We show unambiguous violations of the different macrorealist inequalities, like the Leggett-Garg inequality (LGI) and its variant called Wigner’s form of the Leggett-Garg inequality (WLGI) using a heralded, single-photon-based experimental setup comprising a Mach-Zehnder interferometer followed by a displaced Sagnac interferometer. In our experiment, negative result measurements are implemented as control experiments, in order to validate the presumption of noninvasive measurability used in defining the notion of macrorealism. Among the experiments to date testing macrorealism, the present experiment stands out in comprehensively addressing the relevant loopholes. The clumsiness loophole is addressed through the precision testing of any classical or macrorealist invasiveness involved in the implementation of negative result measurements. This is done by suitably choosing the experimental parameters so that the quantum mechanically predicted validity of the relevant two-time no-signaling in time (NSIT) conditions is maintained in the three pairwise experiments performed to show the violation of LGI or WLGI. Furthermore, importantly, the detection efficiency loophole is addressed in our experimental scheme by adopting suitable modifications in the measurement strategy, enabling the demonstration of the violation of LGI or WLGI for any nonzero detection efficiency. We also show how other relevant loopholes like the multiphoton emission loophole, coincidence loophole, and the preparation state loophole are all closed in the present experiment. We report a LGI violation of $1.32\pm 0.04$ and a WLGI violation of $0.10\pm 0.02$ in our setup, where the magnitudes of violation are respectively 8 times and 5 times the corresponding error values, while agreeing perfectly with the ranges of quantum mechanically predicted values of the LGI and WLGI expressions that we estimate by taking into account the nonidealities of the actual experiment. At the same time, consistent with quantum mechanical predictions, the experimentally observed probabilities satisfy the two-time NSIT conditions up to the order of ${10}^{-2}$. Thus, the noninvasiveness in our implemented negative result measurement is convincingly upper bounded to ${10}^{-2}$.

We introduce an algorithm for the classical simulation of Gaussian boson sampling that is quadratically faster than previously known methods. The complexity of the algorithm is exponential in the number of photon pairs detected, not the number of photons, and is directly proportional to the time required to calculate a probability amplitude for a pure Gaussian state. The main innovation is to use auxiliary conditioning variables to reduce the problem of sampling to the computation of the pure-state probability amplitudes, for which the most computationally expensive step is the calculation of a loop hafnian. We implement and benchmark an improved loop-hafnian algorithm and show that it can be used to compute pure-state probabilities, the dominant step in the sampling algorithm, of events involving up to 50 photons in a single workstation, i.e., without the need of a supercomputer.

An ensemble of noble-gas nuclear spins is a unique quantum system that could maintain coherence for many hours at room temperature and above, owing to exceptional isolation from the environment. This isolation, however, is a mixed blessing, limiting the ability of these ensembles to interface with other quantum systems coherently. Here we show that spin-exchange collisions with alkali-metal atoms render a quantum interface for noble-gas spins without impeding their long coherence times. We formulate the many-body theory of the hybrid system and reveal a collective mechanism that strongly couples the macroscopic quantum states of the two spin ensembles. Despite their stochastic and random nature, weak collisions enable entanglement and reversible exchange of nonclassical excitations in an efficient, controllable, and deterministic process. With recent experiments now entering the strong-coupling regime, this interface paves the way toward realizing hour-long quantum memories and entanglement at room temperature.

Quantum cooperativity is evident in light-matter platforms where quantum-emitter ensembles are interfaced with confined optical modes and are coupled via the ubiquitous electromagnetic quantum vacuum. Cooperative effects can find applications, among other areas, in topological quantum optics, in quantum metrology, or in quantum information. This tutorial provides a set of theoretical tools to tackle the behavior responsible for the onset of cooperativity by extending open quantum system dynamics methods, such as the master equation and quantum Langevin equations, to electron-photon interactions in strongly coupled and correlated quantum-emitter ensembles. The methods are illustrated on a wide range of current research topics such as the design of nanoscale coherent-light sources, highly reflective quantum metasurfaces, or low intracavity power superradiant lasers.

