Quantum entanglement between distant qubits is an important feature of quantum networks. Distribution of entanglement over long distances can be enabled through coherently interfacing qubit pairs via photonic channels. Here, we report the realization of optically generated quantum entanglement between electron spin qubits confined in two distant semiconductor quantum dots. The protocol relies on spin-photon entanglement in the trionic $\mathrm{\Lambda }$ system and quantum erasure of the Raman-photon path information. The measurement of a single Raman photon is used to project the spin qubits into a joint quantum state with an interferometrically stabilized and tunable relative phase. We report an average Bell-state fidelity for $|{\psi }^{(+)}⟩$ and $|{\psi }^{(-)}⟩$ states of $61.6\pm 2.3\%$ and a record-high entanglement generation rate of 7.3 kHz between distant qubits.

The generalization of the multiscale entanglement renormalization ansatz (MERA) to continuous systems, or cMERA [Haegeman et al., Phys. Rev. Lett. 110, 100402 (2013)], is expected to become a powerful variational ansatz for the ground state of strongly interacting quantum field theories. In this Letter, we investigate, in the simpler context of Gaussian cMERA for free theories, the extent to which the cMERA state $|{\mathrm{\Psi }}^{\mathrm{\Lambda }}⟩$ with finite UV cutoff $\mathrm{\Lambda }$ can capture the spacetime symmetries of the ground state $|\mathrm{\Psi }⟩$. For a free boson conformal field theory (CFT) in $1+1$ dimensions, as a concrete example, we build a quasilocal unitary transformation $V$ that maps $|\mathrm{\Psi }⟩$ into $|{\mathrm{\Psi }}^{\mathrm{\Lambda }}⟩$ and show two main results. (i) Any spacetime symmetry of the ground state $|\mathrm{\Psi }⟩$ is also mapped by $V$ into a spacetime symmetry of the cMERA $|{\mathrm{\Psi }}^{\mathrm{\Lambda }}⟩$. However, while in the CFT, the stress-energy tensor $T_{\mu \nu }(x)$ (in terms of which all the spacetime symmetry generators are expressed) is local, and the corresponding cMERA stress-energy tensor $T_{\mu \nu }^{\mathrm{\Lambda }}(x)=V{T}_{\mu \nu }(x)V^{†}$ is quasilocal. (ii) From the cMERA, we can extract quasilocal scaling operators $O_{\alpha }^{\mathrm{\Lambda }}(x)$ characterized by the exact same scaling dimensions ${\mathrm{\Delta }}_{\alpha }$, conformal spins $s_{\alpha }$, operator product expansion coefficients $C_{\alpha \beta \gamma }$, and central charge $c$ as the original CFT. Finally, we argue that these results should also apply to interacting theories.

A new semiclassical “divide-and-conquer” method is presented with the aim of demonstrating that quantum dynamics simulations of high dimensional molecular systems are doable. The method is first tested by calculating the quantum vibrational power spectra of water, methane, and benzene—three molecules of increasing dimensionality for which benchmark quantum results are available—and then applied to ${\mathrm{C}}_{60}$, a system characterized by 174 vibrational degrees of freedom. Results show that the approach can accurately account for quantum anharmonicities, purely quantum features like overtones, and the removal of degeneracy when the molecular symmetry is broken.

We introduce general bounds for the parameter estimation error in nonlinear quantum metrology of many-body open systems in the Markovian limit. Given a $k$-body Hamiltonian and $p$-body Lindblad operators, the estimation error of a Hamiltonian parameter using a Greenberger-Horne-Zeilinger state as a probe is shown to scale as $N^{-[k-(p/2)]}$, surpassing the shot-noise limit for $2k>p+1$. Metrology equivalence between initial product states and maximally entangled states is established for $p\ge 1$. We further show that one can estimate the system-environment coupling parameter with precision $N^{-(p/2)}$, while many-body decoherence enhances the precision to $N^{-k}$ in the noise-amplitude estimation of a fluctuating $k$-body Hamiltonian. For the long-range Ising model, we show that the precision of this parameter beats the shot-noise limit when the range of interactions is below a threshold value.

