We generalize a standard benchmark of reinforcement learning, the classical cartpole balancing problem, to the quantum regime by stabilizing a particle in an unstable potential through measurement and feedback. We use state-of-the-art deep reinforcement learning to stabilize a quantum cartpole and find that our deep learning approach performs comparably to or better than other strategies in standard control theory. Our approach also applies to measurement-feedback cooling of quantum oscillators, showing the applicability of deep learning to general continuous-space quantum control.

The efficient numerical simulation of nonequilibrium real-time evolution in isolated quantum matter constitutes a key challenge for current computational methods. This holds in particular in the regime of two spatial dimensions, whose experimental exploration is currently pursued with strong efforts in quantum simulators. In this work we present a versatile and efficient machine learning inspired approach based on a recently introduced artificial neural network encoding of quantum many-body wave functions. We identify and resolve key challenges for the simulation of time evolution, which previously imposed significant limitations on the accurate description of large systems and long-time dynamics. As a concrete example, we study the dynamics of the paradigmatic two-dimensional transverse-field Ising model, as recently also realized experimentally in systems of Rydberg atoms. Calculating the nonequilibrium real-time evolution across a broad range of parameters, we, for instance, observe collapse and revival oscillations of ferromagnetic order and demonstrate that the reached timescales are comparable to or exceed the capabilities of state-of-the-art tensor network methods.

Superresolution techniques based on intensity measurements after a spatial mode decomposition can overcome the precision of diffraction-limited direct imaging. However, realistic measurement devices always introduce finite crosstalk in any such mode decomposition. Here, we show that any nonzero crosstalk leads to a breakdown of superresolution when the number $N$ of detected photons is large. Combining statistical and analytical tools, we obtain the scaling of the precision limits for weak, generic crosstalk from a device-independent model as a function of the crosstalk probability and $N$. The scaling of the smallest distance that can be distinguished from noise changes from $N^{-1/2}$ for an ideal measurement to $N^{-1/4}$ in the presence of crosstalk.

The Rényi entanglement entropy (REE) is an entanglement quantifier considered as a natural generalization of the entanglement entropy. When it comes to stochastic local operations and classical communication (SLOCC), however, only a limited class of the REEs satisfy the monotonicity condition, while their statistical properties beyond mean values have not been fully investigated. Here, we establish a general condition that the probability distribution of the REE of any order obeys under SLOCC. The condition is obtained by introducing a family of entanglement monotones that contain the higher-order moments of the REEs. The contribution from the higher-order moments imposes a strict limitation on entanglement distillation via SLOCC. We find that the upper bound on success probabilities for entanglement distillation exponentially decreases as the amount of raised entanglement increases, which cannot be captured from the monotonicity of the REE. Based on the strong restriction on entanglement transformation under SLOCC, we design a new method to estimate entanglement in quantum many-body systems from experimentally observable quantities.

A spin strongly driven by two harmonic incommensurate drives can pump energy from one drive to the other at a quantized average rate, in close analogy with the quantum Hall effect. The pumping rate is a nonzero integer in the topological regime, while the trivial regime does not pump. The dynamical transition between the regimes is sharp in the zero-frequency limit and is characterized by a Dirac point in a synthetic band structure. We show that the pumping rate is half-integer quantized at the transition and present universal Kibble-Zurek scaling functions for energy transfer processes. Our results adapt ideas from quantum phase transitions, quantum information, and topological band theory to nonequilibrium dynamics, and identify qubit experiments to observe the universal linear and nonlinear response of a Dirac point in synthetic dimensions.

High-dimensional entanglement promises to greatly enhance the performance of quantum communication and enable quantum advantages unreachable by qubit entanglement. One of the great challenges, however, is the reliable production, distribution, and local certification of high-dimensional sources of entanglement. In this Letter, we present an optical setup capable of producing quantum states with an exceptionally high level of scalability, control, and quality that, together with novel certification techniques, achieve the highest amount of entanglement recorded so far. We showcase entanglement in 32-spatial dimensions with record fidelity to the maximally entangled state ($F=0.933\pm 0.001$) and introduce measurement efficient schemes to certify entanglement of formation ($E_{oF}=3.728\pm 0.006$). Combined with the existing multicore fiber technology, our results will lay a solid foundation for the construction of high-dimensional quantum networks.