Modern quantum experiments provide examples of transport with noncommuting quantities, offering a tool to understand the interplay between thermal and quantum effects. Here we set forth a theory for non-Abelian transport in the linear response regime. Our key insight is to use generalized Gibbs ensembles with noncommuting charges as the basic building blocks and strict charge-preserving unitaries in a collisional setup. The linear response framework is then built using a collisional model between two reservoirs. We show that the transport coefficients obey Onsager reciprocity. Moreover, we find that quantum coherence, associated with the noncommutativity, acts so as to reduce the net entropy production, when compared to the case of commuting transport. This therefore provides a clear connection between quantum coherent transport and dissipation. As an example, we study heat and squeezing fluxes in bosonic systems, characterizing a set of thermosqueezing coefficients with potential applications in metrology and heat-to-work conversion in the quantum regime.

We put forth a unifying formalism for the description of the thermodynamics of continuously monitored systems, where measurements are only performed on the environment connected to a system. We show, in particular, that the conditional and unconditional entropy production, which quantify the degree of irreversibility of the open system’s dynamics, are related to each other by the Holevo quantity. This, in turn, can be further split into an information gain rate and loss rate, which provide conditions for the existence of informational steady states, i.e., stationary states of a conditional dynamics that are maintained owing to the unbroken acquisition of information. We illustrate the applicability of our framework through several examples.

From Feynman diagrams to tensor networks, diagrammatic representations of computations in quantum mechanics have catalyzed progress in physics. These diagrams represent the underlying mathematical operations and aid physical interpretation, but cannot generally be computed with directly. In this paper we introduce the ZXH-calculus, a graphical language based on the ZX-calculus, that we use to represent and reason about many-body states entirely graphically. As a demonstration, we express the one-dimensional (1D) AKLT-state, a symmetry protected topological state, in the ZXH-calculus by developing a representation of spins higher than 1/2 within the calculus. By exploiting the simplifying power of the ZXH-calculus rules we show how this representation straightforwardly recovers the AKLT matrix-product state representation, the existence of topologically protected edge states, and the nonvanishing of a string-order parameter. Extending beyond these known properties, our diagrammatic approach also allows us to analytically derive that the Berry phase of any finite-length 1D AKLT chain is $\pi$. In addition, we provide an alternative proof that the two-dimensional (2D) AKLT-state on a hexagonal lattice can be reduced to a graph state, demonstrating that it is a universal quantum-computing resource. Lastly, we build 2D higher-order topological phases diagrammatically, which we use to illustrate a symmetry-breaking phase transition. Our results show that the ZXH-calculus is a powerful language for representing and computing with physical states entirely graphically, paving the way to develop more efficient many-body algorithms and giving a novel diagrammatic perspective on quantum phase transitions.

Non-Gaussian quantum states have been deterministically prepared and autonomously stabilized in single- and two-mode circuit quantum electrodynamics architectures via engineered dissipation. However, it is currently unknown how to scale up this technique to multimode non-Gaussian systems. Here, we upgrade dissipation engineering to collective (normal) modes of nonlinear resonator arrays and show how to stabilize multimode Schrödinger cat states. These states are multiphoton and multimode quantum superpositions of coherent states in a single normal mode delocalized over an arbitrary number of cavities. We consider tailored dissipative coupling between resonators that are parametrically driven and feature an on-site nonlinearity, which is either a Kerr-type nonlinearity or an engineered two-photon loss. For both types of nonlinearity, we find the same exact closed-form solutions for the two-dimensional steady-state manifold spanned by superpositions of multimode Schrödinger cat states. We further show that, in the Zeno limit of strong dissipative coupling, the even-parity multimode cat state can be deterministically prepared from the vacuum. Remarkably, engineered two-photon loss gives rise to a fast relaxation toward the steady state, protecting the state preparation against decoherence due to intrinsic single-photon losses and imperfections in tailored dissipative coupling, which sets in at longer times. The relaxation time is independent of system size making the state preparation scalable. Multimode cat states are naturally endowed with a noise bias that increases exponentially with system size and can thus be exploited for enhanced robust encoding of quantum information.

