Bistable dynamical systems are widely employed to robustly encode classical bits of information. However, they owe their robustness to inherent losses, making them unsuitable to encode quantum information. Surprisingly, there exists a loss mechanism, known as two-photon dissipation, that provides stability without inducing decoherence. An oscillator exchanging pairs of photons with its environment is expected to reach macroscopic bit-flip times between dynamical states containing only a handful of photons. However, previous implementations have observed bit-flip times saturating in the millisecond range. In this experiment, we design a superconducting resonator endowed with two-photon dissipation, and free of all suspected sources of instabilities and inessential ancillary systems. We attain bit-flip times exceeding 100 s in between states containing about 40 photons. Although a full quantum model is necessary to explain our data, the preparation of coherent superposition states remains inaccessible. This experiment demonstrates that macroscopic bit-flip times are attainable with mesoscopic photon numbers in a two-photon dissipative oscillator.

By tightening the conventional Lieb-Robinson bounds to better handle systems that lack translation invariance, we determine the extent to which “weak links” suppress operator growth in disordered one-dimensional spin chains. In particular, we prove that ballistic growth is impossible when the distribution of coupling strengths $\mu (J)$ has a sufficiently heavy tail at small $J$ and we identify the correct dynamical exponent to use instead. Furthermore, through a detailed analysis of the special case in which the couplings are genuinely random and independent, we find that the standard formulation of Lieb-Robinson bounds is insufficient to capture the complexity of the dynamics—we must distinguish between bounds that hold for all sites of the chain and bounds that hold for a subsequence of sites and we show by explicit example that these two can have dramatically different behaviors. All the same, our result for the dynamical exponent is tight, in that we prove by counterexample that there cannot exist any Lieb-Robinson bound with a smaller exponent. We close by discussing the implications of our results, both major and minor, for numerous applications ranging from quench dynamics to the structure of ground states.

It has been proved that in gapped ground states of locally interacting lattice quantum systems with a finite local Hilbert space, the effect of local perturbations decays exponentially with distance. However, in systems with power-law- ($1/r^{\alpha }$) decaying interactions, no analogous statement has been shown and there are serious mathematical obstacles to proving it with existing methods. In this paper, we prove that when $\alpha$ exceeds the spatial dimension $D$, the effect of local perturbations on local properties a distance $r$ away is upper bounded by a power law $1/r^{{\alpha }_1}$ in gapped ground states, provided that the perturbations do not close the spectral gap. The power-law exponent ${\alpha }_1$ is tight if $\alpha >2D$ and interactions are two-body, where we have ${\alpha }_1=\alpha$. The proof is enabled by a method that avoids the use of quasiadiabatic continuation and incorporates techniques of complex analysis. This method also improves bounds on ground-state correlation decay, even in short-range interacting systems. Our work generalizes the fundamental notion that local perturbations have local effects to power-law interacting systems, with broad implications for numerical simulations and experiments.

The challenge of preparing a system in a designated state spans diverse facets of quantum mechanics. To complete this task of steering quantum states, one can employ quantum control through a sequence of generalized measurements, which direct the system towards the target state. In an active version of this protocol, the obtained measurement readouts are used to adjust the protocol on the go. This enables a sped-up performance relative to the passive version of the protocol, where no active adjustments are included. In this work, we consider such active measurement-driven steering as applied to the challenging case of many-body quantum systems. The target states of highest interest would be those with multipartite entanglement. Such state preparation in a measurement-based protocol is limited by the natural constraints for system-detector couplings. We develop a framework for finding such physically feasible couplings, based on parent Hamiltonian construction. For helpful decision-making strategies, we offer Hilbert-space-orientation techniques, comparable to those used in navigation. The first one is to tie the active-decision protocol to the greedy accumulation of the cost function, such as the target state fidelity. We show the potential of a significant speedup, employing this greedy approach to a broad family of matrix product state targets. For system sizes considered here, an average value of the speedup factor $f$ across this family settles about $20$, for some targets even reaching a few thousands. We also identify a subclass of matrix product state targets, including the ground state of the Affleck-Kennedy-Lieb-Tasaki spin chain, for which the value of $f$ increases with system size. In addition to the greedy approach, the second wayfinding technique is to map out the available measurement actions onto a quantum state machine. A decision-making protocol can be based on such a representation, using semiclassical heuristics. This state-machine-based approach can be applied to a more restricted set of targets, where it sometimes offers advantages over the cost-function-based method. We give an example of a $W$-state preparation, which is accelerated with this method by $f\simeq 3.5$, outperforming the greedy protocol for this target.

