For the driven-dissipative system of two coupled bosonic modes in a nonlinear cavity resonator, we demonstrate a sequence of phase transitions from a trivial steady state to two distinct dissipative time crystalline phases. These effects are already anticipated at the level of the semiclassical analysis of the Lindblad equation using the theory of bifurcations and are further supported by the full quantum treatment. The system is predicted to exhibit different dynamical phases characterized by an oscillating nonequilibrium steady state with nontrivial periodicity, which is a hallmark of time crystals. We expect that these phases can be directly probed in various cavity QED experiments.

Uncertainty relations express limits on the extent to which the outcomes of distinct measurements on a single state can be made jointly predictable. The existence of nontrivial uncertainty relations in quantum theory is generally considered to be a way in which it entails a departure from the classical worldview. However, this perspective is undermined by the fact that there exist operational theories which exhibit nontrivial uncertainty relations but which are consistent with the classical worldview insofar as they admit of a generalized-noncontextual ontological model. This prompts the question of what aspects of uncertainty relations, if any, cannot be realized in this way and so constitute evidence of genuine nonclassicality. We here consider uncertainty relations describing the tradeoff between the predictability of a pair of binary-outcome measurements (e.g., measurements of Pauli $X$ and Pauli $Z$ observables in quantum theory). We show that, for a class of theories satisfying a particular symmetry property, the functional form of this predictability tradeoff is constrained by noncontextuality to be below a linear curve. Because qubit quantum theory has the relevant symmetry property, the fact that its predictability tradeoff describes a section of a circle is a violation of this noncontextual bound, and therefore constitutes an example of how the functional form of an uncertainty relation can witness contextuality. We also deduce the implications for a selected group of operational foils to quantum theory and consider the generalization to three measurements.

We introduce a quantum control technique using polychromatic pulse trains, consisting of pulses with different carrier frequencies, i.e., different detunings with respect to the qubit transition frequency. We derive numerous polychromatic pulse trains, which generate broadband, narrowband, and passband excitation profiles for different target transition probabilities. This makes it possible to create high-fidelity excitation profiles which are either (i) robust to deviations in the experimental parameters, which is attractive for quantum computing, or (ii) more sensitive to such variations, which is attractive for crosstalk elimination and quantum sensing. The method is demonstrated experimentally using one of IBM’s superconducting quantum processors, in a very good agreement between theory and experiment. These results demonstrate both the excellent coherence properties of the IBM qubits and the accuracy, robustness, and flexibility of the proposed quantum control technique. They also show that the detuning is a control parameter which is as efficient as the pulse phase that is commonly used in composite pulses. Hence the method opens a variety of perspectives for quantum control in areas where phase manipulation is difficult or inaccurate.

Using Monte Carlo computer simulations, we investigate the kinetics of phase separation in the two-dimensional conserved Ising model with power-law decaying long-range interactions, the prototypical model for many long-range interacting systems. A long-standing analytical prediction for the characteristic length is shown to be applicable. In the simulation, we relied on our novel algorithm which provides a massive speedup for long-range interacting systems.

We provide the optimal measurement strategy for a class of noisy channels that reduce to the identity channel for a specific value of a parameter (spreading channels). We provide an example that is physically relevant: the estimation of the absolute value of the displacement in the presence of phase randomizing noise. Surprisingly, this noise does not affect the effectiveness of the optimal measurement. We show that, for small displacement, a squeezed vacuum probe field is optimal among strategies with same average energy. A squeezer followed by photodetection is the optimal detection strategy that attains the quantum Fisher information, whereas the customarily used homodyne detection becomes useless in the limit of small displacements, due to the same effect that gives Rayleigh’s curse in optical superresolution. There is a quantum advantage: a squeezed or a Fock state with $N$ average photons allow to asymptotically estimate the parameter with a $\sqrt{N}$ better precision than classical states with same energy.

Crosstalk between target and neighboring spectator qubits due to spillover of control signals represents a major error source limiting the fidelity of two-qubit entangling gates in quantum computers. We show that in our laser-driven trapped-ion system coherent crosstalk error can be modeled as residual $X{\widehat{\sigma }}_{\varphi }$ interaction and can be actively canceled by single-qubit echoing pulses. We propose and demonstrate a crosstalk suppression scheme that eliminates all first-order crosstalk utilizing only local control of target qubits, as opposed to an existing scheme which requires control over all neighboring qubits. We report a two-qubit Bell state fidelity of 99.52(6)% with the echoing pulses applied after collective gates and 99.37(5)% with the echoing pulses applied to each gate in a five-ion chain. This scheme is widely applicable to other platforms with analogous interaction Hamiltonians.