While artificially fabricated patterned metasurfaces are providing paradigm-shifting optical components for classical light manipulation, strongly interacting, controllable, and deterministic quantum interfaces between light and matter in free space remain an outstanding challenge. Here, we theoretically demonstrate how to achieve quantum control of both the electric and magnetic components of an incident single-photon pulse by engineering the collective response of a two-dimensional atomic array. High-fidelity absorption and storage in a long-lived subradiant state, and its subsequent retrieval, are achieved by controlling classically or quantum-mechanically the ac Stark shifts of the atomic levels and suppressing the scattering during the absorption. Quantum wave-front control of the transmitted photon with nearly zero reflection is prepared by coupling the collective state of the array to another photon in a cavity and by engineering a Huygens’ surface of atoms using only a single coherent standing wave. The proposed schemes allow for the generation of entanglement between the cavity, the lattice, and hence the state of the stored, reflected, or transmitted light, and for quantum-state transfer between the cavity and propagating photons. Bipartite entanglement generation is explicitly calculated between a stored single-photon excitation of the array and the cavity photon. We illustrate the control by manipulating the phase, phase superposition, polarization, and direction of a transmitted or reflected photon, providing quantum-optical switches and functional quantum interfaces between light and atoms that could form links in a larger quantum information platform.

Quantum Monte Carlo and quantum simulation are both important tools for understanding quantum many-body systems. As a classical algorithm, quantum Monte Carlo suffers from the sign problem, preventing its application to most fermion systems and real-time dynamics. In this paper, we introduce a novel nonvariational algorithm using quantum simulation as a subroutine to accelerate quantum Monte Carlo by easing the sign problem. The quantum subroutine can be implemented with shallow circuits and, by incorporating error mitigation, can reduce the Monte Carlo variance by several orders of magnitude even when the circuit noise is significant. As such, the proposed quantum algorithm is applicable to near-term noisy quantum hardware.

Nonreciprocal microwave devices, such as circulators and isolators, are needed in high-fidelity qubit readout schemes to unidirectionally route the readout signals and protect the qubits against noise coming from the output chain. However, cryogenic circulators and isolators are prohibitive in scalable superconducting architectures because they rely on magnetic materials. Here we report a fast ($750\mathrm{ns}$) high-fidelity ($95\mathrm{\%}$) quantum nondemolition readout of a coherent superconducting qubit ($T_1=52\mu \mathrm{s}$, $T_{2E}=35\mu \mathrm{s}$) without any nonreciprocal magnetic devices. We use in our readout chain a microwave-controlled qubit readout multichip module (QRMCM) that integrates interferometric directional Josephson devices consisting of an isolator and a reconfigurable isolator or amplifier device, and an off-chip low-pass filter. Using the QRMCM, we demonstrate isolation up to $45\mathrm{dB}$ within $13\mathrm{MHz}$, when both directional devices are operated as isolators, and low-noise amplification in excess of $10\mathrm{dB}$ within a dynamical bandwidth of $10\mathrm{MHz}$, when the reconfigurable device is operated as an amplifier. We also investigate the dependence of the qubit coherence times $T_{\phi }$ and $T_{2E}$ on the isolation response of the QRMCM, which we control in situ using the microwave drives feeding the isolators. Furthermore, by directly comparing the QRMCM performance with that of a state-of-art configuration (with $T_{2E}\approx 2T_1$) that uses a pair of wideband magnetic isolators, we find that the excess pure dephasing measured with the QRMCM (for which $T_{2E}\approx T_1$) is likely limited by the residual thermal photon population in the readout resonator. Improved versions of the QRMCM could replace magnetic circulators and isolators in large superconducting quantum processors.

