Quantum computing algorithms can be decomposed into a universal set of elementary one- and two-qubit gates. Different physical implementations of quantum computing, however, employ interactions that permit direct conditional dynamics on multiple qubits in a single step. In this work, we leverage quantum optimal control techniques to design single continuous laser pulses that implement multi-qubit controlled-phase and -swap (Fredkin) gates on Rydberg atom quantum processors. The identification of robust multi-qubit operations leads to reduced operation time and less decoherence, and the control field provides continuous protection of the atoms from environmental noise. Notably, we find that the controlled-SWAP (Fredkin) gate, implemented using this approach, achieves 99.88% fidelity while accounting for imperfections such as spontaneous emission, laser fluctuations, and Doppler dephasing.

Continuous measurements play a fundamental role in quantum experiments, yet understanding and extracting the maximal possible information in a continuous probe signal remains a significant challenge. In this work, we show that for a wide class of sensors, the quantum Fisher information bound can be saturated through a combined measurement of signals from the original sensor and a suitable system copy. We elucidate the physical mechanism of such a twin-field sensor (TFS) and study its performance across diverse implementations, ranging from two-level atoms to a hybrid quantum Rabi model. In all of these cases, we find that simple photon counting or homodyne detection saturates the theoretical quantum limit. We further prove that the TFS achieves the quantum limits for the joint sensing of pairs of parameters as quantified by the quantum Fisher information matrix.

A recent experiment demonstrated delayed superradiance from 88Sr atoms, which are coupled to a longitudinal mode of a cavity while being excited by a laser pulse propagating along a transversal direction [Nat. Commun. 15, 1084 (2024)]. A coherent picture of the atomic ensemble dynamics in this experiment requires complementary representations of the external driving dynamics and the superradiant dynamics. To complement previous analyses, we introduce these representations by considering in-phase and out-of-phase superpositions of transverse collective spin components of two atomic subensembles, and analyze the dynamics with the corresponding collective Dicke states and Bloch vectors. This approach also explains Ramsey spectroscopy experiments based on the delayed superradiance, and it may be employed to explore other intriguing phenomena, such as weak- to strong-coupling phase transitions and triggered superradiance.

Superradiant emission from long-lived excited states of an atomic ensemble confined in an optical cavity constitutes a practical source of light with narrow linewidth. In the pulsed regime, however, superradiance implies rapid emission and a broadening of the spectrum. Recent experiments have demonstrated constructive and destructive interference of superradiant emission by different strontium atomic transitions. In this article, we show that by modulating the atomic transition frequencies with a magnetic field, it is possible to control the release of the atomic excitation energy as a prolonged pulse or a train of superradiant pulses. By simulations, we show that heterodyne detection of the prolonged superradiance shows extremely sharp spectral features, which leads to significantly reduced frequency uncertainty and fluctuation.

The Swing-UP of the quantum EmitteR population (SUPER) two-color pulsed excitation scheme allows for robust and close to 100% excitation of a two-level quantum emitter using only red detuned light. We analyze the underlying counterintuitive dynamics using a full quantum input-output description of the in- and outgoing light pulses for the case of two coherent free-space input pulses at realistic photon numbers. At the microscopic level, the SUPER mechanism exhibits its nonlinear three-photon Raman-type character, leading to a net photon-number change of -2 in one mode and +1 in the other, as was first guessed from cavity-enhanced model descriptions at low photon numbers. We confirm that in free space, a sufficiently high pulse photon number, much larger than one, is required to achieve high-fidelity inversion. To treat the large coherent-state amplitudes (photon numbers) relevant for SUPER, we extend the quantum input-output formalism to include a cumulant expansion approach. With an interaction-picture formulation, the few exchanged photons that govern the nontrivial dynamics enable direct full-quantum calculations in truncated Hilbert spaces, including treatments in a displacement frame and for initial Fock-state pulses.

We derive parent Hamiltonians in terms of oscillator operators for multimode bosonic cat resource states. The construction separates a universal branch Hamiltonian, which confines each mode to the coherent-state support |⟩, and state-dependent constraint Hamiltonians, which select the desired correlations and symmetry sectors inside the resulting branch manifold. This framework progressively removes degeneracies in the low-energy manifold and yields explicit parent Hamiltonians for GHZ-, cluster-, and W-type cat states. In the large-|α| limit, the bosonic parent Hamiltonians reduce to stabilizer or exchange Hamiltonians acting on an effective logical-qubit basis. The present construction provides a direct bridge between coherent-state bosonic engineering and stabilizer-based quantum information processing.