Silicon offers the enticing opportunity to integrate hybrid quantum-classical computing systems on a single platform. For qubit control and readout, high-frequency signals are required. Therefore, devices that can facilitate its generation are needed. Here, we present a quantum dot-based radio-frequency multiplier operated at cryogenic temperatures. The device is based on the nonlinear capacitance-voltage characteristics of quantum dot systems arising from their low-dimensional density of states. We implement the multiplier in a multigate silicon-nanowire transistor using two complementary device configurations: a single quantum dot coupled to a charge reservoir and a coupled double quantum dot. We study the harmonic voltage conversion as a function of the energy detuning, the multiplication factor, and the harmonic phase noise and find near ideal performance up to a multiplication factor of 10. Our results demonstrate a method for high-frequency conversion that could be readily integrated into silicon-based quantum computing systems and be applied to other semiconductors.

Many quantum computing platforms are based on a two-dimensional (2D) physical layout. Here we explore a concept called looped pipelines, which permits one to obtain many of the advantages of a three-dimensional (3D) lattice while operating a strictly 2D device. The concept leverages qubit shuttling, a well-established feature in platforms like semiconductor spin qubits and trapped-ion qubits. The looped-pipeline architecture has similar hardware requirements to other shuttling approaches, but can process a stack of qubit arrays instead of just one. Even a stack of limited height is enabling for diverse schemes ranging from NISQ-era error mitigation through to fault-tolerant codes. For the former, protocols involving multiple states can be implemented with a space-time resource cost comparable to preparing one noisy copy. For the latter, one can realize a far broader variety of code structures; as an example we consider layered 2D codes within which transversal cnots are available. Under reasonable assumptions this approach can reduce the space-time cost of magic state distillation by 2 orders of magnitude. Numerical modeling using experimentally motivated noise models verifies that the architecture provides this benefit without significant reduction to the code’s threshold.

Distributed quantum information processing and communication protocols demand the ability to generate entanglement among propagating modes. However, thermal fluctuations can severely limit the fidelity and purity of propagating entangled states, especially for low-frequency modes relevant for radio-frequency (rf) signals. Here, we propose nonreciprocity as a resource to render continuous-variable entanglement of propagating modes robust against thermal fluctuations. By utilizing a cold-engineered reservoir, we break the symmetry of reciprocity in a standard two-mode squeezing interaction between a low- and a high-frequency mode and show that the rerouting of thermal fluctuations allows the generation of flying entangled states with high purity. Our approach requires only pairwise Gaussian interactions and is thus ideal for parametric circuit-QED implementations.

Among the emerging technologies with prophesied quantum advantage, quantum communications has already led to fascinating demonstrations—including quantum teleportation to and from satellites. However, all optical communication necessitates the use of optical devices, the comprehensive quantum thermodynamic description of which is still severely lacking. In the present analysis, we prove several versions of Landauer’s principle for noisy polarizers, namely, absorbing linear polarizers and polarizing beam splitters. As main results, we obtain statements of the second law quantifying the minimal amount of heat that is dissipated in the creation of linearly polarized light. Our findings are illustrated with an experimentally tractable example, namely, the temperature dependence of a quantum eraser.