We analyze the quantum dynamics of periodically driven, disordered systems in the presence of long-range interactions. Focusing on the stability of discrete time crystalline (DTC) order in such systems, we use a perturbative procedure to evaluate its lifetime. For 3D systems with dipolar interactions, we show that the corresponding decay is parametrically slow, implying that robust, long-lived DTC order can be obtained. We further predict a sharp crossover from the stable DTC regime into a regime where DTC order is lost, reminiscent of a phase transition. These results are in good agreement with the recent experiments utilizing a dense, dipolar spin ensemble in diamond [Nature (London) 543, 221 (2017)]. They demonstrate the existence of a novel, critical DTC regime that is stabilized not by many-body localization but rather by slow, critical dynamics. Our analysis shows that the DTC response can be used as a sensitive probe of nonequilibrium quantum matter.

We propose to use a dissipatively stabilized nitrogen vacancy (NV) center as a mediator of interaction between two nuclear spins that are protected from decoherence and relaxation of the NV due to the periodical resets of the NV center. Under ambient conditions this scheme achieves highly selective high-fidelity quantum gates between nuclear spins in a quantum register even at large NV-nuclear distances. Importantly, this method allows for the use of nuclear spins as a sensor rather than a memory, while the NV spin acts as an ancillary system for the initialization and readout of the sensor. The immunity to the decoherence and relaxation of the NV center leads to a tunable sharp frequency filter while allowing at the same time the continuous collection of the signal to achieve simultaneously high spectral selectivity and high signal-to-noise ratio.

Directly in the thermodynamic limit, we show how to combine local imaginary and real-time evolution of tensor networks to efficiently and accurately find the nonequilibrium steady states (NESSs) of one-dimensional dissipative quantum lattices governed by a local Lindblad master equation. The imaginary time evolution first bypasses any highly correlated portions of the real-time evolution trajectory by directly converging to the weakly correlated subspace of the NESS, after which, real-time evolution completes the convergence to the NESS with high accuracy. We demonstrate the power of the method with the dissipative transverse field quantum Ising chain. We show that a crossover of an order parameter shown to be smooth in previous finite-size studies remains smooth in the thermodynamic limit.

Collective spins of large atomic samples trapped inside optical resonators can carry quantum information that can be processed in a way similar to quantum computation with continuous variables. It is shown here that by combining the resonators in multipath interferometers one can realize coupling between different samples, and that polynomial Hamiltonians can be constructed by repeated spin rotations and twisting induced by dispersive interaction of the atoms with light. Application can be expected in the efficient simulation of quantum systems.

We consider ground states of quantum spin chains with symmetry-protected topological (SPT) order as resources for measurement-based quantum computation (MBQC). We show that, for a wide range of SPT phases, the computational power of ground states is uniform throughout each phase. This computational power, defined as the Lie group of executable gates in MBQC, is determined by the same algebraic information that labels the SPT phase itself. We prove that these Lie groups always contain a full set of single-qubit gates, thereby affirming the long-standing conjecture that general SPT phases can serve as computationally useful phases of matter.

Nonequilibrium time evolution in isolated many-body quantum systems generally results in thermalization. However, the relaxation process can be very slow, and quasistationary nonthermal plateaux are often observed at intermediate times. The paradigmatic example is a quantum quench in an integrable model with weak integrability breaking; for a long time, the state cannot escape the constraints imposed by the approximate integrability. We unveil a new mechanism of prethermalization, based on the presence of a symmetry of the prequench Hamiltonian, which is spontaneously broken at zero temperature and is explicitly broken by the postquench Hamiltonian. The typical time scale of the phenomenon is proportional to the thermal correlation length of the initial state, which diverges as the temperature is lowered. We show that the prethermal quasistationary state can be approximated by a mixed state that violates cluster decomposition property. We consider two examples: the transverse-field Ising chain, where the full-time evolution is computed analytically, and the (nonintegrable) anisotropic next-nearest-neighbor Ising model, which is investigated numerically.

We characterize the collective modes of a soliton train in a quasi-one-dimensional Fermi superfluid, using a mean-field formalism. In addition to the expected Goldstone and Higgs modes, we find novel long-lived gapped modes associated with oscillations of the soliton cores. The soliton train has an instability that depends strongly on the interaction strength and the spacing of solitons. It can be stabilized by filling each soliton with an unpaired fermion, thus forming a commensurate Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We find that such a state is always dynamically stable, which paves the way for realizing long-lived FFLO states in experiments via phase imprinting.

