We experimentally demonstrate an advanced linear-optical programmable quantum processor that combines two elementary single-qubit programmable quantum gates. We show that this scheme enables direct experimental probing of quantum commutation relations for Pauli operators acting on polarization states of single photons. Depending on a state of two-qubit program register, we can probe either commutation or anticommutation relations. Very good agreement between theory and experiment is observed, indicating high-quality performance of the implemented quantum processor.

Diffusion-limited reactions are usually described within the Smoluchowski theory, which neglects interparticle interactions. We propose a simple way to incorporate excluded-volume effects building on simulations of hard sphere in the presence of a sink. For large values of the sink-to-particle size ratio $R_s$, the measured encounter rate is in good agreement with a simple generalization of the Smoluchowski equation at high densities. Reducing $R_s$, the encounter rate is substantially depressed and becomes even nonmonotonic for $R_s\ll 1$. Concurrently with the saturation of the rate, stationary density waves set in close to the sink. A mean-field analysis helps to shed light on the subtle link between such ordering and the slowing down of the encounter dynamics. Finally, we show how an infinitesimal amount of nonreacting impurities can equally slow down dramatically the reaction.

Single-spin measurements on the ground state of an interacting spin lattice can be used to perform a quantum computation. We show how such measurements can mimic renormalization group transformations and remove the short-ranged variations of the state that can reduce the fidelity of a computation. This suggests that the quantum computational ability of a spin lattice could be a robust property of a quantum phase. We illustrate our idea with the ground state of a rotationally invariant spin-1 chain, which can serve as a quantum computational wire not only at the Affleck-Kennedy-Lieb-Tasaki point, but within the Haldane phase.

Ultracold atoms in optical lattices realize simple condensed matter models. We create an ensemble of $\approx 60$ harmonically trapped 2D Bose-Hubbard systems from a ${}^{87}\mathrm{Rb}$ Bose-Einstein condensate in an optical lattice and use a magnetic resonance imaging approach to select a few 2D systems for study, thereby eliminating ensemble averaging. Our identification of the transition from superfluid to Mott insulator, as a function of both atom density and lattice depth, is in excellent agreement with a universal state diagram [M. Rigol et al., Phys. Rev. A 79 053605 (2009)] suitable for our trapped system. In agreement with theory, our data suggest a failure of the local density approximation in the transition region.

The proton momentum distribution, accessible by deep inelastic neutron scattering, is a very sensitive probe of the potential of mean force experienced by the protons in hydrogen-bonded systems. In this work we introduce a novel estimator for the end-to-end distribution of the Feynman paths, i.e., the Fourier transform of the momentum distribution. In this formulation, free particle and environmental contributions factorize. Moreover, the environmental contribution has a natural analogy to a free energy surface in statistical mechanics, facilitating the interpretation of experiments. The new formulation is not only conceptually but also computationally advantageous. We illustrate the method with applications to an empirical water model, ab initio ice, and one dimensional model systems.

We consider the security of continuous-variable quantum cryptography as we approach the classical limit, i.e., when the unknown preparation noise at the sender’s station becomes significantly noisy or thermal (even by as much as ${10}^4$ times greater than the variance of the vacuum mode). We show that, provided the channel transmission losses do not exceed 50%, the security of quantum cryptography is not dependent on the channel transmission, and is therefore incredibly robust against significant amounts of excess preparation noise. We extend these results to consider for the first time quantum cryptography at wavelengths considerably longer than optical and find that regions of security still exist all the way down to the microwave.

In the past decade there has been considerable interest in nonequilibrium free energy theorems. These theorems show how the difference between the free energies of two equilibrium states of a system are related to distributions of work along nonequilibrium pathways. Here we significantly extend these theorems by relating the possibly inaccessible equilibrium average of any phase variable to the distribution of work along nonequilibrium paths. The result is elegant and analogous to the static umbrella sampling used with Monte Carlo simulations. The umbrella weight, which is related to the nonequilibrium work, is easy to obtain and efficient to compute. Furthermore, its average may be obtained from the existing nonequilibrium free energy theorem.