Quantum error correction holds the key to scaling up quantum computers. Cosmic ray events severely impact the operation of a quantum computer by causing chip-level catastrophic errors, essentially erasing the information encoded in a chip. Here, we present a distributed error correction scheme to combat the devastating effect of such events by introducing an additional layer of quantum erasure error correcting code across separate chips. We show that our scheme is fault tolerant against chip-level catastrophic errors and discuss its experimental implementation using superconducting qubits with microwave links. Our analysis shows that in state-of-the-art experiments, it is possible to suppress the rate of these errors from 1 per 10 s to less than 1 per month.

Many quantum algorithms involve the evaluation of expectation values. Optimal strategies for estimating a single expectation value are known, requiring a number of state preparations that scales with the target error $ϵ$ as $\mathcal{O}(1/ϵ)$. In this Letter, we address the task of estimating the expectation values of $M$ different observables, each to within additive error $ϵ$, with the same $1/ϵ$ dependence. We describe an approach that leverages Gilyén et al.’s quantum gradient estimation algorithm to achieve $\mathcal{O}(\sqrt{M}/ϵ)$ scaling up to logarithmic factors, regardless of the commutation properties of the $M$ observables. We prove that this scaling is worst-case optimal in the high-precision regime if the state preparation is treated as a black box, even when the operators are mutually commuting. We highlight the flexibility of our approach by presenting several generalizations, including a strategy for accelerating the estimation of a collection of dynamic correlation functions.

We report the experimental generation of all four frequency-bin Bell states in a single versatile setup via successive pumping of spontaneous parametric down-conversion with single and dual spectral lines. Our scheme utilizes intensity modulation to control the pump configuration and offers turn-key generation of any desired Bell state using only off-the-shelf telecommunication equipment. We employ Bayesian inference to reconstruct the density matrices of the generated Bell states, finding fidelities $\ge 97\%$ for all cases. Additionally, we demonstrate the sensitivity of the frequency-bin Bell states to common-mode and differential-mode temporal delays traversed by the photons comprising the state—presenting the potential for either enhanced resolution or nonlocal sensing enabled by our complete Bell basis synthesizer.

We address a new setting where the second law is under question: thermalizations in a quantum superposition of causal orders, enacted by the so-called quantum switch. This superposition has been shown to be associated with an increase in the communication capacity of the channels, yielding an apparent violation of the data-processing inequality and a possibility to separate hot from cold. We analyze the thermodynamics of this information capacity increasing process. We show how the information capacity increase is compatible with thermodynamics. We show that there may indeed be an information capacity increase for consecutive thermalizations obeying the first and second laws of thermodynamics if these are placed in an indefinite order and moreover that only a significantly bounded increase is possible. The increase comes at the cost of consuming a thermodynamic resource, the free energy of coherence associated with the switch.

Unsharp measurements are widely seen as the key resource for recycling the nonlocality of an entangled state shared between several sequential observers. Contrasting this, we here show that nonlocality can be recycled using only standard, projective, qubit measurements. Focusing on the Clauser-Horne-Shimony-Holt inequality and allowing parties to share classical randomness, we determine the optimal trade-off in the magnitude of Bell violations for a maximally entangled state. We then find that nonmaximally entangled states make possible larger sequential violations, which contrasts the standard Clauser-Horne-Shimony-Holt scenario. Furthermore, we show that nonlocality can be recycled using projective qubit measurements even when no shared classical randomness is available. We discuss the implications of our results for experimental implementations of sequential nonlocality.

We address the problem of closing the detection efficiency loophole in Bell experiments, which is crucial for real-world applications. Every Bell inequality has a critical detection efficiency $\eta$ that must be surpassed to avoid the detection loophole. Here, we propose a general method for reducing the critical detection efficiency of any Bell inequality to arbitrary low values. This is accomplished by entangling two particles in $N$ orthogonal subspaces (e.g., $N$ degrees of freedom) and conducting $N$ Bell tests in parallel. Furthermore, the proposed method is based on the introduction of penalized $N$-product (PNP) Bell inequalities, for which the so-called simultaneous measurement loophole is closed, and the maximum value for local hidden-variable theories is simply the $N$th power of the one of the Bell inequality initially considered. We show that, for the PNP Bell inequalities, the critical detection efficiency decays exponentially with $N$. The strength of our method is illustrated with a detailed study of the PNP Bell inequalities resulting from the Clauser-Horne-Shimony-Holt inequality.

