We show that an array of polar molecules interacting with Rydberg atoms is a promising hybrid system for scalable quantum computation. Quantum information is stored in long-lived hyperfine or rotational states of molecules, which interact indirectly through resonant dipole-dipole interactions with Rydberg atoms. A two-qubit gate based on this interaction has a duration of $1\mu \mathrm{s}$ and an achievable fidelity of 99.9%. The gate has little sensitivity to the motional states of the particles—the molecules can be in thermal states, the atoms do not need to be trapped during Rydberg excitation, the gate does not heat the molecules, and heating of the atoms has a negligible effect. Within a large, static array, the gate can be applied to arbitrary pairs of molecules separated by tens of micrometres, making the scheme highly scalable. The molecule-atom interaction can also be used for rapid qubit initialization and efficient, nondestructive qubit readout, without driving any molecular transitions. Single-qubit gates are driven using microwave pulses alone, exploiting the strong electric dipole transitions between rotational states. Thus, all operations required for large-scale quantum computation can be done without moving the molecules or exciting them out of their ground electronic states.

We describe a quantum information architecture consisting of a hybrid array of optically trapped molecules and atoms. This design leverages the large transition dipole moments of Rydberg atoms to mediate fast, high-fidelity gates between qubits encoded in coherent molecular degrees of freedom. Error channels of detuning, decay, pulse area noise, and leakage to other molecular states are discussed. The molecule-Rydberg interaction can also be used to enable nondestructive molecule detection and rotational state readout. We consider a specific near-term implementation of this scheme using NaCs molecules and Cs Rydberg atoms, showing that it is possible to implement 300-ns gates with a potential fidelity of $>99.9\mathrm{\%}$.

We investigate topological order on fractal geometries embedded in $n$ dimensions. We consider the $n$-dimensional lattice with holes at all length scales the corresponding fractal (Hausdorff) dimension of which is $D_H=n-\delta$. In particular, we diagnose the existence of the topological order through the lens of quantum information and geometry, i.e., via its equivalence to a quantum error-correcting code with a macroscopic code distance or the presence of macroscopic systoles in systolic geometry. We first prove a no-go theorem that ${\mathbb{Z}}_N$ topological order cannot survive on any fractal embedded in two spatial dimensions and with $D_H=2-\delta$. For fractal-lattice models embedded in three dimensions (3D) or higher spatial dimensions, ${\mathbb{Z}}_N$ topological order survives if the boundaries on the holes condense only loop or, more generally, $k$-dimensional membrane excitations ($k\ge 2$), thus predicting the existence of fractal topological quantum memories (at zero temperature) or topological codes that are embeddable in 3D. Moreover, for a class of models that contain only loop or membrane excitations and are hence self-correcting on an $n$-dimensional manifold, we prove that ${\mathbb{Z}}_N$ topological order survives on a large class of fractal geometries independent of the type of hole boundary and is hence extremely robust. We further construct fault-tolerant logical gates in the ${\mathbb{Z}}_2$ version of these fractal models, which we term fractal surface codes, using their connection to global and higher-form topological symmetries equivalent to sweeping the corresponding gapped domain walls. In particular, we discover a logical controlled-controlled-Z (ccz) gate corresponding to a global symmetry in a class of fractal codes embedded in 3D with Hausdorff dimension asymptotically approaching $D_H=2+ϵ$ for arbitrarily small $ϵ$, which hence only requires a space overhead $\mathrm{\Omega }(d^{2+ϵ})$, where $d$ is the code distance. This in turn leads to the surprising discovery of certain exotic gapped boundaries that only condense the combination of loop excitations and certain gapped domain walls. We further obtain logical $C^{p}Z$ gates with $p\le n-1$ on fractal codes embedded in $n$ dimensions. In particular, for the logical $C^{n-1}Z$ in the $n\mathrm{th}$ level of the Clifford hierarchy, we can reduce the space overhead to $\mathrm{\Omega }(d^{n-1+ϵ})$. On the mathematical side, our findings in this paper also lead to the discovery of macroscopic relative systoles in a class of fractal geometries.

