By exploring a different function of plasma regulated by nonlinear waves and their transient bifurcations, we propose a boosting scheme for an object consisting of pure solid hydrogen medium irradiated by spatiotemporally designed high-intensity lasers to nearly the speed of light. This is achieved by two processes. One is the slow process via the formation of the shocklike structure in the medium and subsequent adiabatic compression exceeding 20 times the solid density to a width narrower than the local Debye length. This results in the frozen-in dynamics of the plasma regulated by the parameter ${\rho }_e/{\gamma }_e$ ([electron charge density]/[electron relativistic factor]), which tends to be spatially less sensitive through the cancellation between laser ponderomotive and relativistic nonlinearities in a highly nonlinear regime. The other is the fast process of the transient bifurcation of the shock to a soliton leading to an explosion, which splits the structure into two shock structures propagating in opposite directions, i.e., one is boosted forward as the reaction of the other ejected backward as a fuel. The entire sequence of the processes causing compression and explosion, leading to the acceleration of bulk medium, are found to be highly stable and then robust without causing any serious instability even including the nonuniformity of laser intensity associated with a tight laser focal spot.

Recent studies of genotype-phenotype maps have reported universally enhanced phenotypic robustness to genotype mutations, a feature essential to evolution. Virtually all of these studies make a simplifying assumption that each genotype—represented as a sequence—maps deterministically to a single phenotype, such as a discrete structure. Here we introduce probabilistic genotype-phenotype (PrGP) maps, where each genotype maps to a vector of phenotype probabilities, as a more realistic and universal language for investigating robustness in a variety of physical, biological, and computational systems. We study three model systems to show that PrGP maps offer a generalized framework which can handle uncertainty emerging from various physical sources: (1) thermal fluctuation in RNA folding, (2) external field disorder in the spin-glass ground state search problem, and (3) superposition and entanglement in quantum circuits, which are realized experimentally on IBM quantum computers. In all three cases, we observe a biphasic robustness scaling which is enhanced relative to random expectation for more frequent phenotypes and approaches random expectation for less frequent phenotypes. We derive an analytical theory for the behavior of PrGP robustness, and we demonstrate that the theory is highly predictive of empirical robustness.

We address the challenge of incorporating encoded quantum memories into an exact secret key rate analysis for small and intermediate-scale quantum repeaters. To this end, we introduce the check matrix model and quantify the resilience of stabilizer codes of up to eleven qubits against Pauli noise, obtaining analytical expressions for effective logical error probabilities. Generally, we find that the five-qubit and Steane codes either outperform more complex, larger codes in the experimentally relevant parameter regimes or have a lower resource overhead. Subsequently, we apply our results to calculate lower bounds on the asymptotic secret key rate in memory-corrected quantum repeaters when using the five-qubit or Steane codes on the memory qubits. The five-qubit code drastically increases the effective memory coherence time, reducing a phase flip probability of $1\%$ to $0.001\%$ when employing an error syndrome identification adapted to the quantum noise channel. Furthermore, it mitigates the impact of faulty Bell state measurements and imperfect state preparation, lowering the minimally required depolarization parameter for nonzero secret key rates in an eight-segment repeater from $98.4\%$ to $96.4\%$. As a result, the memory-corrected quantum repeater can often generate secret keys in experimental parameter regimes where the unencoded repeater fails to produce a secret key. In an eight-segment repeater, one can even achieve nonvanishing secret key rates up to distances of 2000 km for memory coherence times of $t_c=10$ s or less using multiplexing. Assuming a zero-distance link-coupling efficiency $p_0=0.7$, a depolarization parameter $\mu =0.99, t_c=10$ s, and an 800 km total repeater length, we obtain a secret key rate of 4.85 Hz, beating both the unencoded repeater that provides 1.25 Hz and ideal twin-field quantum key distribution with 0.71 Hz at GHz clock rates.

Understanding the physical mechanisms of brain functions has always been a challenging problem in the fields of nonlinear dynamics and network science. A promising approach to address this problem is by studying signal propagation on brain cognitive networks. So far, in the context of signal propagation, some progress has been achieved on complex networks, especially on the Caenorhabditis elegans network, but little attention has been paid to the empirical cognitive networks of the human brain, which are the networks responsible for cognitive tasks. Here we study how neural firings are propagated in the empirical cognitive networks of human brain. We find that the firing propagation can be seriously influenced by both the global topology of the network and the local topology of the source node. There is an optimal range of coupling strength related to synchronization for each source node, and multiple source nodes favor firing propagation. Further, we show that peripheral nodes of a network may have stronger ability of firing propagation than hub nodes. Interestingly, a remote firing propagation is observed, where firings are not propagated in a sequential rule, but propagated to farther distant nodes without the firings of intermediate nodes. A detailed theoretical analysis is provided to explain both the firing propagation and remote firing propagation.