Fracton models provide examples of novel gapped quantum phases of matter that host intrinsically immobile excitations and therefore lie beyond the conventional notion of topological order. Here, we calculate optimal error thresholds for quantum error correcting codes based on fracton models. By mapping the error-correction process for bit-flip and phase-flip noises into novel statistical models with Ising variables and random multibody couplings, we obtain models that exhibit an unconventional subsystem symmetry instead of a more usual global symmetry. We perform large-scale parallel tempering Monte Carlo simulations to obtain disorder-temperature phase diagrams, which are then used to predict optimal error thresholds for the corresponding fracton code. Remarkably, we found that the X-cube fracton code displays a minimum error threshold (7.5%) that is much higher than 3D topological codes such as the toric code (3.3%), or the color code (1.9%). This result, together with the predicted absence of glass order at the Nishimori line, shows great potential for fracton phases to be used as quantum memory platforms.

Quantum state preparation is an important subroutine for quantum computing. We show that any $n$-qubit quantum state can be prepared with a $\mathrm{\Theta }(n)$-depth circuit using only single- and two-qubit gates, although with a cost of an exponential amount of ancillary qubits. On the other hand, for sparse quantum states with $d⩾2$ nonzero entries, we can reduce the circuit depth to $\mathrm{\Theta }(\log (nd))$ with $O(nd\log d)$ ancillary qubits. The algorithm for sparse states is exponentially faster than best-known results and the number of ancillary qubits is nearly optimal and only increases polynomially with the system size. We discuss applications of the results in different quantum computing tasks, such as Hamiltonian simulation, solving linear systems of equations, and realizing quantum random access memories, and find cases with exponential reductions of the circuit depth for all these three tasks. In particular, using our algorithm, we find a family of linear system solving problems enjoying exponential speedups, even compared to the best-known quantum and classical dequantization algorithms.

The hierarchical equations of motion (HEOM), derived from the exact Feynman-Vernon path integral, is one of the most powerful numerical methods to simulate the dynamics of open quantum systems. Its applicability has so far been limited to specific forms of spectral reservoir distributions and relatively elevated temperatures. Here we solve this problem and introduce an effective treatment of quantum noise in frequency space by systematically clustering higher order Matsubara poles, equivalent to an optimized rational decomposition. This leads to an elegant extension of the HEOM to arbitrary temperatures and very general reservoirs in combination with efficiency, high accuracy, and long-time stability. Moreover, the technique can directly be implemented in other approaches such as Green’s function, stochastic, and pseudomode formulations. As one highly nontrivial application, for the subohmic spin-boson model at vanishing temperature the Shiba relation is quantitatively verified which predicts the long-time decay of correlation functions.

In molecular simulation and fluid mechanics, the coupling of a particle domain with a continuum representation of its embedding environment is an ongoing challenge. In this Letter, we show a novel approach where the latest version of the adaptive resolution scheme (AdResS), with noninteracting tracers as particles’ reservoir, is combined with a fluctuating hydrodynamics (FHD) solver. The resulting algorithm, supported by a solid mathematical model, allows for a physically consistent exchange of matter and energy between the particle domain and its fluctuating continuum reservoir. Numerical tests are performed to show the validity of the algorithm. Differently from previous algorithms of the same kind, the current approach allows for simulations where, in addition to density fluctuations, also thermal fluctuations can be accounted for, thus large complex molecular systems, as, for example, hydrated biological membranes in a thermal field, can now be efficiently treated.

Quantum computers promise considerable speedups with respect to their classical counterparts. However, the identification of the innately quantum features that enable these speedups is challenging. In the continuous-variable setting—a promising paradigm for the realization of universal, scalable, and fault-tolerant quantum computing—contextuality and Wigner negativity have been perceived as two such distinct resources. Here we show that they are in fact equivalent for the standard models of continuous-variable quantum computing. While our results provide a unifying picture of continuous-variable resources for quantum speedup, they also pave the way toward practical demonstrations of continuous-variable contextuality and shed light on the significance of negative probabilities in phase-space descriptions of quantum mechanics.

We consider quantum circuits composed of single-qubit operations and global entangling gates generated by Ising-type Hamiltonians. It is shown that such circuits can implement a large class of unitary operators commonly used in quantum algorithms at a very low cost—using a constant or effectively constant number of global entangling gates. Specifically, we report constant-cost implementations of Clifford operations with and without ancillae, constant-cost implementation of the multiply-controlled gates with linearly many ancillae, and an $\mathrm{O}({\log }^{*}(n))$ cost implementation of the $n$-controlled single-target gates using logarithmically many ancillae. This shows a significant asymptotic advantage of circuits enabled by the global entangling gates.