The detection of topological phases of matter has become a central issue in recent years. Conventionally, the realization of a specific topological phase in condensed matter physics relies on probing the underlying surface band dispersion or quantum transport signature of a real material, which may be imperfect or even absent. On the other hand, quantum simulation offers an alternative approach to directly measure the topological invariant on a universal quantum computer. However, experimentally demonstrating high-dimensional topological phases remains a challenge due to the technical limitations of current experimental platforms. Here, we investigate the three-dimensional topological insulators in the AIII (chiral unitary) symmetry class, which yet lack experimental realization. Using the nuclear magnetic resonance system, we experimentally demonstrate their topological properties, where a dynamical quenching approach is adopted and the dynamical bulk-boundary correspondence in the momentum space is observed. As a result, the topological invariants are measured with high precision on the band-inversion surface, exhibiting robustness to the decoherence effect. Our Letter paves the way toward the quantum simulation of topological phases of matter in higher dimensions and more complex systems through controllable quantum phases transitions.

We present a rigorous explicit expression for an extensive number of local conserved quantities in the $XYZ$ spin-$1/2$ chain with general coupling constants. All the coefficients of operators in each local conserved quantity are calculated. We also confirm that our result can be applied to the case of the $XXZ$ chain with a magnetic field in the $z$-axis direction.

We employ spherical $t$-designs for the systematic construction of solids whose rotational degrees of freedom can be made robust to decoherence due to external fluctuating fields while simultaneously retaining their sensitivity to signals of interest. Specifically, the ratio of signal phase accumulation rate from a nearby source to the decoherence rate caused by fluctuating fields from more distant sources can be incremented to any desired level by using increasingly complex shapes. This allows for the generation of long-lived macroscopic quantum superpositions of rotational degrees of freedom and the robust generation of entanglement between two or more such solids with applications in robust quantum sensing and precision metrology as well as quantum registers.

Alice and Bob each have half of a pair of entangled qubits. Bob measures his half and then passes his qubit to a second Bob who measures again and so on. The goal is to maximize the number of Bobs that can have an expected violation of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality with the single Alice. This scenario was introduced in [R. Silva , Phys. Rev. Lett. 114, 250401 (2015)] where the authors mentioned evidence that when the Bobs act independently and with unbiased inputs then at most two of them can expect to violate the CHSH inequality with Alice. Here we show that, contrary to this evidence, arbitrarily many independent Bobs can have an expected CHSH violation with the single Alice. Our proof is constructive and our measurement strategies can be generalized to work with a larger class of two-qubit states that includes all pure entangled two-qubit states. Since violation of a Bell inequality is necessary for device-independent tasks, our work represents a step towards an eventual understanding of the limitations on how much device-independent randomness can be robustly generated from a single pair of qubits.

Even in the presence of conservation laws, one can perform arbitrary transformations on a system if given access to a suitable reference frame, since conserved quantities may be exchanged between the system and the frame. Here we explore whether these quantities can be separated into different parts of the reference frame, with each part acting as a “battery” for a distinct quantity. For systems composed of spin-$\frac{1}{2}$ particles, we show that the components of angular momentum $S_x$, $S_y$, and $S_z$ (noncommuting conserved quantities) may be separated in this way, and also provide several extensions of this result. These results also play a key role in the quantum thermodynamics of noncommuting conserved quantities.

Quantum hypothesis testing is a central task in the entire field of quantum information theory. Understanding its ultimate limits will give insight into a wide range of quantum protocols and applications, from sensing to communication. Although the limits of hypothesis testing between quantum states have been completely clarified by the pioneering works of Helstrom in the 1970s, the more difficult problem of hypothesis testing with quantum channels, i.e., channel discrimination, is less understood. This is mainly due to the complications coming from the use of input entanglement and the possibility of employing adaptive strategies. In this Letter, we establish a lower limit for the ultimate error probability affecting the discrimination of an arbitrary number of quantum channels. We also show that this lower bound is achievable when the channels have certain symmetries. As an example, we apply our results to the problem of channel position finding, where the goal is to identify the location of a target channel among multiple background channels. In this general setting, we find that the use of entanglement offers a great advantage over strategies without entanglement, with nontrivial implications for data readout, target detection, and quantum spectroscopy.

