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.

We consider quantum error-correcting subsystem codes whose gauge generators realize a translation-invariant, free-fermion-solvable spin model. In this setting, errors are suppressed by a Hamiltonian whose terms are the gauge generators of the code and whose exact spectrum and eigenstates can be found via a generalized Jordan-Wigner transformation. Such solutions are characterized by the frustration graph of the Hamiltonian: the graph whose vertices are Hamiltonian terms, which are neighboring if the terms anticommute. We provide methods for embedding a given frustration graph in the anticommutation relations of a spin model and present the first known example of an exactly solvable spin model with a two-dimensional free-fermion description and exact topological qubits. This model can be viewed as a free-fermionized version of the two-dimensional Bacon-Shor code. Using graph-theoretic tools to study the unit cell, we give an efficient algorithm for deciding if a given translation-invariant spin model is solvable, and explicitly construct the solution. Further, we examine the energetics of these exactly solvable models from the graph-theoretic perspective and show that the relevant gaps of the spin model correspond to known graph-theoretic quantities: the skew energy and the median eigenvalue of an oriented graph. Finally, we numerically search for models that have large spectral gaps above the ground-state spin configuration and thus exhibit particularly robust thermal suppression of errors. These results suggest that optimal models will have low dimensionality and odd coordination numbers, and that the primary limit to energetic error suppression is the skew energy difference between different symmetry sectors rather than single-particle excitations of the free fermions.

Randomized benchmarking (RB) is the gold standard for experimentally evaluating the quality of quantum operations. The current framework for RB is centered on groups and their representations but this can be problematic. For example, Clifford circuits need up to $O(n^2)$ gates and thus Clifford RB cannot scale to larger devices. Attempts to remedy this include new schemes such as linear cross-entropy benchmarking (XEB), cycle benchmarking, and nonuniform RB but they do not fall within the group-based RB framework. In this work, we formulate the universal randomized benchmarking (URB) framework, which does away with the group structure and also replaces the recovery-gate-plus-measurement component with a general “postprocessing” positive operator-valued measurement (POVM). Not only does this framework cover most of the existing benchmarking schemes but it also gives the language for and helps inspire the formulation of new schemes. We specifically consider a class of URB schemes called twirling schemes. For twirling schemes, the postprocessing POVM approximately factorizes into an intermediate channel, inverting maps, and a final measurement. This leads us to study the twirling map corresponding to the gate ensemble specified by the scheme. We prove that if this twirling map is strictly within unit distance of the Haar twirling map in induced diamond norm, the probability of measurement as a function of gate length is a single exponential decay up to small error terms. The core technical tool we use is the matrix perturbation theory of linear operators on quantum channels.

We introduce a morphing procedure that can be used to generate new quantum codes from existing quantum codes. In particular, we morph the 15-qubit Reed-Muller code to obtain a [[10,1,2]] code that is the smallest-known stabilizer code with a fault-tolerant logical $T$ gate. In addition, we construct a family of hybrid color-toric codes by morphing the color code. Our code family inherits the fault-tolerant gates of the original color code, implemented via constant-depth local unitaries. As a special case of this construction, we obtain toric codes with fault-tolerant multiqubit control-$Z$ gates. We also provide an efficient decoding algorithm for hybrid color-toric codes in two dimensions and numerically benchmark its performance for phase-flip noise. We expect that morphing may also be a useful technique for modifying other code families such as triorthogonal codes.

Transforming stand-alone qubits into a functional, general-purpose quantum processing unit requires an architecture where many-body quantum entanglement can be generated and controlled in a coherent, modular, and measurable fashion. Electronic circuits promise a well-developed pathway for large-scale integration once a mature library of quantum-compatible elements have been developed. In the domain of superconducting circuits, fluxonium has recently emerged as a promising qubit due to its high-coherence and large anharmonicity, yet its scalability has not been systematically explored. In this work, we present a blueprint for a high-performance fluxonium-based quantum processor that addresses the challenges of frequency crowding, and both quantum and classical crosstalk. The main ingredients of this architecture include high-anharmonicity circuits, multipath couplers to entangle qubits where spurious longitudinal coupling can be nulled, circuit designs that are compatible with multiplexed microwave circuitry, and strongly coupled readout channels that do not require complex, frequency-sculpted elements to maintain coherence. In addition, we explore robust and resource-efficient protocols for quantum logical operations, then perform numerical simulations to validate the expected performance of this proposed processor with respect to gate fidelity, fabrication yield, and logical error suppression. Lastly, we discuss practical considerations to implement the architecture and achieve the anticipated performance.