Several architectures have been proposed for quantum neural networks (QNNs), with the goal of efficiently performing machine learning tasks on quantum data. Rigorous scaling results are urgently needed for specific QNN constructions to understand which, if any, will be trainable at a large scale. Here, we analyze the gradient scaling (and hence the trainability) for a recently proposed architecture that we call dissipative QNNs (DQNNs), where the input qubits of each layer are discarded at the layer’s output. We find that DQNNs can exhibit barren plateaus, i.e., gradients that vanish exponentially in the number of qubits. Moreover, we provide quantitative bounds on the scaling of the gradient for DQNNs under different conditions, such as different cost functions and circuit depths, and show that trainability is not always guaranteed. Our work represents the first rigorous analysis of the scalability of a perceptron-based QNN.

Phase-insensitive optical amplifiers uniformly amplify each quadrature of an input field and are of both fundamental and technological importance. We find the quantum limit on the precision of estimating the gain of a quantum-limited phase-insensitive amplifier using a multimode probe that may also be entangled with an ancilla system. In stark contrast to the sensing of loss parameters, the average photon number $N$ and number of input modes $M$ of the probe are found to be equivalent and interchangeable resources for optimal gain sensing. All pure-state probes whose reduced state on the input modes to the amplifier is diagonal in the multimode number basis are proven to be quantum optimal under the same gain-independent measurement. We compare the best precision achievable using classical probes to the performance of an explicit photon-counting-based estimator on quantum probes and show that an advantage exists even for single-photon probes and inefficient photodetection. A closed-form expression for the energy-constrained Bures distance between two product amplifier channels is also derived.

Majorana zero modes (MZMs) promise a platform for topologically protected fermionic quantum computation. However, creating multiple MZMs and generating (directly or via measurements) the requisite transformations (e.g., braids) pose significant challenges. We introduce fermion-parity-based computation (FPBC): a measurement-based scheme, modeled on Pauli-based computation, that uses efficient classical processing to virtually increase the number of available MZMs and which, given magic state inputs, operates without transformations. FPBC requires all MZM parities to be measurable, but this conflicts with constraints in proposed MZM hardware. We thus introduce a design in which all parities are directly measurable and which is hence well suited for FPBC. While developing FPBC, we identify the “logical braid group” as the fermionic analog of the Clifford group.

We investigate the quantum metrological power of typical continuous-variable (CV) quantum networks. Particularly, we show that most CV quantum networks provide an entanglement to quantum states in distant nodes that enables one to achieve the Heisenberg scaling in the number of modes for distributed quantum displacement sensing, which cannot be attained using an unentangled probe state. Notably, our scheme only requires local operations and measurements after generating an entangled probe using the quantum network. In addition, we find a tolerable photon-loss rate that maintains the quantum enhancement. Finally, we numerically demonstrate that even when CV quantum networks are composed of local beam splitters, the quantum enhancement can be attained when the depth is sufficiently large.

The eigenstate thermalization hypothesis explains the emergence of the thermodynamic equilibrium in isolated quantum many-body systems by assuming a particular structure of the observable’s matrix elements in the energy eigenbasis. Schematically, it postulates that off-diagonal matrix elements are random numbers and the observables can be described by random matrix theory (RMT). To what extent a RMT description applies, more precisely at which energy scale matrix elements of physical operators become truly uncorrelated, is, however, not fully understood. We study this issue by introducing a novel numerical approach to probe correlations between matrix elements for Hilbert-space dimensions beyond those accessible by exact diagonalization. Our analysis is based on the evaluation of higher moments of operator submatrices, defined within energy windows of varying width. Considering nonintegrable quantum spin chains, we observe that matrix elements remain correlated even for narrow energy windows corresponding to timescales of the order of thermalization time of the respective observables. We also demonstrate that such residual correlations between matrix elements are reflected in the dynamics of out-of-time-ordered correlation functions.

We propose a quantum-enhanced heat engine with entanglement. The key feature of our scheme is superabsorption, which facilitates enhanced energy absorption by entangled qubits. Whereas a conventional engine with $N$ separable qubits provides power with a scaling of $P=\mathrm{\Theta }(N)$, our engine uses superabsorption to provide power with a quantum scaling of $P=\mathrm{\Theta }(N^2)$. This quantum heat engine also exhibits a scaling advantage over classical ones composed of $N$-particle Langevin systems. Our work elucidates the quantum properties allowing for the enhancement of performance.

