of fault-tolerant quantum computing. Leading proposals for fault-tolerant quantum computation require codes with an exceedingly rare property, a transversal non-Clifford gate. Codes with the desired property are presented for $d$-level qudit systems with prime $d$. The codes use $n=d-1$ qudits and can detect up to $\sim d/3$ errors. We quantify the performance of these codes for one approach to quantum computation known as magic-state distillation. Unlike prior work, we find performance is always enhanced by increasing $d$.

The computational efficiency of stochastic simulation algorithms is notoriously limited by the kinetic trapping of the simulated trajectories within low energy basins. Here we present a new method that overcomes kinetic trapping while still preserving exact statistics of escape paths from the trapping basins. The method is based on path factorization of the evolution operator and requires no prior knowledge of the underlying energy landscape. The efficiency of the new method is demonstrated in simulations of anomalous diffusion and phase separation in a binary alloy, two stochastic models presenting severe kinetic trapping.

Quantum mass acquisition, in which a massless (quasi)particle becomes massive due to quantum corrections, is predicted to occur in several subfields of physics. However, its experimental observation remains elusive since the emergent energy gap is too small. We show that a spinor Bose-Einstein condensate is an excellent candidate for the observation of such a peculiar phenomenon as the energy gap turns out to be 2 orders of magnitude larger than the zero-point energy. This extraordinarily large energy gap is a consequence of the dynamical instability. The propagation velocity of the resultant massive excitation mode is found to be decreased by the quantum corrections as opposed to phonons.

Qubit readout is commonly performed by thresholding a collection of analog detector signals to obtain a sequence of single-shot bit values. The intrinsic irreversibility of the mapping from analog to digital signals discards soft information associated with an a posteriori confidence that can be assigned to each bit value when a detector is well characterized. Accounting for soft information, we show significant improvements in enhanced state detection with the quantum repetition code as well as quantum state or parameter estimation. These advantages persist in spite of non-Gaussian features of realistic readout models, experimentally relevant small numbers of qubits, and finite encoding errors. These results show useful and achievable advantages for a wide range of current experiments on quantum state tomography, parameter estimation, and qubit readout.

We consider an open system near a quantum critical point that is suddenly moved towards the critical point. The bath-dominated diffusive nonequilibrium dynamics after the quench is shown to follow scaling behavior, governed by a critical exponent that emerges in addition to the known equilibrium critical exponents. We determine this exponent and show that it describes universal prethermalized coarsening dynamics of the order parameter in an intermediate time regime. Implications of this quantum critical prethermalization are: (i) a power law rise of order and correlations after an initial collapse of the equilibrium state and (ii) a crossover to thermalization that occurs arbitrarily late for sufficiently shallow quenches.

We introduce a superconducting qubit architecture that combines high-coherence qubits and tunable qubit-qubit coupling. With the ability to set the coupling to zero, we demonstrate that this architecture is protected from the frequency crowding problems that arise from fixed coupling. More importantly, the coupling can be tuned dynamically with nanosecond resolution, making this architecture a versatile platform with applications ranging from quantum logic gates to quantum simulation. We illustrate the advantages of dynamical coupling by implementing a novel adiabatic controlled-z gate, with a speed approaching that of single-qubit gates. Integrating coherence and scalable control, the introduced qubit architecture provides a promising path towards large-scale quantum computation and simulation.

We study analytically an intermittent search process in one dimension. There is an immobile target at the origin and a searcher undergoes a discrete time jump process starting at $x_0\ge 0$, where successive jumps are drawn independently from an arbitrary jump distribution $f(\eta )$. In addition, with a probability $0\le r<1$, the position of the searcher is reset to its initial position $x_0$. The efficiency of the search strategy is characterized by the mean time to find the target, i.e., the mean first passage time (MFPT) to the origin. For arbitrary jump distribution $f(\eta )$, initial position $x_0$ and resetting probability $r$, we compute analytically the MFPT. For the heavy-tailed Lévy stable jump distribution characterized by the Lévy index $0<\mu <2$, we show that, for any given $x_0$, the MFPT has a global minimum in the $(\mu ,r)$ plane at $\mathbf{(}{\mu }^{*}(x_0),r^{*}(x_0)\mathbf{)}$. We find a remarkable first-order phase transition as $x_0$ crosses a critical value $x_0^{*}$ at which the optimal parameters change discontinuously. Our analytical results are in good agreement with numerical simulations.