One of the most fundamental results in quantum information theory is that no measurement can perfectly discriminate between nonorthogonal quantum states. In this work, we investigate quantum advantages for discrimination tasks over noncontextual theories by considering a maximum-confidence measurement that unifies different strategies of quantum state discrimination, including minimum-error and unambiguous discrimination. We first show that maximum-confidence discrimination, as well as unambiguous discrimination, contains contextual advantages. We then consider a semi-device-independent scenario of certifying maximum-confidence measurement. The scenario naturally contains undetected events, making it a natural setting to explore maximum-confidence measurements. We show that the certified maximum confidence in quantum theory also contains contextual advantages. Our results establish how the advantages of quantum theory over a classical model may appear in a realistic scenario of a discrimination task.

Quantum transduction between the microwave and optical domains is an outstanding challenge for long-distance quantum networks based on superconducting qubits. For all transducers realized to date, the generally weak light-matter coupling does not allow high transduction efficiency, large bandwidth, and low noise simultaneously. Here we show that a large electric dipole moment of an exciton in an optically active self-assembled quantum dot molecule (QDM) efficiently couples to a microwave resonator field at the single-photon level. This allows for transduction between microwave and optical photons without coherent optical pump fields to enhance the interaction. With an on-chip device, we demonstrate a sizeable single-photon coupling strength of 16 MHz. Thanks to the fast exciton decay in the QDM, the transduction bandwidth between an optical and microwave resonator photon reaches several 100 s of MHz. We also show that the transduction process via the QDM is fully coherent within the measurement error range.

In certain special circumstances, such as in the vicinity of a black hole or in a uniformly accelerating frame, vacuum fluctuations appear to give rise to a finite-temperature environment. This effect, currently without experimental confirmation, can be interpreted as a manifestation of quantum entanglement after tracing out vacuum modes in an unobserved region. In this work, we identify a class of experimentally accessible quantum systems where thermal density matrices emerge from vacuum entanglement. We show that reduced density matrices of lower-dimensional subsystems embedded in $D$-dimensional gapped Dirac fermion vacuum, either on a lattice or continuum, have a thermal form with respect to a lower-dimensional Dirac Hamiltonian. Strikingly, we show that vacuum entanglement can even conspire to make a subsystem of a gapped system at zero temperature appear as a hot gapless system. We propose concrete experiments in cold-atom quantum simulators to observe the vacuum-entanglement-induced thermal states.

Principal component analysis (PCA) is a dimensionality reduction method in data analysis that involves diagonalizing the covariance matrix of the dataset. Recently, quantum algorithms have been formulated for PCA based on diagonalizing a density matrix. These algorithms assume that the covariance matrix can be encoded in a density matrix, but a concrete protocol for this encoding has been lacking. Our work aims to address this gap. Assuming amplitude encoding of the data, with the data given by the ensemble $\{p_i,|{\psi }_i⟩\}$, then one can easily prepare the ensemble average density matrix $\overline{\rho }=\sum _i{p}_i|{\psi }_i⟩⟨{\psi }_i|$. We first show that $\overline{\rho }$ is precisely the covariance matrix whenever the dataset is centered. For quantum datasets, we exploit global phase symmetry to argue that there always exists a centered dataset consistent with $\overline{\rho }$, and hence $\overline{\rho }$ can always be interpreted as a covariance matrix. This provides a simple means for preparing the covariance matrix for arbitrary quantum datasets or centered classical datasets. For uncentered classical datasets, our method is so-called “PCA without centering,” which we interpret as PCA on a symmetrized dataset. We argue that this closely corresponds to standard PCA, and we derive equations and inequalities that bound the deviation of the spectrum obtained with our method from that of standard PCA. We numerically illustrate our method for the Modified National Institute of Standards and Technology (MNIST) handwritten digit dataset. We also argue that PCA on quantum datasets is natural and meaningful, and we numerically implement our method for molecular ground-state datasets.

