Distributed quantum information processing is based on the transmission of quantum data over lossy channels between quantum processing nodes. These nodes may be separated by a few microns or on planetary scale distances, but transmission losses due to absorption and/or scattering in the channel are the major source of error for most distributed quantum information tasks. Of course, quantum error correction (QEC) and detection techniques can be used to mitigate such effects, but error detection approaches have severe performance limitations due to the signaling constraints between nodes, and so error correction approaches are preferable—assuming one has sufficient high quality local operations. Typically, performance comparisons between loss-mitigating codes assume one encoded qubit per photon. However, single photons can carry more than one qubit of information and so our focus in this Letter is to explore whether loss-based QEC codes utilizing quantum multiplexed photons are viable and advantageous, especially as photon loss results in more than one qubit of information being lost. We show that quantum multiplexing enables significant resource reduction, in terms of the number of single-photon sources, while at the same time maintaining (or even lowering) the number of 2-qubit gates required. Further, our multiplexing approach requires only conventional optical gates already necessary for the implementation of these codes.

We consider the number ${\mathcal{N}}_{{\theta }_A}(\theta )$ of eigenvalues $e^{i{\theta }_j}$ of a random unitary matrix, drawn from ${\mathrm{CUE}}_{\beta }(N)$, in the interval ${\theta }_j\in [{\theta }_A,\theta ]$. The deviations from its mean, ${\mathcal{N}}_{{\theta }_A}(\theta )-\mathbb{E}[{\mathcal{N}}_{{\theta }_A}(\theta )]$, form a random process as function of $\theta$. We study the maximum of this process, by exploiting the mapping onto the statistical mechanics of log-correlated random landscapes. By using an extended Fisher-Hartwig conjecture supplemented with the freezing duality conjecture for log-correlated fields, we obtain the cumulants of the distribution of that maximum for any $\beta >0$. It exhibits combined features of standard counting statistics of fermions (free for $\beta =2$ and with Sutherland-type interaction for $\beta \ne 2$) in an interval and extremal statistics of the fractional Brownian motion with Hurst index $H=0$. The $\beta =2$ results are expected to apply to the statistics of zeroes of the Riemann Zeta function.

We consider an ensemble of indistinguishable quantum machines and show that quantum statistical effects can give rise to a genuine quantum enhancement of the collective thermodynamic performance. When multiple indistinguishable bosonic work resources are coupled to an external system, the internal energy change of the external system exhibits an enhancement arising from permutation symmetry in the ensemble, which is absent when the latter consists of distinguishable work resources.

Family-Vicsek scaling is one of the most essential scale-invariant laws emerging in surface-roughness growth of classical systems. In this Letter, we theoretically elucidate the emergence of the Family-Vicsek scaling even in a strongly interacting quantum bosonic system by introducing a surface-height operator. This operator is comprised of a summation of local particle-number operators at a simultaneous time, and thus the observation of the surface roughness in the quantum many-body system and its scaling behavior are accessible to current experiments of ultracold atoms.

We report a systematic study of finite-temperature spin transport in quantum and classical one-dimensional magnets with isotropic spin interactions, including both integrable and nonintegrable models. Employing a phenomenological framework based on a generalized Burgers’ equation in a time-dependent stochastic environment, we identify four different universality classes of spin fluctuations. These comprise, aside from normal spin diffusion, three types of superdiffusive transport: the Kardar-Parisi-Zhang universality class and two distinct types of anomalous diffusion with multiplicative logarithmic corrections. Our predictions are supported by extensive numerical simulations on various examples of quantum and classical chains. Contrary to common belief, we demonstrate that even nonintegrable spin chains can display a diverging spin diffusion constant at finite temperatures.

It is well known in quantum mechanics that a large energy gap between a Hilbert subspace of specific interest and the remainder of the spectrum can suppress transitions from the quantum states inside the subspace to those outside due to additional couplings that mix these states, and thus approximately lead to a constrained dynamics within the subspace. While this statement has widely been used to approximate quantum dynamics in various contexts, a general and quantitative justification stays lacking. Here we establish an observable-based error bound for such a constrained-dynamics approximation in generic gapped quantum systems. This universal bound is a linear function of time that only involves the energy gap and coupling strength, provided that the latter is much smaller than the former. We demonstrate that either the intercept or the slope in the bound is asymptotically saturable by simple models. We generalize the result to quantum many-body systems with local interactions, for which the coupling strength diverges in the thermodynamic limit while the error is found to grow no faster than a power law $t^{d+1}$ in $d$ dimensions. Our work establishes a universal and rigorous result concerning nonequilibrium quantum dynamics.

