We present an exact analytic expression for the Hong-Ou-Mandel manifold (HOMM) for any number of identical microring resonators (MRRs) in a linear chain. The HOMM is the higher-dimensional manifold of solutions for which the HOM effect is obtained; for the types of MRR systems investigated in this work, it is a one-dimensional curve. We investigate the extreme stability of this HOMM, showing that the HOM effect in linear arrays of MRRs is highly robust. We further use this expression to derive three figures of merit for the HOMM of linear chains of MRRs: the minimum MRR coupling value ${\tau }_c$, the curvature of the one-dimensional HOMM ${\overline{\xi }}_N$, and the 5% tolerance in the probability for complete destructive interference to occur on the HOMM $\delta {\tau }_N$. We promote these metrics to characterize the pros and cons of various linear chains of MRRs and inform design and fabrication.

The quantum instruction set (QIS) is defined as the quantum gates that are physically realizable by controlling the qubits in quantum hardware. Compiling quantum circuits into the product of the gates in a properly defined QIS is a fundamental step in quantum computing. We here propose the quantum variational instruction set (QuVIS) formed by flexibly designed multiqubit gates for higher speed and accuracy of quantum computing. The controlling of qubits for realizing the gates in a QuVIS is variationally achieved using the fine-grained time optimization algorithm. Significant reductions in both the error accumulation and time cost are demonstrated in realizing the swaps of multiple qubits and quantum Fourier transformations, compared with the compiling by a standard QIS such as the quantum microinstruction set (QuMIS, formed by several one- and two-qubit gates including one-qubit rotations and controlled-not gates). With the same requirement on quantum hardware, the time cost for QuVIS is reduced to less than one-half of that for QuMIS. Simultaneously, the error is suppressed algebraically as the depth of the compiled circuit is reduced. As a general compiling approach with high flexibility and efficiency, QuVIS can be defined for different quantum circuits and be adapted to the quantum hardware with different interactions.

A core principle of quantum theory is that nonorthogonal quantum states cannot be perfectly distinguished with single-shot measurements. However, it is possible to exclude a subset of nonorthogonal states without error in certain circumstances. Here we implement a quantum state elimination measurement which unambiguously rules out two of four pure, nonorthogonal quantum states—ideally without error and with unit success probability. This is a generalized quantum measurement with six outcomes, where each outcome corresponds to excluding a pair of states. Our experimental realization uses single photons, with information encoded in a four-dimensional state using optical path and polarization degrees of freedom. The prepared state is incorrectly ruled out up to $3.3\left(2\right)\%$ of the time.

X-ray free-electron lasers (XFELs) are now able to provide tunable pairs of intense sub-fs pulses in the soft x-ray regime, paving the way for time-resolved investigations of attosecond charge migration in molecules. However, the stochastic shot-to-shot variation of the XFEL pulses may degrade and eventually hide the observable features. We show by means of state-of-the-art calculations that the damping of the charge migration induced by 260 eV pulses in p-aminophenol due to the shot-to-shot variation of pulses generated at the Linac Coherent Light Source is negligible in comparison to the natural damping due to the intrinsic fluctuation of the initial molecular geometry. This result gives us confidence in the utility of XFEL sub-fs pulses for the measurement of charge migration and other ultrafast charge dynamics.

Air-plasma is a convenient and table-top source for the broadband and coherent terahertz (THz) wave generation. However, the lack of enhancement and frequency-selecting methods for this source impedes its wide applications. Dealing with this issue, here we demonstrate a unique methodology using two spatially crossed air-plasmas. THz yields can be significantly enhanced by a factor of 7 when the two temporally overlapped THz waves are in-phase or nearly eliminated when in antiphase. This enhancement could be interpreted by using the four-wave mixing model. Meanwhile, the spectral interference of the THz amplitudes is observed and reconstructed. It enables the frequency-selectable narrow-band THz output under the suitable time delays between the two air-plasmas. These results overcome the saturation and suppression of the plasma-based THz technology and emphasize that the coherence between the THz emissions from the two filaments is a prerequisite of our methodology. Our research provides an unusual approach in enhancing and engineering the THz wave and can help to gain more insight into the mechanism of plasma-based THz generation.