Concatenating bosonic error-correcting codes with qubit codes can substantially boost the error-correcting power of the original qubit codes. It is not clear how to concatenate optimally, given that there are several bosonic codes and concatenation schemes to choose from, including the recently discovered Gottesman-Kitaev-Preskill (GKP) – stabilizer codes [Phys. Rev. Lett. 125, 080503 (2020)] that allow protection of a logical bosonic mode from fluctuations of the conjugate variables of the mode. We develop efficient maximum-likelihood decoders for and analyze the performance of three different concatenations of codes taken from the following set: qubit stabilizer codes, analog or Gaussian stabilizer codes, GKP codes, and GKP-stabilizer codes. We benchmark decoder performance against additive Gaussian white noise, corroborating our numerics with analytical calculations. We observe that the concatenation involving GKP-stabilizer codes outperforms the more conventional concatenation of a qubit stabilizer code with a GKP code in some cases. We also propose a GKP-stabilizer code that suppresses fluctuations in both conjugate variables without extra quadrature squeezing and formulate qudit versions of GKP-stabilizer codes.

We propose a new class of error-correcting dynamic codes in two and three dimensions that has no explicit connection to any parent subsystem code. The two-dimensional code, which we call the CSS (Calderbank-Shor-Steane) honeycomb code, is geometrically similar to that of the honeycomb code by Hastings and Haah and also dynamically embeds an instantaneous toric code. However, unlike the honeycomb code, it possesses an explicit CSS structure and its gauge checks do not form a subsystem code. Nevertheless, we show that our dynamic protocol conserves logical information and possesses a threshold for error correction. We generalize this construction to three dimensions and obtain a code that fault tolerantly alternates between realizing two type-I fracton models, the checkerboard and the X-cube model. Finally, we show the compatibility of our CSS honeycomb-code protocol and the honeycomb code by showing the possibility of randomly switching between the two protocols without information loss while still measuring error syndromes. We call this more general aperiodic structure “dynamic tree codes,” which we also generalize to three dimensions. We construct a probabilistic finite automaton prescription that generates dynamic tree codes correcting any single-qubit Pauli errors and can be viewed as a step toward the development of practical fault-tolerant random codes.

Recent progress in the development of quantum technologies has enabled the direct investigation of the dynamics of increasingly complex quantum many-body systems. This motivates the study of the complexity of classical algorithms for this problem in order to benchmark quantum simulators and to delineate the regime of quantum advantage. Here, we present classical algorithms for approximating the dynamics of local observables and nonlocal quantities such as the Loschmidt echo, where the evolution is governed by a local Hamiltonian. For short times, their computational cost scales polynomially with the system size and the inverse of the approximation error. In the case of local observables, the proposed algorithm has a better dependence on the approximation error than algorithms based on the Lieb-Robinson bound. Our results use cluster-expansion techniques adapted to the dynamical setting, for which we give a novel proof of their convergence. This has important physical consequences besides our efficient algorithms. In particular, we establish a novel quantum speed limit, a bound on dynamical phase transitions, and a concentration bound for product states evolved for short times.

Long-range entanglement—the backbone of topologically ordered states—cannot be created in finite time using local unitary circuits, or, equivalently, adiabatic state preparation. Recently, it has come to light that single-site measurements provide a loophole, allowing for finite-time state preparation in certain cases. Here we show how this observation imposes a complexity hierarchy on long-range entangled states based on the minimal number of measurement layers required to create the state, which we call “shots.” First, similar to Abelian stabilizer states, we construct single-shot protocols for creating any non-Abelian quantum double of a group with nilpotency class 2 (such as $D_4$ or $Q_8$). We show that after the measurement, the wave function always collapses into the desired non-Abelian topological order, conditional on recording the measurement outcome. Moreover, the clean quantum double ground state can be deterministically prepared via feedforward—gates that depend on the measurement outcomes. Second, we provide the first constructive proof that a finite number of shots can implement the Kramers-Wannier duality transformation (i.e., the gauging map) for any solvable symmetry group. As a special case, this gives an explicit protocol to prepare twisted quantum doubles for all solvable groups. Third, we argue that certain topological orders, such as nonsolvable quantum doubles or Fibonacci anyons, define nontrivial phases of matter under the equivalence class of finite-depth unitaries and measurement, which cannot be prepared by any finite number of shots. Moreover, we explore the consequences of allowing gates to have exponentially small tails, which enables, for example, the preparation of any Abelian anyon theory, including chiral ones. This hierarchy paints a new picture of the landscape of long-range entangled states, with practical implications for quantum simulators.