We use a new approach to study the large fluctuations of a heavy-tailed system, where the standard large-deviations principle does not apply. Large-deviations theory deals with tails of probability distributions and the rare events of random processes, for example, spreading packets of particles. Mathematically, it concerns the exponential falloff of the density of thin-tailed systems. Here we investigate the spatial density $P_t(x)$ of laser-cooled atoms, where at intermediate length scales the shape is fat tailed. We focus on the rare events beyond this range, which dominate important statistical properties of the system. Through a novel friction mechanism induced by the laser fields, the density is explored with the recently proposed non-normalized infinite-covariant density approach. The small and large fluctuations give rise to a bifractal nature of the spreading packet. We derive general relations which extend our theory to a class of systems with multifractal moments.

A quantum critical system described at low energy by a conformal field theory (CFT) and subjected to a time-periodic boundary drive displays multiple dynamical regimes, depending on the drive frequency. We compute the behavior of quantities including the entanglement entropy and Loschmidt echo, confirming analytic predictions from field theory by exact numerics on the transverse field Ising model and demonstrate universality by adding nonintegrable perturbations. The dynamics naturally separate into three regimes: a slow-driving limit, which has an interpretation as multiple quantum quenches with amplitude corrections from CFT; a fast-driving limit, in which the system behaves as though subject to a single quantum quench; and a crossover regime displaying heating. The universal Floquet dynamics in all regimes can be understood using a combination of boundary CFT and Kibble-Zurek scaling arguments.

The essence of both classical and quantum engines is to extract useful energy (work) from stochastic energy sources, e.g., thermal baths. In Maxwell’s demon engines, work extraction is assisted by a feedback control based on measurements performed by a demon, whose memory is erased at some nonzero energy cost. Here we propose a new type of quantum Maxwell’s demon engine where work is directly extracted from the measurement channel, such that no heat bath is required. We show that in the Zeno regime of frequent measurements, memory erasure costs eventually vanish. Our findings provide a new paradigm to analyze quantum heat engines and work extraction in the quantum world.

In many quantum information applications, a minimum detection efficiency must be exceeded to ensure success. Protocols depending on the violation of a Bell inequality, for instance, may be subject to the so-called detection loophole: Imperfect detectors may yield spurious violations, which consequently cannot be used to ensure, say, quantum cryptographic security. Hence, we investigate the possibility of giving lower bounds on detector efficiency even if an adversary has full control over both the source and the detectors. To this end, we present a technique to systematically derive Bell inequalities free from the detection loophole using only the observed measurements statistics. The violation of these inequalities certifies that the detectors used exceed a certain minimal efficiency.

We investigate graphs that can be disconnected into small components by removing a vanishingly small fraction of their vertices. We show that, when a controllable quantum network is described by such a graph and the gaps in eigenfrequencies and in transition frequencies are bounded exponentially in the number of vertices, the network is efficiently controllable, in the sense that universal quantum computation can be performed using a control sequence polynomial in the size of the network while controlling a vanishingly small fraction of subsystems. We show that networks corresponding to finite-dimensional lattices are efficiently controllable and explore generalizations to percolation clusters and random graphs. We show that the classical computational complexity of estimating the ground state of Hamiltonians described by controllable graphs is polynomial in the number of subsystems or qubits.

We consider the problem of characterizing the set of input-output correlations that can be generated by an arbitrarily given quantum measurement. Our main result is to provide a closed-form, full characterization of such a set for any qubit measurement, and to discuss its geometrical interpretation. As applications, we further specify our results to the cases of real and complex symmetric, informationally complete measurements and mutually unbiased bases of a qubit, in the presence of isotropic noise. Our results provide the optimal device-independent tests of quantum measurements.

We introduce an exact replica method for the study of critical systems with quenched bond randomness in two dimensions. For the $q$-state Potts model, we show that a line of renormalization group fixed points interpolates from weak to strong randomness as $q-2$ grows from small to large values. This theory exhibits a $q$-independent sector, and allows at the same time for a correlation length exponent which keeps the Ising value and continuously varying magnetization exponent and effective central charge. These findings appear to solve long-standing numerical and theoretical puzzles, and to illustrate the peculiarities which may characterize the conformal field theories of random fixed points.