Photonic polarization qubits are widely used in quantum computation and quantum communication due to the robustness in transmission and the easy qubit manipulation. An integrated quantum memory for polarization qubits is a useful building block for large-scale integrated quantum networks. However, on-demand storing polarization qubits in an integrated quantum memory is a long-standing challenge due to the anisotropic absorption of solids and the polarization-dependent features of microstructures. Here we demonstrate a reliable on-demand quantum memory for polarization qubits, using a depressed-cladding waveguide fabricated in a ${{}^{151}\mathrm{Eu}}^{3+}:{\mathrm{Y}}_2{\mathrm{SiO}}_5$ crystal. The site-2 ${{}^{151}\mathrm{Eu}}^{3+}$ ions in ${\mathrm{Y}}_2{\mathrm{SiO}}_5$ crystal provides a near-uniform absorption for arbitrary polarization states and a new pump sequence is developed to prepare a wideband and enhanced absorption profile. A fidelity of $99.4\pm 0.6\%$ is obtained for the qubit storage process with an input of 0.32 photons per pulse, together with a storage bandwidth of 10 MHz. This reliable integrated quantum memory for polarization qubits reveals the potential for use in the construction of integrated quantum networks.

The reaction coordinate describing a transition between reactant and product is a fundamental concept in the theory of chemical reactions. Within transition-path theory, a quantitative definition of the reaction coordinate is found in the committor, which is the probability that a trajectory initiated from a given microstate first reaches the product before the reactant. Here we develop an information-theoretic origin for the committor and show how selecting transition paths from a long ergodic equilibrium trajectory induces entropy production which exactly equals the information that system dynamics provide about the reactivity of trajectories. This equality of entropy production and dynamical information generation also holds at the level of arbitrary individual coordinates, providing parallel measures of the coordinate’s relevance to the reaction, each of which is maximized by the committor.

We consider the $N$ particle classical Riesz gas confined in a one-dimensional external harmonic potential with power-law interaction of the form $1/r^k$, where $r$ is the separation between particles. As special limits it contains several systems such as Dyson’s log-gas ($k\to 0^{+}$), the Calogero-Moser model ($k=2$), the 1D one-component plasma ($k=-1$), and the hard-rod gas ($k\to \infty$). Despite its growing importance, only large-$N$ field theory and average density profile are known for general $k$. In this Letter, we study the fluctuations in the system by looking at the statistics of the gap between successive particles. This quantity is analogous to the well-known level-spacing statistics which is ubiquitous in several branches of physics. We show that the variance goes as $N^{-b_k}$ and we find the $k$ dependence of $b_k$ via direct Monte Carlo simulations. We provide supporting arguments based on microscopic Hessian calculation and a quadratic field theory approach. We compute the gap distribution and study its system size scaling. Except in the range $-1<k<0$, we find scaling for all $k>-2$ with both Gaussian and non-Gaussian scaling forms.

One of the most basic notions in physics is the partitioning of a system into subsystems and the study of correlations among its parts. In this Letter, we explore this notion in the context of quantum reference frame (QRF) covariance, in which this partitioning is subject to a symmetry constraint. We demonstrate that different reference frame perspectives induce different sets of subsystem observable algebras, which leads to a gauge-invariant, frame-dependent notion of subsystems and entanglement. We further demonstrate that subalgebras which commute before imposing the symmetry constraint can translate into noncommuting algebras in a given QRF perspective after symmetry imposition. Such a QRF perspective does not inherit the distinction between subsystems in terms of the corresponding tensor factorizability of the kinematical Hilbert space and observable algebra. Since the condition for this to occur is contingent on the choice of QRF, the notion of subsystem locality is frame dependent.

We study quantum annealing in the quantum Ising model coupled to a thermal environment. When the speed of quantum annealing is sufficiently slow, the system evolves following the instantaneous thermal equilibrium. This quasistatic and isothermal evolution, however, fails near the end of annealing because the relaxation time grows infinitely, therefore yielding excess energy from the thermal equilibrium. We develop a phenomenological theory based on this picture and derive a scaling relation of the excess energy after annealing. The theoretical results are numerically confirmed using a novel non-Markovian method that we recently proposed based on a path-integral representation of the reduced density matrix and the infinite time evolving block decimation. In addition, we discuss crossovers from weak to strong coupling as well as from the adiabatic to quasistatic regime, and propose experiments on the D-Wave quantum annealer.