We determined the Newtonian constant of gravitation $G$ by interferometrically measuring the change in spacing between two free-hanging pendulum masses caused by the gravitational field from large tungsten source masses. We find a value for $G$ of $(6.67234\pm 0.00014)\times {10}^{-11}{\mathrm{m}}^3{\mathrm{kg}}^{-1}{\mathrm{s}}^{-2}$. This value is in good agreement with the 1986 Committee on Data for Science and Technology (CODATA) value of $(6.67259\pm 0.00085)\times {10}^{-11}{\mathrm{m}}^3{\mathrm{kg}}^{-1}{\mathrm{s}}^{-2}$ [Rev. Mod. Phys. 59, 1121 (1987)] but differs from some more recent determinations as well as the latest CODATA recommendation of $(6.67428\pm 0.00067)\times {10}^{-11}{\mathrm{m}}^3{\mathrm{kg}}^{-1}{\mathrm{s}}^{-2}$ [Rev. Mod. Phys. 80, 633 (2008)].

In dispersive readout schemes, qubit-induced nonlinearity typically limits the measurement fidelity by reducing the signal-to-noise ratio (SNR) when the measurement power is increased. Contrary to seeing the nonlinearity as a problem, here we propose to use it to our advantage in a regime where it can increase the SNR. We show analytically that such a regime exists if the qubit has a many-level structure. We also show how this physics can account for the high-fidelity avalanchelike measurement recently reported by Reed et al. [arXiv:1004.4323v1].

We analyze the Jaynes-Cummings model of quantum optics, in the strong-dispersive regime. In the bad-cavity limit and on time scales short compared to the atomic coherence time, the dynamics are those of a nonlinear oscillator. A steady-state nonperturbative semiclassical analysis exhibits a finite region of bistability delimited by a pair of critical points, unlike the usual dispersive bistability from a Kerr nonlinearity. This analysis explains our quantum trajectory simulations that show qualitative agreement with recent experiments from the field of circuit quantum electrodynamics.

We consider the evolution of a qubit (spin $1/2$) under the simultaneous continuous measurement of three noncommuting qubit operators ${\widehat{\sigma }}_x$, ${\widehat{\sigma }}_y$, and ${\widehat{\sigma }}_z$. For identical ideal detectors, the qubit state evolves by approaching a pure state with a random direction in the Bloch vector space and by undergoing locally isotropic diffusion in the perpendicular directions. The quantum state conditioned on the complete detector record is used to assess the fidelity of classically inspired estimates based on running time averages and discrete time bin detector outputs.

We invoke the black-hole–qubit correspondence to derive the classification of four-qubit entanglement. The $U$-duality orbits resulting from timelike reduction of string theory from $D=4$ to $D=3$ yield 31 entanglement families, which reduce to nine up to permutation of the four qubits.

We report quantum coherence measurements of a superconducting qubit whose design is a hybrid of several existing types. Excellent coherence times are found: $T_2^{*}\sim T_1\sim 1.5\mu \mathrm{s}$. The topology of the qubit is that of a traditional three-junction flux qubit, but it has a large shunting capacitance, and the ratio of the junction critical currents is chosen so that the qubit potential has a single-well form. The qubit has a sizable nonlinearity, but its sign is reversed compared with most other popular qubit designs. The qubit is read out dispersively using a high-$Q$ resonator in a $\lambda /2$ configuration.

We address the degradation of continuous variable (CV) entanglement in a noisy channel focusing on the set of photon-number entangled states. We exploit several separability criteria and compare the resulting separation times with the value of non-Gaussianity at any time, thus showing that in the low-temperature regime: (i) non-Gaussianity is a bound for the relative entropy of entanglement and (ii) Simon’s criterion provides a reliable estimate of the separation time also for non-Gaussian states. We provide several evidences supporting the conjecture that Gaussian entanglement is the most robust against noise, i.e., it survives longer than a non-Gaussian one, and that this may be a general feature for CV systems in Markovian channels.