The hypothetical axion particle (of unknown mass) is a leading candidate for dark matter (DM). Many experiments search for axions with microwave cavities, where an axion may convert into a cavity photon, leading to a feeble excess in the output power of the cavity. Recent work [Backes et al., Nature 590, 238 (2021)] has demonstrated that injecting squeezed vacuum into the cavity can substantially accelerate the axion search. Here, we go beyond and provide a theoretical framework to leverage the benefits of quantum squeezing in a network setting consisting of many sensor cavities. By forming a local sensor network, the signals among the cavities can be combined coherently to boost the axion search. Furthermore, injecting multipartite entanglement across the cavities—generated by splitting a squeezed vacuum—enables a global noise reduction. We explore the performance advantage of such a local, entangled sensor network, which enjoys both coherence between the axion signals and entanglement between the sensors. Our analyses are pertinent to next-generation DM-axion searches aiming to leverage a network of sensors and quantum resources in an optimal way. Finally, we assess the possibility of using a more exotic quantum state, the Gottesman-Kitaev-Preskill (GKP) state. Despite a constant-factor improvement in the scan time relative to a single-mode squeezed state in the ideal case, the advantage of employing a GKP state disappears when a practical measurement scheme is considered.

Quantum state-resolved spectroscopy was recently achieved for ${\mathrm{C}}_{60}$ molecules when cooled by buffer gas collisions and probed with a midinfrared frequency comb. This rovibrational quantum state resolution for the largest molecule on record is facilitated by the remarkable symmetry and rigidity of ${\mathrm{C}}_{60}$, which also present new opportunities and challenges to explore energy transfer between quantum states in this many-atom system. Here we combine state-specific optical pumping, buffer gas collisions, and ultrasensitive intracavity nonlinear spectroscopy to initiate and probe the rotation-vibration energy transfer and relaxation. This approach provides the first detailed characterization of ${\mathrm{C}}_{60}$ collisional energy transfer for a variety of collision partners, and determines the rotational and vibrational inelastic collision cross sections. These results compare well with our theoretical modeling of the collisions, and establish a route towards quantum state control of a new class of unprecedentedly large molecules.

Hexagonal boron nitride is a van der Waals material that hosts visible-wavelength quantum emitters at room temperature. However, experimental identification of the quantum emitters’ electronic structure is lacking, and key details of their charge and spin properties remain unknown. Here, we probe the optical dynamics of quantum emitters in hexagonal boron nitride using photon emission correlation spectroscopy. Several quantum emitters exhibit ideal single-photon emission with noise-limited photon antibunching, $g^{(2)}(0)=0$. The photoluminescence emission lineshapes are consistent with individual vibronic transitions. However, polarization-resolved excitation and emission suggests the role of multiple optical transitions, and photon emission correlation spectroscopy reveals complicated optical dynamics associated with excitation and relaxation through multiple electronic excited states. We compare the experimental results to quantitative optical dynamics simulations, develop electronic structure models that are consistent with the observations, and discuss the results in the context of ab initio theoretical calculations.

Quantum metrology protocols exploiting ensembles of $N$ two-level systems and Ramsey-style measurements are ubiquitous. However, in many cases excess readout noise severely degrades the measurement sensitivity; in particular in sensors based on ensembles of solid-state defect spins. We present a dissipative “spin-amplification” protocol that allows us to dramatically improve the sensitivity of such schemes, even in the presence of realistic intrinsic dissipation and noise. Our method is based on exploiting collective (i.e., superradiant) spin decay, an effect that is usually seen as a nuisance because it limits spin-squeezing protocols. We show that our approach can allow a system with a highly imperfect spin readout to approach standard-quantum-limit-like scaling in $N$ within a factor of 2, without needing to change the actual readout mechanism. Our ideas are compatible with several state-of-the-art experimental platforms where an ensemble of solid-state spins ($\mathrm{NV}$ centers, $\mathrm{SiV}$ centers) is coupled to a common microwave or mechanical mode.

Novel qubits with intrinsic noise protection constitute a promising route for improving the coherence of quantum information in superconducting circuits. However, many protected superconducting qubits exhibit relatively low transition frequencies, which could make their integration with conventional transmon circuits challenging. In this work, we propose and study a scheme for entangling a tunable transmon with a Cooper-pair parity-protected qubit, a paradigmatic example of a low-frequency protected qubit that stores quantum information in opposite Cooper-pair parity states on a superconducting island. By tuning the external flux on the transmon, we show that noncomputational states can mediate a two-qubit entangling gate that preserves the Cooper-pair parity independent of the detailed pulse sequence. Interestingly, the entangling gate bears similarities to a controlled-phase gate in conventional transmon devices. Hence, our results suggest that standard high-precision gate calibration protocols could be repurposed for operating heterogeneous quantum processors.