We construct a dynamical decoupling protocol for accurately generating local and global symmetries in general many-body systems. Multiple commuting and noncommuting symmetries can be created by means of a self-similar-in-time (“polyfractal”) drive. The result is an effective Floquet Hamiltonian that remains local and avoids heating over exponentially long times. This approach can be used to realize a wide variety of quantum models, and nonequilibrium quantum phases.

Unsharp measurements are increasingly important for foundational insights in quantum theory and quantum information applications. Here, we report an experimental implementation of unsharp qubit measurements in a sequential communication protocol, based on a quantum random access code. The protocol involves three parties; the first party prepares a qubit system, the second party performs operations that return both a classical and quantum outcome, and the latter is measured by the third party. We demonstrate a nearly optimal sequential quantum random access code that outperforms both the best possible classical protocol and any quantum protocol that utilizes only projective measurements. Furthermore, while only assuming that the involved devices operate on qubits and that detected events constitute a fair sample, we demonstrate the noise-robust characterization of unsharp measurements based on the sequential quantum random access code. We apply this characterization towards quantifying the degree of incompatibility of two sequential pairs of quantum measurements.

Strong interaction between light and matter waves, such as electron beams in electron microscopes, has recently emerged as a new tool for manipulating the electron wave packets. Here, we systematically investigate electron-light interactions from first principles. We show that enhanced coupling can be achieved for systems involving slow electron wave packets interacting with plasmonic nanoparticles, due to simultaneous classical recoil and quantum mechanical photon absorption and emission processes. For slow electrons with longitudinal broadenings longer than the dimensions of nanoparticles, phase matching between slow electrons and plasmonic oscillations is manifested as an additional degree of freedom to control the strength of coupling. Our findings pave the way toward a systematic and realistic understanding of electron-light interactions beyond adiabatic approximations, and lay the ground for the realization of matter-wave interferometry and boson-sampling devices involving light and matter waves.

An outstanding challenge for quantum information processing using bosonic systems is Gaussian errors such as excitation loss and added thermal noise errors. Thus, bosonic quantum error correction is essential. Most bosonic quantum error correction schemes encode a finite-dimensional logical qubit or qudit into noisy bosonic oscillator modes. In this case, however, the infinite-dimensional bosonic nature of the physical system is lost at the error-corrected logical level. On the other hand, there are several proposals for encoding an oscillator mode into many noisy oscillator modes. However, these oscillator-into-oscillators encoding schemes are in the class of Gaussian quantum error correction. Therefore, these codes cannot correct practically relevant Gaussian errors due to the established no-go theorems that state that Gaussian errors cannot be corrected by using only Gaussian resources. Here, we circumvent these no-go results and show that it is possible to correct Gaussian errors by using Gottesman-Kitaev-Preskill (GKP) states as non-Gaussian resources. In particular, we propose a non-Gaussian oscillator-into-oscillators code, namely the GKP two-mode squeezing code, and demonstrate that it can quadratically suppress additive Gaussian noise errors in both the position and momentum quadratures except for a small sublogarithmic correction. Furthermore, we demonstrate that our GKP two-mode squeezing code is near optimal in the weak noise limit by proving via quantum information theoretic tools that quadratic noise suppression is optimal when we use two physical oscillator modes. Lastly, we show that our non-Gaussian oscillator encoding scheme can also be used to correct excitation loss and thermal noise errors, which are dominant error sources in many realistic bosonic systems.

Weak-value amplification (WVA) is a metrological protocol that amplifies ultrasmall physical effects. However, the amplified outcomes necessarily occur with highly suppressed probabilities, leading to the extensive debate on whether the overall measurement precision is improved in comparison to that of conventional measurement (CM). Here, we experimentally demonstrate the unambiguous advantages of WVA that overcome practical limitations including noise and saturation of photodetection and maintain a shot-noise-scaling precision for a large range of input light intensity well beyond the dynamic range of the photodetector. The precision achieved by WVA is 6 times higher than that of CM in our setup. Our results clear the way for the widespread use of WVA in applications involving the measurement of small signals including precision metrology and commercial sensors.