Quantum coherence is the foundation of almost all departures from classical physics and is exhibited when a quantum system is in a superposition of different basis states. Here, the coherent superposition of three motional Fock states of a single trapped ion is experimentally certified, with a procedure that does not produce false positives. As the motional state cannot be directly interrogated, our scheme uses an interference pattern generated by projective measurement of the coupled qubit state. The minimum number of coherently superposed states is inferred from a series of threshold values based on analysis of the interference pattern. This demonstrates that high-level coherence can be verified and investigated with simple nonideal control methods that are well suited to noisy intermediate-scale quantum devices.

The presence of valley states is a significant obstacle to realizing quantum information technologies in silicon quantum dots, as leakage into alternate valley states can introduce errors into the computation. We use a perturbative analytical approach to study the dynamics of exchange-coupled quantum dots with valley degrees of freedom. We show that if the valley splitting is large and electrons are not properly initialized to valley eigenstates, then the time evolution of the system will lead to spin-valley entanglement. Spin-valley entanglement will also occur if the valley splitting is small and electrons are not initialized to the same valley state. Additionally, we show that for small valley splitting, spin-valley entanglement does not affect the measurement probabilities of two-qubit systems; however, systems with more qubits will be affected. This means that two-qubit gate fidelities measured in two-qubit systems may miss the effects of valley degrees of freedom. Our work shows how the existence of valleys may adversely affect multiqubit fidelities even when the system temperature is very low. Although this is not an immediate problem in $\mathrm{Si}$ qubits, because the current focus is on controlling individual qubits, our work points to a possible future issue in many-qubit $\mathrm{Si}$ circuits.

We investigate the correlations that can arise between Alice and Bob in prepare-and-measure communication scenarios where the source (Alice) and the measurement device (Bob) can share prior entanglement. The paradigmatic example of such a scenario is the quantum dense-coding protocol, where the communication capacity of a qudit can be doubled if a two-qudit entangled state is shared between Alice and Bob. We provide examples of correlations that actually require more general protocols based on higher-dimensional entangled states. This motivates us to investigate the set of correlations that can be obtained from communicating either a classical or a quantum $d$-dimensional system in the presence of an unlimited amount of entanglement. We show how such correlations can be characterized by a hierarchy of semidefinite programming relaxations by reducing the problem to a noncommutative polynomial optimization problem. We also introduce an alternative relaxation hierarchy based on the notion of informationally restricted quantum correlations, which, though it represents a strict (nonconverging) relaxation scheme, is less computationally demanding. As an application, we introduce device-independent tests of the dimension of classical and quantum systems that, in contrast to previous results, do not make the implicit assumption that Alice and Bob share no entanglement. We also establish several relations between communication with and without entanglement as resources for creating correlations.

The development and wide application of quantum technologies highly depend on the capacity of the communication channels distributing entanglement. Space-division multiplexing (SDM) enhances data channel transmission capacity in classical telecommunication and bears the potential to transfer the idea to quantum communication using current infrastructure. Here, we demonstrate a SDM of polarization-entangled photons over a 411 m long 19-core multicore fiber distributing polarization-entangled photon pairs through up to 12 channels simultaneously. The quality of the multiplexed transfer is evidenced by high polarization visibility and Clauser–Horne–Shimony–Holt (CHSH) Bell inequality violation for each pair of opposite cores. Our distribution scheme shows high stability over 24 h without any active polarization stabilization and can be effortlessly adapted to a higher number of channels. This technique increases the quantum-channel capacity and allows the reliable implementation of quantum networks of multiple users based on a single entangled photon pair source.