We theoretically study the dynamics of $n$-level spin-orbit coupled alkaline-earth fermionic atoms with $\mathrm{SU}(n)$ symmetric interactions. We consider three-dimensional lattices with tunneling along one dimension, and the internal levels treated as a synthetic dimension, realizing an $n$-leg flux ladder. Laser driving is used to couple the internal levels and to induce an effective magnetic flux through the ladder. We focus on the dense and strongly interacting regime, where in the absence of flux the system behaves as a Mott insulator with suppressed motional dynamics. At integer and fractional ratios of the laser Rabi frequency to the onsite interactions, the system exhibits resonant features in the dynamics. These resonances occur when interactions help overcome kinetic constraints upon the tunneling of atoms, thus enabling motion. Different resonances allow for the development of complex chiral current patterns. The resonances resemble those appearing in the longitudinal Hall resistance when the magnetic field is varied. We characterize the dynamics by studying the system’s long-time relaxation behavior as a function of flux, number of internal levels $n$, and interaction strength. We observe a series of nontrivial prethermal plateaus caused by the emergence of resonant processes at successive orders in perturbation theory. We discuss protocols to observe the predicted phenomena under current experimental conditions.

Einstein-Rosen-Podolsky (EPR) steering or quantum steering describes the “spooky action at a distance” that one party is able to remotely alter the states of the other if they share a certain entangled state. Generally, it admits an operational interpretation as the task of verifying entanglement without trust in the steering party’s devices, making it lie intermediately between Bell nonlocality and entanglement. Together with the asymmetrical nature, quantum steering has attracted a considerable interest from theoretical and experimental sides over the past decades. In this Perspective, we present a brief overview of the EPR steering with emphasis on the recent progress, discuss current challenges, opportunities, and propose various future directions. We look to the future, which directs research to a larger-scale level beyond massless and microscopic systems to reveal steering of higher dimensionality, and to build up steered networks composed of multiple parties.

Levitating charged particles in ultrahigh vacuum provides a preeminent platform for quantum information processing, for quantum-enhanced force and torque sensing, for probing physics beyond the standard model, and for high-mass tests of the quantum superposition principle. Existing setups, ranging from single atomic ions to ion chains and crystals to charged molecules and nanoparticles, are crucially impacted by fluctuating electric fields emanating from nearby electrodes used to control the motion. In this article, we provide a theoretical toolbox for describing the rotational and translational quantum dynamics of charged nano- to microscale objects near metallic and dielectric surfaces, as characterized by macroscopic dielectric response functions. The resulting quantum master equations describe the coherent surface-particle interaction, due to image charges and Casimir-Polder potentials, as well as surface-induced decoherence and heating, with the experimentally observed frequency and distance scaling. We explicitly evaluate the master equations for relevant setups, thereby providing the framework for describing and mitigating surface-induced decoherence as required in future quantum technological applications.

We construct a novel three-dimensional quantum cellular automaton (QCA) based on a system with short-range entangled bulk and chiral semion boundary topological order. We argue that either the QCA is nontrivial, i.e., not a finite-depth circuit of local quantum gates, or there exists a two-dimensional commuting projector Hamiltonian realizing the chiral semion topological order [characterized by $U(1{)}_2$ Chern-Simons theory]. Our QCA is obtained by first constructing the Walker-Wang Hamiltonian of a certain premodular tensor category of order four, then condensing the deconfined bulk boson at the level of lattice operators. We show that the resulting Hamiltonian hosts chiral semion surface topological order in the presence of a boundary and can be realized as a non-Pauli stabilizer code on qubits, from which the QCA is defined. The construction is then generalized to a class of QCAs defined by non-Pauli stabilizer codes on $2^n$-dimensional qudits that feature surface anyons described by $U(1{)}_{2^n}$ Chern-Simons theory. Our results support the conjecture that the group of nontrivial three-dimensional QCAs is isomorphic to the Witt group of nondegenerate braided fusion categories.