Quantum neural networks have been widely studied in recent years, given their potential practical utility and recent results regarding their ability to efficiently express certain classical data. However, analytic results to date rely on assumptions and arguments from complexity theory. Because of this, there is little intuition as to the source of the expressive power of quantum neural networks or for which classes of classical data any advantage can be reasonably expected to hold. Here, we study the relative expressive power between a broad class of neural network sequence models and a class of recurrent models based on Gaussian operations with non-Gaussian measurements. We explicitly show that quantum contextuality is the source of an unconditional memory separation in the expressivity of the two model classes. We use this intuition to study the relative performance of our introduced model on a standard translation data set exhibiting linguistic contextuality. In doing so, we demonstrate that our introduced quantum models are able to outperform state-of-the-art classical models even in practice.

Encoding quantum information onto bosonic systems is a promising route to quantum error correction. In a cat code, this encoding relies on the confinement of the dynamics of the system onto the two-dimensional manifold spanned by Schrödinger cats of opposite parity. In dissipative cat qubits, an engineered dissipation scheme combining two-photon drive and two-photon loss has been used to autonomously stabilize this manifold, ensuring passive protection against, e.g., bit-flip errors regardless of their origin. Similarly, in Kerr-cat qubits, where highly performing gates can be engineered, two-photon drive and Kerr nonlinearity cooperate to confine the system to a twofold-degenerate ground-state manifold spanned by cat states of opposite parity. Dissipative, Hamiltonian, and hybrid confinement mechanisms have been investigated at resonance, i.e., for driving frequencies matching that of the cavity. Here, we propose a critical cat code, where both two-photon loss and Kerr nonlinearity are present and the two-photon drive is allowed to be out of resonance. The performance of this code is assessed via the spectral theory of Liouvillians in all configurations ranging from the purely dissipative to the Kerr limit. We show that large detunings and small, but non-negligible, two-photon loss rates are fundamental to achieve optimal performance. We further demonstrate that the competition between nonlinearity and detuning results in a first-order dissipative phase transition, leading to a squeezed vacuum steady state. We show that to achieve the maximal suppression of the logical bit-flip rate requires initializing the system in the metastable state emerging from the first-order transition and we detail a protocol to do so. Efficiently operating over a broad range of detuning values, the critical cat code is particularly resistant to random frequency shifts characterizing multiple-qubit operations, opening avenues for the realization of reliable protocols for scalable and concatenated bosonic qubit architectures.

Robust gate sequences are widely used to reduce the sensitivity of gate operations to experimental imperfections. Typically, the optimization minimizes the average gate error; however, recent work in quantum error correction has demonstrated that the performance of encoded logical qubits is sensitive to not only the average error rate but also the type of errors that occur. Here, we present a family of Rydberg-blockade gates for neutral-atom qubits that are robust against two common major imperfections: intensity inhomogeneity and Doppler shifts. These gates outperform existing gates for moderate or large imperfections. We also consider the logical performance of these gates in the context of an erasure-biased qubit based on metastable ${}^{171}$$\mathrm{Yb}$. In this case, we observe that the robust gates outperform existing gates for even very small values of the imperfections, because they maintain the native large bias toward erasure errors for these qubits. These results significantly reduce the laser stability and atomic temperature requirements to achieve fault-tolerant quantum computing with neutral atoms. The approach of optimizing gates for logical-qubit performance may be applied to other qubit platforms.

We introduce a novel family of protocols for entangling gates for neutral atom qubits based on the Rydberg blockade mechanism. These protocols realize controlled-phase gates through a series of global laser pulses that are on resonance with the Rydberg excitation frequency. We analyze these protocols with respect to their robustness against calibration errors of the Rabi frequency or shot-to-shot laser intensity fluctuations, and show that they display robustness in various fidelity measures. In addition, we discuss adaptations of these protocols in order to make them robust to atomic-motion-induced Doppler shifts as well.