Machine learning (ML) is a promising approach for performing challenging quantum-information tasks such as device characterization, calibration, and control. ML models can train directly on the data produced by a quantum device while remaining agnostic to the quantum nature of the learning task. However, these generic models lack physical interpretability and usually require large datasets in order to learn accurately. Here we incorporate features of quantum mechanics in the design of our ML approach to characterize the dynamics of a quantum device and learn device parameters. This physics-inspired approach outperforms physics-agnostic recurrent neural networks trained on numerically generated and experimental data obtained from continuous weak measurement of a driven superconducting transmon qubit. This demonstration shows how leveraging domain knowledge improves the accuracy and efficiency of this characterization task, thus laying the groundwork for more scalable characterization techniques.

The controlled preparation of the excited state in a quantum emitter is a prerequisite for its usage as a single-photon source—a key building block for quantum technologies. In this paper, we propose a coherent excitation scheme using off-resonant pulses. In the usual Rabi scheme, these pulses would not lead to a significant occupation. This is overcome by using a frequency-modulated pulse to swing up the excited-state population. The same effect can be obtained using two pulses with different strong detunings of the same sign. We theoretically analyze the applicability of the scheme to a semiconductor quantum dot. In this case, the excitation is several millielectronvolts below the band gap, i.e., far away from the detection frequency, allowing for easy spectral filtering, and does not rely on any auxiliary particles such as phonons. Our scheme has the potential to lead to the generation of close-to-ideal photons.

The scalability of photonic implementations of fault-tolerant quantum computing based on Gottesman-Kitaev-Preskill (GKP) qubits is injured by the requirements of inline squeezing and reconfigurability of the linear optical network. In this work we propose a topologically error-corrected architecture that does away with these elements at no cost—in fact, at an advantage—to state preparation overheads. Our computer consists of three modules: a two-dimensional (2D) array of probabilistic sources of GKP states; a depth-four circuit of static beam splitters, phase shifters, and short delay lines; and a 2D array of homodyne detectors. The symmetry of our proposed circuit allows us to combine the effects of finite squeezing and uniform photon loss within the noise model, resulting in more comprehensive threshold estimates. These jumps over both architectural and analytical hurdles considerably expedite the construction of a photonic quantum computer.

We demonstrate a method that merges the quantum filter diagonalization (QFD) approach for hybrid quantum-classical solution of the time-independent electronic Schrödinger equation with a low-rank double factorization (DF) approach for the representation of the electronic Hamiltonian. In particular, we explore the use of a novel sparse “compressed” double factorization (C-DF) truncation of the Hamiltonian within the time-propagation elements of QFD, while retaining a similarly compressed but numerically converged double-factorized representation of the Hamiltonian for the operator expectation values needed in the QFD quantum matrix elements. The new C-DF method is found to provide substantial additional compression at any given accuracy metric over the traditional “explicit” double factorization approach. Together with significant circuit reduction optimizations and number-preserving postselection and echo-sequencing error mitigation strategies, the method is found to provide accurate predictions for low-lying eigenspectra in a number of representative molecular systems, while requiring reasonably short circuit depths and modest measurement costs. The method is demonstrated by experiments on noise-free simulators, simulations including models of decoherence and shot-noise, and real quantum hardware.

This tutorial aims at giving an introductory treatment of the circuit analysis of superconducting qubits, i.e., two-level systems in superconducting circuits. It also touches upon couplings between such qubits and how microwave driving and these couplings can be used for single- and two-qubit gates, as well as how to include noise when calculating the dynamics of the system. We also discuss higher-dimensional superconducting qudits. The tutorial is intended for new researchers with limited or no experience with the field but should be accessible to anyone with a bachelor’s degree in physics. The tutorial introduces the basic methods used in quantum circuit analysis, starting from a circuit diagram and ending with a quantized Hamiltonian, that may be truncated to the lowest levels. We provide examples of all the basic techniques throughout the discussion, while in the last part of the tutorial we discuss several of the most commonly used circuits for quantum-information applications. This includes both worked examples of single qubits and examples of how to analyze the coupling methods that allow multiqubit operations. In several detailed appendices, we provide the interested reader with an introduction to more advanced techniques for handling larger circuit designs.