An ionizing particle passing through a liquid generates acoustic signals via local heat deposition. We delve into modeling such acoustic signals in the case of a single particle that interacts with the liquid electromagnetically in a generic way. We present a systematic way of introducing corrections due to viscosity using a perturbative approach so that our solution is valid at large distances from the interaction point. A computational simulation framework to perform the calculations described is also provided. The methodology developed is then applied to predict the acoustic signal of relativistic muons in various liquids as a toy model.

We present a methodology for the linear-response time-dependent density functional theory (LR-TDDFT) calculation of the dynamic density response function of warm dense matter in the adiabatic approximation that can be used with any available exchange-correlation (XC) functional across Jacob's ladder and across temperature regimes. The uniqueness of the presented approach is that it can go beyond the adiabatic local density approximation and adiabatic generalized gradient approximation while preserving the self-consistency between the Kohn-Sham (KS) response function and adiabatic XC kernel for extended systems. The key ingredient to the presented method is the combination of the adiabatic XC kernel from the direct perturbation approach with the macroscopic dynamic KS response from the standard LR-TDDFT method using KS orbitals. We demonstrate the application of the method for the example of warm dense hydrogen, for which we perform a detailed analysis of the KS density response function, the random phase approximation result, the total density response function, and of the adiabatic XC kernel. The analysis is performed using local density approximation, generalized gradient approximation, and meta-generalized gradient approximation level approximations for the XC effects. The presented method is directly applicable to disordered systems such as liquid metals, warm dense matter, and dense plasmas.

Topological properties of quantum systems are among the most intriguing emerging phenomena in condensed matter physics. A crucial property of topological systems is the symmetry-protected robustness towards local noise. Experiments have demonstrated topological phases of matter in various quantum systems. However, using the robustness of such modes to stabilize quantum correlations is still a highly sought-after milestone. In this work, we put forward a concept of using topological modes to stabilize fully entangled quantum states, and we demonstrate the stability of the entanglement with respect to parameter fluctuations. Specifically, we see that entanglement remains stable against parameter fluctuations in the topologically nontrivial regime, while entanglement in the trivial regime is highly susceptible to local noise. We supplement our scheme with an experimentally realistic and detailed proposal based on coupled superconducting resonators and qubits. Our proposal sets an approach for generating long-lived quantum modes with robustness towards disorder in the circuit parameters via a bottom-up experimental approach relying on easy-to-engineer building blocks.

Quantum computers have been widely speculated to offer significant advantages in obtaining the ground state of difficult Hamiltonian in chemistry and physics. In this work, we first propose a Lyapunov control-inspired strategy to accelerate the well-established imaginary-time method for ground-state preparation. We also dig for the source of acceleration of the imaginary-time process under Lyapunov control with theoretical understanding and dynamic process visualization. To make the method accessible in the noisy intermediate-scale quantum era, we further propose a variational form of the algorithm that could work with shallow quantum circuits. Through numerical experiments on a broad spectrum of realistic models, including molecular systems, 2D Heisenberg models, and Sherrington-Kirkpatrick models, we show that imaginary-time control may substantially accelerate the imaginary-time evolution for all systems and even generate orders of magnitude acceleration (suggesting order-of-magnitude acceleration) for challenging molecular Hamiltonians involving small energy gaps as impressive special cases. Finally, with a proper selection of the control Hamiltonian, the new variational quantum algorithm does not incur additional measurement costs compared to the original variational quantum imaginary-time algorithm.