There are processes that cannot generate entanglement but may, nevertheless, amplify entanglement already present in a system. Here, we show that a nonentangling operation can increase the Schmidt number of a quantum state only if it can generate entanglement with some nonzero probability. This is in stark contrast to the case where the parties of a quantum network are only able to control their joint state by local operations and classical communication (LOCC). There, being able to apply operations probabilistically (stochastic LOCC) does not increase the Schmidt number. Our findings show that certain nonentangling operations become entangling when specific measurement outcomes are selected. This naturally leads us to the class of stochastically nonentangling maps, which are those that cannot generate entanglement even probabilistically. Intrigued by this finding, we devise a Schmidt number for quantum channels that quantifies whether a channel can generate entanglement probabilistically. Moreover, we show that a channel is nonentangling if and only if its dual map is witness preserving-it takes entanglement witnesses to witnesses. Based on this finding, we derive inequalities whose violation signals that a process generates entanglement.

A single quantum pulse undergoing parametric amplification feeds into at most two pulses in the output. In this work, we present an efficient, analytical method for finding the quantum state of these output modes. Our method applies the amplification to the vacuum rather than to the input state, and subsequently applies a transformed version of the operator that creates the input state from vacuum. Given the input and output pulse mode functions, the method is analytical, and therefore computationally very efficient, and it can be readily generalized to multiple non-vacuum input modes. We exemplify the method by computing the output quantum states resulting from the input of a coherent, a Schrödinger cat, and a single photon input quantum state. We further employ the method to obtain the quantum state in one of the two output modes heralded upon detection of vacuum in the other, least populated, mode.

The finite speed of light of pulses implies propagation delays between the generation of light, the interaction with different elements along its path and the final detection at the output of networks and interferometers. We show that it is possible to take these delays into account with a theoretical method which evades quantization of the full continuum of field modes. We illustrate the use of this method by analyzing Ramsey excitation of an atom by a split and delayed quantum pulse.

Generating non-Gaussian states and converting them into traveling wave packets is crucial yet challenging for scalable, fault-tolerant quantum computing. We present a hardware-efficient approach that simultaneously achieves both tasks by combining an engineered nonlinear dissipation with a linear transmission loss from a superconducting circuit to a waveguide. This combination of dissipative channels leverages low-order interactions to induce a high-order nonlinearity, enabling deterministic emission of a wide range of non-Gaussian, error-correctable states, such as Schrödinger cat states, Gottesman-Kitaev-Preskill states, and pair-cat states. We identify experimental superconducting-circuit platforms and realistic parameter regimes for our proposal.

We explore a two-node, entanglement-enhanced sensor network for differential phase sensing that exploits decoherence-free subspaces to suppress common-mode noise, a primary limitation of many state-of-the-art quantum sensors. We identify a class of entangled states that, while not strictly optimal, achieve the same asymptotic sensitivity scaling as optimal states and can be prepared efficiently from initially unentangled atomic ensembles. Importantly, the preparation time decreases with increasing system size, which makes the states compatible with realistic noise processes in present-day quantum sensors that operate with large particle numbers but lack full error correction. We illustrate these ideas using two cavity-mediated preparation protocols: (i) coherent, unitary entanglement generation analogous to bosonic two-mode squeezing, yielding Heisenberg scaling, and (ii) dissipative preparation through collective emission into a shared cavity mode, providing a square-root improvement beyond the standard quantum limit. Numerical simulations show that both approaches remain effective at experimentally realistic cavity cooperativities, establishing a practical path toward scalable, quantum-enhanced differential phase sensing.

In this article, we propose that superradiant echoes can be achieved at room temperature by applying a laser illumination and a microwave Hahn echo sequence to a diamond with a high concentration of nitrogen-vacancy (NV) centers placed in a dielectric microwave cavity. We identify that the combined action of two microwave driving pulses and a free evolution imprints a frequency grating among NV spin sub-ensembles, and the multiple re-phasing of the grated spin sub-ensembles leads to multiple superradiant echoes through a collective coupling with the cavity. Furthermore, we show that the superradiant echoes can be actively tailored through the microwave pulses and the laser illumination by adjusting the grating parameters, and the multiple re-phasing dynamics is analogous to the one leading to superradiant beats in atomic optical clock systems. In the future, the spin sub-ensembles grating and the resulting echoes can be further optimized with dynamical decoupling, which might pave the way for applications in quantum sensing.

We present a scheme for implementing a high-fidelity non-linear phase shift on a photonic state. The scheme is based on repeated scattering off a two-level quantum emitter embedded in a chiral or one-sided waveguide. The waveguide is equipped with elements inducing second-order dispersion and temporal phase shifts, which effectively form a harmonic trap and confine the photon pulses to a Gaussian shape. The same quantum emitter can be used for each scattering, and thus, only one quantum emitter is needed in this scheme. To illustrate the application of our scheme for photonic quantum computing and quantum communication, we analyze the implementation of a control-Z gate and a deterministic Bell-state analyzer for photonic qubits. Through numerical optimization, we show that we can reach a control-Z gate fidelity of ℱ∼ 99.2% (ℱ∼ 96%) and a success probability of P_s ∼ 99.6 % (P_s∼ 98 %) for a Bell-state measurement with N=17 (N=5) scatterings.