Using a combination of Boltzmann’s equation and virial expansion, we study the effect of three-body losses and interactions on the momentum distribution of a homogeneous unitary Bose gas in the dilute limit where quantum correlations are negligible. The comparison of our results to the recent measurement made at JILA on a unitary gas of ${}^{85}\mathrm{Rb}$ allows us to determine an experimental fugacity $z=0.5(1)$.

We present an efficient method for the characterization of two coupled discrete quantum systems, one of which can be controlled and measured. For two systems with transition frequencies ${\omega }_q$, ${\omega }_r$, and coupling strength $g$ we show how to obtain estimates of $g$ and ${\omega }_r$ whose error decreases exponentially in the number of measurement shots rather than as a power law expected in simple approaches. Our algorithm can thereby identify $g$ and ${\omega }_r$ simultaneously with high precision in a few hundred measurement shots. This is achieved by adapting measurement settings upon data as it is collected. We also introduce a method to eliminate erroneous estimates with small overhead. Our algorithm is robust against the presence of relaxation and typical noise. Our results are applicable to many candidate technologies for quantum computation, in particular, for the characterization of spurious two-level systems in superconducting qubits or stripline resonators.

The phenomenon of monogamy of Bell inequality violations is interesting both from the fundamental perspective as well as in cryptographic applications such as the extraction of randomness and secret bits. In this article, we derive new and stronger monogamy relations for violations of Bell inequalities in general no-signaling theories. These relations are applicable to the class of binary output correlation inequalities known as xor games, and to free unique games. In many instances of interest, we show that the derived relation provides a significant strengthening over previously known results. Our result connects, for the first time, the property of monogamy with that crucial part of the Bell expression that is necessary for revealing a contradiction with local realistic predictions, thus shifting the paradigm in the field of monogamy of correlations.

We investigate the out-of-equilibrium behavior of a dissipative gas of Rydberg atoms that features a dynamical transition between two stationary states characterized by different excitation densities. We determine the structure and properties of the phase diagram and identify the universality class of the transition, both for the statics and the dynamics. We show that the proper dynamical order parameter is in fact not the excitation density and find evidence that the dynamical transition is in the “model $A$” universality class; i.e., it features a nontrivial ${\mathbb{Z}}_2$ symmetry and a dynamics with nonconserved order parameter. This sheds light on some relevant and observable aspects of dynamical transitions in Rydberg gases. In particular it permits a quantitative understanding of a recent experiment [C. Carr, Phys. Rev. Lett. 111, 113901 (2013)] which observed bistable behavior as well as power-law scaling of the relaxation time. The latter emerges not due to critical slowing down in the vicinity of a second order transition, but from the nonequilibrium dynamics near a so-called spinodal line.

We study the effect of suddenly turning on a long-range interaction in a spinless Fermi gas in two dimensions. The short- to intermediate-time dynamics is described using the method of bosonization of the Fermi surface. The space-time dependence of the nonequilibrium fermion density matrix as well as the evolution after the quench of the discontinuity at the Fermi momentum of the momentum distribution are computed. We find that the asymptotic state predicted by bosonization is consistent with the existence of a prethermalization plateau, which is also predicted by a perturbative approach in terms of the fermionic degrees of freedom. The bosonized representation, however, explicitly allows for the construction of the generalized Gibbs ensemble describing the prethermalized state.

The quantum random energy model provides a mean-field description of the equilibrium spin glass transition. We show that it further exhibits a many-body localization–delocalization (MBLD) transition when viewed as a closed quantum system. The mean-field structure of the model allows an analytically tractable description of the MBLD transition using the forward-scattering approximation and replica techniques. The predictions are in good agreement with the numerics. The MBLD transition lies at energy density significantly above the equilibrium spin glass transition, indicating that the closed system dynamics freezes well outside of the traditional glass phase. We also observe that the structure of the eigenstates at the MBLD critical point changes continuously with the energy density, raising the possibility of a family of critical theories for the MBLD transition.