In fault-tolerant quantum computing, quantum algorithms are implemented through quantum circuits capable of error correction. These circuits are typically constructed based on specific quantum error correction codes, with consideration given to the characteristics of the underlying physical platforms. Optimizing these circuits within the constraints of today's quantum computing technologies, particularly in terms of error rates, qubit counts, and network topologies, holds substantial implications for the feasibility of quantum applications in the near future. This paper presents a toolkit for designing and analyzing fault-tolerant quantum circuits. We introduce a framework for representing stabilizer circuits using classical low-density parity-check (LDPC) codes. Each codeword in the representation corresponds to a quantum-mechanical equation regarding the circuit, formalizing the correlations utilized in parity checks and delineating logical operations within the circuit. Consequently, the LDPC code provides a means of quantifying fault tolerance and verifying logical operations. We outline the procedure for generating LDPC codes from circuits using the Tanner graph notation, alongside proposing graph-theory tools for constructing fault-tolerant quantum circuits from classical LDPC codes. These findings offer a systematic approach to applying classical error correction techniques in optimizing existing fault-tolerant protocols and developing new ones. As an example, we develop a resource-efficient scheme for universal fault-tolerant quantum computing on hypergraph product codes based on the LDPC representation.

Two-dimensional Mott insulators host antiferromagnetic (AFM) correlations that are predicted to enhance the attractive interaction between empty (holons) and doubly occupied (doublons) sites, creating a novel pathway for exciton formation. However, experimental confirmation of this spin-mediated binding mechanism remains elusive. Leveraging the distinct magnetic critical properties of the Mott antiferromagnets ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ and ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$, we show using time-resolved THz spectroscopy that excitons exist only at temperatures below where short-range AFM correlation develops. The excitons remain stable up to photodoping densities approaching the predicted excitonic Mott insulator-to-metal transition, revealing a unique robustness against screening. Our results establish the viability of spin-bound excitons and introduce opportunities for excitonic control through magnetic degrees of freedom.

The high motility of synaptic weights raises the question of how the brain can retain its functionality in the face of constant synaptic remodeling. Here we used the whisker system of rats and mice to study the interplay between synaptic plasticity (motility) and the transmission of sensory signals downstream. Rats and mice probe their surroundings by rhythmically moving their whiskers back and forth. The azimuthal position of a whisker can be estimated from the activity of whisking neurons that respond selectively to a preferred phase along the whisking cycle. These preferred phases are widely distributed on the ring. However, simple models for the transmission of the whisking signal downstream predict a distribution of preferred phases that is an order of magnitude narrower than empirically observed. Here, we suggest that synaptic plasticity in the form of spike-timing-dependent plasticity (STDP) may provide a solution to this conundrum. This hypothesis is addressed in the framework of a modeling study that investigated the STDP dynamics in a population of synapses that propagates the whisking signal downstream. The findings showed that, for a wide range of parameters, STDP dynamics do not relax to a fixed point. As a result, the preferred phases of downstream neurons drift in time at a nonuniform velocity, which in turn induces a nonuniform distribution of the preferred phases of the downstream population. This demonstrates how functionality, in terms of the distribution of preferred phases, can be retained not simply despite, but because of constant synaptic motility. Our analysis leads to several key empirical predictions to test this hypothesis.

Tensor network algorithms can efficiently simulate complex quantum many-body systems by utilizing knowledge of their structure and entanglement. These methodologies have been adapted recently for solving the Navier-Stokes equations, which describe a spectrum of fluid phenomena, from the aerodynamics of vehicles to weather patterns. Within this quantum-inspired paradigm, velocity is encoded as matrix product states (MPS), effectively harnessing the analogy between interscale correlations of fluid dynamics and entanglement in quantum many-body physics. This particular tensor structure is also called quantics tensor train (QTT). By utilizing NVIDIA's cuQuantum library to perform parallel tensor computations on GPUs, our adaptation speeds up simulations by up to 12.1 times. This allows us to study the algorithm in terms of its applicability, scalability, and performance. By simulating two qualitatively different but commonly encountered 2D flow problems at high Reynolds numbers up to $1\times {10}^7$ using a fourth-order time stepping scheme, we find that the algorithm has a potential advantage over direct numerical simulations in the turbulent regime as the requirements for grid resolution increase drastically. In addition, we derive the scaling $\chi =\mathcal{O}(\text{poly}(1/\epsilon ))$ for the maximum bond dimension $\chi$ of MPS representing turbulent flow fields, with an error $\epsilon$, based on the spectral distribution of turbulent kinetic energy. Our findings motivate further exploration of related quantum algorithms and other tensor network methods.

We introduce a class of imperfection-protected nonlinear isolators designed to operate at exceptional point degeneracies (EPDs) of the Bloch modes of periodic photonic structures. These Bloch EPDs are responsible for slow light and the emergence of a scattering frozen mode regime (FMR). When a weak spectral asymmetry is introduced, the group velocity in their proximity varies sharply, boosting the directional nature of the nonlinear interactions and leading to extreme isolation.

We investigate the electrical transport properties of the minivalley polarized state proposed recently in slightly doped Bernal bilayer graphene (BLG) in large electric displacement fields. By minimizing the Hartree-Fock (HF) energy functional, we first confirm the appearance of minivalley polarized phase. At the low carrier doping regime, the one-pocket state will be stabilized where only one of the trigonal-wrapping-induced Fermi pockets near the atomic-valley center is filled. Then we study the electrical transport of the one-pocket state by solving the Boltzmann equation. We find that the valley polarization could be easily flopped by an in-plane electrical field, which will lead to hysteresis loop in the direct current (DC) $I\text{−}V$ curves. Such irreversible current responses in the DC limit will directly induce strong nonlinear and nonreciprocal alternating current (AC) responses, which has been already observed in the recent experiments on BLG.