We present an exact rate analysis for a secret key that can be shared among two parties employing a linear quantum repeater chain. One of our main motivations is to address the question whether simply placing quantum memories along a quantum communication channel can be beneficial in a realistic setting. The underlying model assumes deterministic entanglement swapping of single-spin quantum memories and it excludes probabilistic entanglement distillation, and thus two-way classical communication, on higher nesting levels. Within this framework, we identify the essential properties of any optimal repeater scheme: entanglement distribution in parallel, entanglement swapping as soon and parallel quantum storage as little as possible. While these features are obvious or trivial for the simplest repeater with one middle station, for more stations they cannot always be combined. We propose an optimal scheme including channel loss and memory dephasing, proving its optimality for the case of two stations and conjecturing it for the general case. In an even more realistic setting, we consider additional tools and parameters such as memory cutoffs, multiplexing, initial state and swapping gate fidelities, and finite link coupling efficiencies in order to identify potential regimes in memory-assisted quantum key distribution beyond one middle station that exceed the rates of the smallest quantum repeaters as well as those obtainable in all-optical schemes unassisted by stationary memory qubits and two-way classical communication. Our analytical treatment enables us to determine simultaneous trade-offs between various parameters, their scaling, and their influence on the performance ordering among different types of protocols, comparing two-photon interference after dual-rail qubit transmission with one-photon interference of single-rail qubits or, similarly, optical interference of coherent states. We find that for experimental parameter values that are highly demanding but not impossible (up to 10 s coherence time, about 80% link coupling, and state or gate infidelities in the regime of 1%–2%), one secret bit can be shared per second at a total channel loss budget of 157.6 dB, i.e. a total distance of 800 km for a fiber attenuation length of 22 km with repeater stations placed at every 100 km—a clear improvement over realistic twin-field or, much more pronouncedly, ideal point-to-point quantum key distribution at GHz clock rates.

Reinforcement learning (RL) is an important field of research in machine learning that is increasingly being applied to complex optimization problems in physics. In parallel, concepts from physics have contributed to important advances in RL with developments such as entropy-regularized RL. While these developments have led to advances in both fields, obtaining analytical solutions for optimization in entropy-regularized RL is currently an open problem. In this paper, we establish a mapping between entropy-regularized RL and research in nonequilibrium statistical mechanics focusing on Markovian processes conditioned on rare events. In the long-time limit, we apply approaches from large deviation theory to derive exact analytical results for the optimal policy and optimal dynamics in Markov decision process (MDP) models of reinforcement learning. The results obtained lead to an analytical and computational framework for entropy-regularized RL which is validated by simulations. The mapping established in this work connects current research in reinforcement learning and nonequilibrium statistical mechanics, thereby opening avenues for the application of analytical and computational approaches from one field to cutting-edge problems in the other.

The Landauer principle sets a fundamental thermodynamic constraint on the minimum amount of heat that must be dissipated to erase one logical bit of information through a quasistatically slow protocol. For finite time information erasure, the thermodynamic costs depend on the specific physical realization of the logical memory and how the information is erased. Here we treat the problem within the paradigm of a Brownian particle in a symmetric double-well potential. The two minima represent the two values of a logical bit, 0 and 1, and the particle's position is the current state of the memory. The erasure protocol is realized by applying an external time-dependent tilting force. We derive analytical tools to evaluate the work required to erase a classical bit of information in finite time via an arbitrary continuous erasure protocol, which is a relevant setting for practical applications. Importantly, our method is not restricted to the average work, but instead gives access to the full work distribution arising from many independent realizations of the erasure process. Using the common example of an erasure protocol that changes linearly with time acting on a double-parabolic potential, we explicitly calculate all relevant quantities and verify them numerically.

An efficient approach that considers a high-intensity twisted laser of moderate energy (few J) is proposed to generate collimated proton bunches with multi-10 MeV energies from a double-layer hydrogen target. Three-dimensional particle-in-cell simulations demonstrate the formation of a highly collimated and energetic ($\sim 40$ MeV) proton bunch, whose divergence is $\sim 6.5$ times smaller compared to the proton bunch driven by a Gaussian laser containing the same energy. Supported by theoretical modeling of relativistic self-focusing in near-critical plasma, we establish a regime that allows for consistent acceleration of high-energetic proton bunches with low divergence under experimentally feasible conditions for twisted drivers.