Gottesman-Kitaev-Preskill (GKP) states are a central resource for fault-tolerant optical continuous-variable quantum computing. However, their realization in the optical domain remains to be demonstrated. Here we propose a method for preparing GKP states using a cavity QED system that can be realized in several platforms, such as trapped atoms, quantum dots, or diamond color centers. We then further combine the protocol with the previously proposed breeding protocol by Vasconcelos et al. to relax the demands on the quality of the QED system, finding that GKP states with more than 10 dB squeezing could be achieved in near-future experiments.

Long-distance quantum state transfer (QST), which can be achieved with the help of quantum teleportation, is a core element of important quantum protocols. A typical situation for QST based on teleportation is one in which two remote communication partners (Alice and Bob) are far from the entanglement source (Charlie). Because of the atmospheric turbulence, it is challenging to implement the Bell-state measurement after photons propagate in atmospheric channels. In previous long-distance free-space experiments, Alice and Charlie always perform local Bell-state measurement before the entanglement distribution process is completed. Here, by developing a highly stable interferometer to project the photon into a hybrid path-polarization dimension and utilizing the satellite-borne entangled photon source, we demonstrate proof-of-principle QST at the distance of over 1200 km assisted by prior quantum entanglement shared between two distant ground stations with the satellite Micius. The average fidelity of transferred six distinct quantum states is $0.82\pm 0.01$, exceeding the classical limit of $2/3$ on a single copy of a qubit.

We develop a variational principle to determine the quantum controls and initial state that optimizes the quantum Fisher information, the quantity characterizing the precision in quantum metrology. When the set of available controls is limited, the exact optimal initial state and the optimal controls are, in general, dependent on the probe time, a feature missing in the unrestricted case. Yet, for time-independent Hamiltonians with restricted controls, the problem can be approximately reduced to the unconstrained case via Floquet engineering. In particular, we find for magnetometry with a time-independent spin chain containing three-body interactions, even when the controls are restricted to one- and two-body interaction, that the Heisenberg scaling can still be approximately achieved. Our results open the door to investigate quantum metrology under a limited set of available controls, of relevance to many-body quantum metrology in realistic scenarios.

We analytically compute the full counting statistics of charge transfer in a classical automaton of interacting charged particles. Deriving a closed-form expression for the moment generating function with respect to a stationary equilibrium state, we employ asymptotic analysis to infer the structure of charge current fluctuations for a continuous range of timescales. The solution exhibits several unorthodox features. Most prominently, on the timescale of typical fluctuations the probability distribution of the integrated charge current in a stationary ensemble without bias is distinctly non-Gaussian despite diffusive behavior of dynamical charge susceptibility. While inducing a charge imbalance is enough to recover Gaussian fluctuations, we find that higher cumulants grow indefinitely in time with different exponents, implying singular scaled cumulants. We associate this phenomenon with the lack of a regularity condition on moment generating functions and the onset of a dynamical critical point. In effect, the scaled cumulant generating function does not, irrespectively of charge bias, represent a faithful generating function of the scaled cumulants, yet the associated Legendre dual yields the correct large-deviation rate function. Our findings hint at novel types of dynamical universality classes in deterministic many-body systems.

We propose and demonstrate a protocol for high-fidelity indirect readout of trapped ion hyperfine qubits, where the state of a ${}^9{\mathrm{Be}}^{+}$ qubit ion is mapped to a ${}^{25}{\mathrm{Mg}}^{+}$ readout ion using laser-driven Raman transitions. By partitioning the ${}^9{\mathrm{Be}}^{+}$ ground-state hyperfine manifold into two subspaces representing the two qubit states and choosing appropriate laser parameters, the protocol can be made robust to spontaneous photon scattering errors on the Raman transitions, enabling repetition for increased readout fidelity. We demonstrate combined readout and back-action errors for the two subspaces of ${1.2}_{-0.6}^{+1.1}\times {10}^{-4}$ and $0_{-0}^{+1.9}\times {10}^{-5}$ with 68% confidence while avoiding decoherence of spectator qubits due to stray resonant light that is inherent to direct fluorescence detection.