We study a minimal non-Markovian model of superdiffusion which originates from long-range velocity correlations within the generalized Langevin equation approach. The model allows for a three-dimensional Markovian embedding. The emergence of a transient hyperdiffusion, $⟨\Delta x^2(t)⟩\propto t^{2+\lambda }$, with $\lambda \sim 1–3$ is detected in tilted washboard potentials before it ends up in a ballistic asymptotic regime. We relate this phenomenon to a transient heating of particles $T_{\mathrm{kin}}(t)\propto t^{\lambda }$ from the thermal bath temperature $T$ to some maximal kinetic temperature $T_{\max }$. This hyperdiffusive transient regime ceases when the particles arrive at the maximal kinetic temperature.

We investigate the coherent quantum time evolution of a driven mesoscopic chain of two-level systems that interact via the van der Waals interaction in their excited state. The Hamiltonian is the sum of a classical lattice gas Hamiltonian and an off-diagonal driving term without classical counterpart. Starting from a product state we observe—beyond a certain interaction strength—thermalization of the system with respect to observables of the classical lattice gas. This transition can be studied experimentally with Rydberg atoms, ions, or polar molecules. We suggest how to experimentally determine the temperature of the thermal state which should allow for thermometry of the internal degrees of freedom of cold Rydberg gases whose external dynamics is frozen.

Quantum state reconstruction of weak propagating microwaves to date requires the use of linear amplifiers. We introduce a theory which, even in the presence of significant amplifier noise, allows one to use these devices for measuring all quadrature moments of propagating quantum microwaves based on cross correlations from a dual-path amplification setup. Simultaneously, the detector noise properties are determined, allowing for tomography. We demonstrate the feasibility of our novel concept by proof-of-principle experiments with classical mixtures of weak coherent microwaves.

The leading relativistic and recoil corrections to bound state $g$ factors of particles with arbitrary spin are calculated. It is shown that these corrections are universal for any spin and depend only on the free particle gyromagnetic ratios. To prove this universality we develop nonrelativistic quantum electrodynamics (NRQED) for charged particles with an arbitrary spin. The coefficients in the NRQED Hamiltonian for higher spin particles are determined only by the requirements of Lorentz invariance and local charge conservation in the respective relativistic theory. For spin one charged particles, the NRQED Hamiltonian follows from the renormalizable QED of the charged vector bosons. We show that universality of the leading relativistic and recoil corrections can be explained with the help of the Bargmann-Michael-Telegdi equation.

It is not so well known that measurement-free quantum error correction protocols can be designed to achieve fault-tolerant quantum computing. Despite their potential advantages in terms of the relaxation of accuracy, speed, and addressing requirements, they have usually been overlooked since they are expected to yield a very bad threshold. We show that this is not the case. We design fault-tolerant circuits for the 9-qubit Bacon-Shor code and find an error threshold for unitary gates and preparation of $p_{(p,g)\mathrm{thresh}}=3.76\times {10}^{-5}$ (30% of the best known result for the same code using measurement) while admitting up to $1/3$ error rates for measurements and allocating no constraints on measurement speed. We further show that demanding gate error rates sufficiently below the threshold pushes the preparation threshold up to $p_{(p)\mathrm{thresh}}=1/3$.

The spatial fluctuations of deformation are studied in the creep in Andrade’s power law and the logarithmic phases, using paper samples. Measurements by the digital image correlation technique show that the relative strength of the strain rate fluctuations increases with time, in both creep regimes. In the Andrade creep phase characterized by a power-law decay of the strain rate ${ϵ}_t\sim t^{-\theta }$, with $\theta \approx 0.7$, the fluctuations obey $\Delta {ϵ}_t\sim t^{-\gamma }$, with $\gamma \approx 0.5$. The local deformation follows a data collapse appropriate for a phase transition. Similar behavior is found in a crystal plasticity model, with a jamming or yielding transition.