Quantum computing promises to speed up machine-learning algorithms. However, noisy intermediate-scale quantum (NISQ) devices pose engineering challenges to realizing quantum machine-learning (QML) advantages. Recently, a series of QML computational models inspired by the noise-tolerant dynamics of the brain has emerged as a means to circumvent the hardware limitations of NISQ devices. In this paper, we introduce a quantum version of a recurrent neural network (RNN), a well-known model for neural circuits in the brain. Our quantum RNN (qRNN) makes use of the natural Hamiltonian dynamics of an ensemble of interacting spin-1/2 particles as a means for computation. In the limit where the Hamiltonian is diagonal, the qRNN recovers the dynamics of the classical version. Beyond this limit, we observe that the quantum dynamics of the qRNN provide it with quantum computational features that can aid it in computation. To this end, we study a fixed-geometry qRNN, i.e., a quantum reservoir computer, based on arrays of Rydberg atoms and show that the Rydberg reservoir is indeed capable of replicating the learning of several cognitive tasks such as multitasking, decision making, and long-term memory by taking advantage of several key features of this platform such as interatomic species interactions and quantum many-body scars.

The goal of digital quantum simulation is to approximate the dynamics of a given target Hamiltonian via a sequence of quantum gates, a procedure known as Trotterization. The quality of this approximation can be controlled by the so-called Trotter step that governs the number of required quantum gates per unit simulation time. The stroboscopic dynamics generated by Trotterization is effectively described by a time-independent Hamiltonian, referred to as the Floquet Hamiltonian. In this work, we propose Floquet Hamiltonian learning to reconstruct the experimentally realized Floquet Hamiltonian order by order in the Trotter step. This procedure is efficient, i.e., it requires a number of measurements that scales polynomially in the system size, and can be readily implemented in state-of-the-art experiments. With numerical examples, we propose several applications of our method in the context of verification of quantum devices: from the characterization of the distinct sources of errors in digital quantum simulators to determining the optimal operating regime of the device. We show that our protocol provides the basis for feedback-loop design and calibration of new types of quantum gates. Furthermore, it can be extended to the case of nonunitary dynamics and used to learn Floquet Liouvillians, thereby offering a way of characterizing the dissipative processes present in noisy intermediate-scale quantum devices.

Variational quantum circuits are used in quantum machine learning and variational quantum simulation tasks. Designing good variational circuits or predicting how well they perform for given learning or optimization tasks is still unclear. Here we discuss these problems, analyzing variational quantum circuits using the theory of neural tangent kernels. We define quantum neural tangent kernels, and derive dynamical equations for their associated loss function in optimization and learning tasks. We analytically solve the dynamics in the frozen limit, or lazy training regime, where variational angles change slowly and a linear perturbation is good enough. We extend the analysis to a dynamical setting, including quadratic corrections in the variational angles. We then consider a hybrid quantum classical architecture and define a large-width limit for hybrid kernels, showing that a hybrid quantum classical neural network can be approximately Gaussian. The results presented here show limits for which analytical understandings of the training dynamics for variational quantum circuits, used for quantum machine learning and optimization problems, are possible. These analytical results are supported by numerical simulations of quantum machine-learning experiments.

Attaining fault tolerance while maintaining low overhead is one of the main challenges in a practical implementation of quantum circuits. One major technique that can overcome this problem is the flag technique, in which high-weight errors arising from a few faults can be detected by a few ancillas and distinguished using subsequent syndrome measurements. The technique can be further improved using the fact that, for some families of codes, errors of any weight are logically equivalent if they have the same syndrome and weight parity, as shown in our previous work [Tansuwannont and Leung, Phys. Rev. A 104, 042410 (2021)]. In this work, we develop a notion of distinguishable fault set that captures both concepts of flags and weight parities, and extend the use of weight parities in error correction to families of capped and recursive capped color codes. We also develop fault-tolerant protocols for error correction, measurement, state preparation, and logical $T$-gate implementation via code switching, which are sufficient for performing fault-tolerant Clifford computation on a capped color code, and performing fault-tolerant universal quantum computation on a recursive capped color code. Our protocols for a capped or a recursive capped color code of any distance require only two ancillas, assuming that the ancillas can be reused. The concept of distinguishable fault set also leads to a generalization of the definitions of fault-tolerant gadgets proposed by Aliferis, Gottesman, and Preskill.