The quantum neural network is one of the promising applications for near-term noisy intermediate-scale quantum computers. A quantum neural network distills the information from the input wave function into the output qubits. In this Letter, we show that this process can also be viewed from the opposite direction: the quantum information in the output qubits is scrambled into the input. This observation motivates us to use the tripartite information—a quantity recently developed to characterize information scrambling—to diagnose the training dynamics of quantum neural networks. We empirically find strong correlation between the dynamical behavior of the tripartite information and the loss function in the training process, from which we identify that the training process has two stages for randomly initialized networks. In the early stage, the network performance improves rapidly and the tripartite information increases linearly with a universal slope, meaning that the neural network becomes less scrambled than the random unitary. In the latter stage, the network performance improves slowly while the tripartite information decreases. We present evidences that the network constructs local correlations in the early stage and learns large-scale structures in the latter stage. We believe this two-stage training dynamics is universal and is applicable to a wide range of problems. Our work builds bridges between two research subjects of quantum neural networks and information scrambling, which opens up a new perspective to understand quantum neural networks.

One of the most widespread methods to determine if a quantum state is entangled, or to quantify its entanglement dimensionality, is by measuring its fidelity with respect to a pure state. In this Letter, we find a large class of states whose entanglement cannot be detected in this manner; we call them unfaithful. We find that unfaithful states are ubiquitous in information theory. For small dimensions, we check numerically that most bipartite states are both entangled and unfaithful. Similarly, numerical searches in low dimensions show that most pure entangled states remain entangled but become unfaithful when a certain amount of white noise is added. We also find that faithfulness can be self-activated, i.e., there exist instances of unfaithful states whose tensor powers are faithful. To explore how the fidelity approach limits the quantification of entanglement dimensionality, we generalize the notion of an unfaithful state to that of a $D$ unfaithful state, one that cannot be certified as $D$-dimensionally entangled by measuring its fidelity with respect to a pure state. For describing such states, we additionally introduce a hierarchy of semidefinite programming relaxations that fully characterizes the set of states of Schmidt rank at most $D$.

The clustering property of an equilibrium bipartite correlation is one of the most general thermodynamic properties in noncritical many-body quantum systems. Herein, we consider the thermalization properties of a system class exhibiting the clustering property. We investigate two regimes, namely, regimes of high and low density of states corresponding to high- and low-energy regimes, respectively. We show that the clustering property is connected to several properties on the eigenstate thermalization through the density of states. Remarkably, the eigenstate thermalization is obtained in the low-energy regime with a sparse density of states, which is typically seen in gapped systems. For the high-energy regime, we demonstrate the ensemble equivalence between microcanonical and canonical ensembles even for a subexponentially small energy shell with respect to the system size, which eventually leads to the weak version of eigenstate thermalization.

We report the observation of the quantum walks of a phonon, a vibrational quantum, in a trapped-ion crystal. By employing the capability to prepare and observe the localized wave packet of a phonon, the propagation of a single radial local phonon in a four-ion linear crystal is observed with single-site resolution. The results show an agreement with numerical calculations, indicating the predictability and reproducibility of the phonon system. These characteristics may contribute advantageously in the advanced studies of quantum walks, as well as boson sampling and quantum simulation.

In this work, we establish a relation between entanglement entropy and fractal dimension $D$ of generic many-body wave functions, by generalizing the result of Page [Phys. Rev. Lett. 71, 1291 (1993)] to the case of sparse random pure states (SRPS). These SRPS living in a Hilbert space of size $N$ are defined as normalized vectors with only $N^D$ ($0\le D\le 1$) random nonzero elements. For $D=1$, these states used by Page represent ergodic states at an infinite temperature. However, for $0<D<1$, the SRPS are nonergodic and fractal, as they are confined in a vanishing ratio $N^D/N$ of the full Hilbert space. Both analytically and numerically, we show that the mean entanglement entropy ${\mathcal{S}}_1(A)$ of a subsystem $A$, with Hilbert space dimension $N_A$, scales as $\overline{{\mathcal{S}}_1}(A)\sim D\ln N$ for small fractal dimensions $D$, $N^D<N_A$. Remarkably, $\overline{{\mathcal{S}}_1}(A)$ saturates at its thermal (Page) value at an infinite temperature, $\overline{{\mathcal{S}}_1}(A)\sim \ln N_A$ at larger $D$. Consequently, we provide an example when the entanglement entropy takes an ergodic value even though the wave function is highly nonergodic. Finally, we generalize our results to Renyi entropies ${\mathcal{S}}_q(A)$ with $q>1$ and to genuine multifractal states and also show that their fluctuations have ergodic behavior in a narrower vicinity of the ergodic state $D=1$.