Bayes’ rule, $\mathbb{P}(B|A)\mathbb{P}(A)=\mathbb{P}(A|B)\mathbb{P}(B)$, is one of the simplest yet most profound, ubiquitous, and far-reaching results of classical probability theory, with applications in any field utilizing statistical inference. Many attempts have been made to extend this rule to quantum systems, the significance of which we are only beginning to understand. In this work, we develop a systematic framework for defining Bayes’ rule in the quantum setting, and we show that a vast majority of the proposed quantum Bayes’ rules appearing in the literature are all instances of our definition. Moreover, our Bayes’ rule is based upon a simple relationship between the notions of state over time and a time-reversal-symmetry map, both of which are introduced here.

We study multiparameter sensing of two-dimensional (2D) and three-dimensional (3D) vector fields within the Bayesian framework for $\mathrm{SU(2)}$ quantum interferometry. We establish a method to determine the optimal quantum sensor, which establishes the fundamental limit on the precision of simultaneously estimating multiple parameters with an $N$-atom sensor. Keeping current experimental platforms in mind, we present sensors that have limited entanglement capabilities and yet significantly outperform sensors that operate without entanglement and approach the optimal quantum sensor in terms of performance. Furthermore, we show how these sensors can be implemented on current programmable quantum sensors with variational quantum circuits by minimizing a metrological cost function. The resulting circuits prepare tailored entangled states and perform measurements in an appropriate entangled basis to realize the best-possible quantum sensor given the native entangling resources available on a given sensor platform. Notable examples include a 2D and 3D quantum “compass” and a 2D sensor that provides a scalable improvement over unentangled sensors. Our results on optimal and variational multiparameter quantum metrology are useful for advancing precision measurements in fundamental science and ensuring the stability of quantum computers, which can be achieved through the incorporation of optimal quantum sensors in a quantum feedback loop.

In this work, we study the single-shot performance of higher-dimensional hypergraph product codes decoded using belief propagation and ordered-statistics decoding [P. Panteleev and G. Kalachev, Quantum 5, 585 (2021)]. We find that decoding data-qubit and syndrome-measurement errors together in a single stage leads to single-shot thresholds that greatly exceed all previously observed single-shot thresholds for these codes. For the three-dimensional toric code and a phenomenological noise model, our results are consistent with a sustainable threshold of 7.1% for $Z$ errors, compared to the threshold of 2.90% previously found using a two-stage decoder [Quintavalle et al., 2021]. For the four-dimensional (4D) toric code, for which both $X$ and $Z$ error correction is single shot, our results are consistent with a sustainable single-shot threshold of 4.3%, which is even higher than the threshold of 2.93% for the two-dimensional toric code for the same noise model but using $L$ rounds of stabilizer measurement. We also explore the performance of balanced-product and 4D hypergraph-product codes, which we show lead to a reduction in qubit overhead compared the surface code for phenomenological error rates as high as 1%.

We develop a phase-estimation method with a distinct feature: its maximal run time (which determines the circuit depth) is $\delta /ϵ$, where $ϵ$ is the target precision, and the preconstant $\delta$ can be arbitrarily close to $0$ as the initial state approaches the target eigenstate. The total cost of the algorithm satisfies the Heisenberg-limited scaling $\tilde{\mathcal{O}}({ϵ}^{-1})$. As a result, our algorithm may significantly reduce the circuit depth for performing phase-estimation tasks on early fault-tolerant quantum computers. The key technique is a simple subroutine called quantum complex exponential least squares (QCELS). Our algorithm can be readily applied to reduce the circuit depth for estimating the ground-state energy of a quantum Hamiltonian, when the overlap between the initial state and the ground state is large. If this initial overlap is small, we can combine our method with the Fourier-filtering method developed in [Lin and Tong, PRX Quantum 3, 010318, 2022], and the resulting algorithm provably reduces the circuit depth in the presence of a large relative overlap compared to $ϵ$. The relative-overlap condition is similar to a spectral-gap assumption but it is aware of the information in the initial state and is therefore applicable to certain Hamiltonians with small spectral gaps. We observe that the circuit depth can be reduced by around 2 orders of magnitude in numerical experiments under various settings.