Starting from an experimentally feasible atomic setup, we derive a stochastic Schr & ouml;dinger equation that captures the homodyne detection record of a strongly interacting system. Applying the rotating wave approximation to the linear atom-light coupling, we arrive at a reduced equation formulated solely in terms of atomic operators. In the appropriate limit, this equation converges to that of Gaussian continuous quantum measurement-revealing that the complexities of real-world detection can, under certain conditions, echo the elegance of idealized theory. To illustrate the utility of this framework, we numerically study the Bose-Hubbard model under continuous observation, showing that time-domain analysis of the measurement signal uncovers rich dynamical features, including quantum jumps, that are obscured in ensemble-averaged spectral data.

We derive a stochastic Schrödinger equation that describes the homodyne measurement record of a strongly interacting atomic system. We derive this equation for a general system, where we use the rotating wave approximation in the linear atom-light interaction part, and the resulting equation is expressed in terms of the atomic operators only. Weak measurements are theoretically described in terms of positive operator-valued measures. Among different weak measurement schemes, several earlier references studied the Gaussian quantum continuous measurement in detail. Here we consider a homodyne measurement setup. We then demonstrate that the derived equation for this setup in the appropriate limit is the same as the one obtained while performing a Gaussian quantum continuous measurement.

Artificial quantum systems with synthetic dimensions enable exploring novel quantum phenomena difficult to create in conventional materials. These synthetic degrees of freedom increase the system's dimensionality without altering its physical structure, accessing higher-dimensional physics in lower-dimensional setups. However, synthetic quantum systems often suffer from intrinsic disorder, causing rapid decoherence that limits scalability, a major obstacle in quantum information science. Here, we show that introducing just a few long-range interactions can mitigate decoherence, creating persistent collective coherence in highly symmetric collective excited states. We term this universal phenomenon "supercoherence" and show its exceptional robustness against disorder up to a dynamical phase transition at critical interaction strength and disorder. Supercoherence stabilizes not only coherence but also all other quantum properties of the states, challenging traditional views on the inevitability of decoherence in disordered interacting quantum systems and suggesting new opportunities for quantum memory and information processing.

The density matrix yields probabilistic information about the outcome of measurements on a quantum system, but it does not distinguish between classical randomness in the preparation of the system and entanglement with its environment. Here, we show that retrodiction, employing both prior and posterior knowledge, gives rise to conditional probabilities for measurements on a single system, that can witness if it is part of a larger composite system. The degree of certainty with which one can retrodict the outcomes of multiple measurements on a system can witness both the existence and the quantitative nature of its entanglement with the environment.

Nitrogen-vacancy (NV) centers in diamond have been successfully coupled to various optical structures to enhance their radiation by the Purcell effect. The participation of many NV centers in these studies may naturally lead to cooperative emission and superradiance, and our recent experimental study with a diamond membrane in a fiber-based ultranarrow optical cavity demonstrated nonlinear radiation and fast photon bunching as signatures of the collective effects. In this theoretical article, we go beyond the simple model used in the previous study to address more phenomena, such as the appearance of bunching shoulders in second-order correlation function, Rabi splitting in steady-state spectrum, and population dynamics on excited Dicke states, which for moderate pumping explains the observed collective effects. Overall, our results can guide further experiments with NV centers, and they are also relevant for other solid-state color centers, such as silicon-vacancy centers in diamond and silicon carbide, boron-vacancy centers, and carbon-related centers in hexagonal boron nitride.

In this article, we present a stochastic collective density-matrix approach to numerically study the conditional dynamics of large systems of identical particles in the presence of individual and collective dissipation, as described by stochastic master equations. To illustrate the application potential of the approach, we use it to study the conditional spin squeezing of hundreds of identical atoms in a bad optical cavity subject to homodyne detection. We demonstrate that the conditional spin squeezing can be vividly illustrated by a Gaussian-like distribution on the quantum states of the atomic ensemble, and we examine the influence of various processes, such as the individual atomic dissipation, on this distribution. In the future, the present approach can be used to reveal measurement effects of multiple-level atoms system, to explore generation of exotic nonclassical states, such as cat states, and to gauge approximate approaches, such as the stochastic mean-field approach.

We present a hardware-efficient approach to prepare single mode travelling wave packets in non-Gaussian bosonic states with a superconducting circuit platform. Such states enable secure deterministic quantum communication between distant quantum processor units. Rather than first producing the non-Gaussian states in a cavity mode by a nonlinear process and subsequently releasing it to a waveguide, we propose and analyze a scheme that applies a combination of linear and nonlinear interactions and losses to form and emit the states in wave packets, controlled by the coherent excitation of the system. The system is subject to a non-linear anti-Hermitian Hamiltonian of high order due to losses of lower order, and our proposal enables efficient and deterministic creation of propagating two- and four-component cat states, grid states, and entangled pair-cat states.