We develop a strategy for tensor network algorithms that allows to deal very efficiently with lattices of high connectivity. The basic idea is to fine grain the physical degrees of freedom, i.e., decompose them into more fundamental units which, after a suitable coarse graining, provide the original ones. Thanks to this procedure, the original lattice with high connectivity is transformed by an isometry into a simpler structure, which is easier to simulate via usual tensor network methods. In particular this enables the use of standard schemes to contract infinite 2D tensor networks—such as corner transfer matrix renormalization schemes—which are more involved on complex lattice structures. We prove the validity of our approach by numerically computing the ground-state properties of the ferromagnetic spin-1 transverse-field Ising model on the 2D triangular and 3D stacked triangular lattice, as well as of the hardcore and softcore Bose-Hubbard models on the triangular lattice. Our results are benchmarked against those obtained with other techniques, such as perturbative continuous unitary transformations and graph projected entangled pair states, showing excellent agreement and also improved performance in several regimes.

We consider the most general set of integrable deformations extending the $T\overline{T}$ deformation of two-dimensional relativistic QFTs. They are CDD deformations of the theory’s factorized $S$ matrix related to the higher-spin conserved charges. Using a mirror version of the generalized Gibbs ensemble, we write down the finite-volume expectation value of the higher-spin charges, and derive a generalized flow equation that every charge must obey under a generalized $T\overline{T}$ deformation. This also reproduces the known flow equations on the nose.

Stochastic methods with quantum jumps are often used to solve open quantum system dynamics. Moreover, they provide insight into fundamental topics, such as the role of measurements in quantum mechanics and the description of non-Markovian memory effects. However, there is no unified framework to use quantum jumps to describe open-system dynamics in any regime. We solve this issue by developing the rate operator quantum jump (ROQJ) approach. The method not only applies to both Markovian and non-Markovian evolutions, but also allows us to unravel master equations for which previous methods do not work. In addition, ROQJ yields a rigorous measurement-scheme interpretation for a wide class of dynamics, including a set of master equations with negative decay rates, and sheds light on different types of memory effects which arise when using stochastic quantum jump methods.

This Letter unravels an interesting property of a one-dimensional lattice model that describes a single itinerant spinless fermion (excitation) coupled to zero-dimensional (dispersionless) bosons through two different nonlocal coupling mechanisms. Namely, below a critical value of the effective excitation-boson coupling strength, the exact ground state of this model is the zero-quasimomentum Bloch state of a bare (i.e., completely undressed) excitation. It is demonstrated here how this last property of the lattice model under consideration can be exploited for a fast, deterministic preparation of multipartite $W$ states in a readily realizable system of inductively coupled superconducting qubits and microwave resonators.

In this Letter, we introduce a “coherence equality” that is satisfied by any classical communication—i.e., conveyed by a localized carrier traveling along well defined directions. In contrast, this equality is violated when the carrier is prepared in coherent quantum superposition of communication directions. This is phrased in terms of the success probability of a certain communication task, which is always constant and equal to $1/2$ in the classical case. On the other hand, we develop two simple quantum schemes that deviate systematically from the classical value, thus, violating the coherence equality. Such a violation can also be exploited as an operational way to witness spatial quantum superpositions without requiring us to recombine the modes in a standard interferometer, but only by means of spatially separated local measurements.

In this Letter, we propose a new approach to process high-dimensional quantum information encoded in a photon frequency domain. In contrast to previous approaches based on nonlinear optical processes, no active control of photon energy is required. Arbitrary unitary transformation and projection measurement can be realized with passive photonic circuits and time-resolving detection. A systematic circuit design for a quantum frequency comb with arbitrary size has been given. The criteria to verify quantum frequency correlation has been derived. By considering the practical condition of the detector’s finite response time, we show that high-fidelity operation can be readily realized with current device performance. This work will pave the way towards scalable and high-fidelity quantum information processing based on high-dimensional frequency encoding.

We address the study of quantum metrology enhanced by indefinite causal order, demonstrating a quadratic advantage in the estimation of the product of two average displacements in a continuous variable system. We prove that no setup where the displacements are used in a fixed order can have root-mean-square error vanishing faster than the Heisenberg limit $1/N$, where $N$ is the number of displacements contributing to the average. In stark contrast, we show that a setup that probes the displacements in a superposition of two alternative orders yields a root-mean-square error vanishing with super-Heisenberg scaling $1/N^2$, which we prove to be optimal among all superpositions of setups with definite causal order. Our result opens up the study of new measurement setups where quantum processes are probed in an indefinite order, and suggests enhanced tests of the canonical commutation relations, with potential applications to quantum gravity.