It is generally accepted that the role of quantum decoherence is to spoil the quantum superpositions and to yield the emergence of the classical behaviors from quantum mechanics. Contrary to the common knowledge of decoherence, we propose a scheme to generate a steady-state bright source of strongly sub-Poissonian squeezed light using the environmentally induced decoherence. The disappearance of the process of decoherence disables the generation of the squeezed state of the combination modes, while the presence of the decoherence results in the strongly nonclassical light source at the sub-shot-noise level and even near-perfect sub-Poissonian squeezed state of light. This excludes the use of the paradigm that the good insulation of a quantum system from its surrounding environment is highly desirable to explore its quantum property and fuel the growth of quantum information science. The interactions with the atom make no contribution to the preparation of squeezed light. These counterintuitive results are originated from the intrinsic quantum reservoir in the dressed-atom combination mode picture, which may open the door to exploring high levels of squeezing induced by the decoherence in the stationary regime.

We explore the interplay between symmetry and randomness in quantum information. Adopting a geometric approach, we consider states as $H$ equivalent if related by a symmetry transformation characterized by the group $H$. We then introduce the Haar measure on the homogeneous space $\mathbb{U}/H$, characterizing true randomness for $H$-equivalent systems. While this mathematical machinery is well studied by mathematicians, it has seen limited application in quantum information. Our work addresses this gap, providing an example of utilizing homogeneous spaces to characterize symmetry in quantum information. This is followed by a discussion of approximations of true randomness, commencing with $t$-wise independent approximations and defining $t$ designs on $\mathbb{U}/H$ and $H$-equivalent states. Transitioning further, we explore pseudorandomness, defining pseudorandom unitaries and states within homogeneous spaces. Finally, as a practical demonstration of our findings, we study the expressibility of quantum machine learning Ansätze in homogeneous spaces. Our work provides a fresh perspective on the relationship between randomness and symmetry in the quantum world.

The volunteer's dilemma is a well-known game in game theory that models the conflict players face when deciding whether to volunteer for a collective benefit, knowing that volunteering incurs a personal cost. In this work we introduce a quantum variant of the classical volunteer's dilemma, generalizing it by allowing players to utilize quantum strategies. Employing the Eisert-Wilkens-Lewenstein quantization framework, we analyze a multiplayer quantum volunteer's dilemma scenario with an arbitrary number of players, where the cost of volunteering is shared equally among the volunteers. We derive analytical expressions for the players' expected payoffs and demonstrate the quantum game's advantage over the classical game. In particular, we prove that the quantum volunteer's dilemma possesses symmetric Nash equilibria with larger expected payoffs compared to the unique symmetric Nash equilibrium of the classical game, wherein players use mixed strategies. Furthermore, we show that the quantum Nash equilibria we identify are Pareto optimal. Our findings reveal distinct dynamics in volunteer's dilemma scenarios when players adhere to quantum rules, underscoring a strategic advantage of decision making in quantum settings.

Magic-angle twisted bilayer graphene (MATBG) presents a fascinating platform for investigating the effects of electron interactions in topological flat bands. The Bistritzer-MacDonald (BM) model provides a simplified quantitative description of the flat bands. Introducing long-range Coulomb interactions leads to an interacting BM (IBM) Hamiltonian, a momentum-space continuum description which offers a very natural starting point for many-body studies of MATBG. Accurate and reliable many-body computations in the IBM model are challenging, however, and have been limited mostly to special fillings or smaller lattice sizes. We employ a state-of-the-art auxiliary-field quantum Monte Carlo (AFQMC) method to study the IBM model, which constrains the sign problem to enable accurate treatment of large system sizes. We determine ground-state properties and quantify errors compared to mean-field theory calculations. Our calculations identify correlated metal states and their competition with the insulating Kramers intervalley-coherent state at both half-filling and charge neutrality. Additionally, we investigate one- and three-quarter fillings, and examine the effect of many-body corrections beyond single Slater determinant solutions. We discuss the effect that details of the IBM Hamiltonian have on the results, including different forms of double-counting corrections, and the need to establish and precisely specify many-body Hamiltonians to allow more direct and quantitative comparisons with experiments in MATBG.

A class of signed joint probability measures for $n$ arbitrary quantum observables is derived and studied based on quasicharacteristic functions with symmetrized operator orderings of Margenau-Hill type. It is shown that the Wigner distribution associated with these observables can be rigorously approximated by such measures. These measures are given by affine combinations of Dirac delta distributions supported over the finite spectral range of the quantum observables and give the correct probability marginals when coarse-grained along any principal axis. We specialize to bivariate quasiprobability distributions for the spin measurements of spin-$1/2$ particles and derive their closed-form expressions. As a side result, we point out a connection between the convergence of these particle approximations and the Mehler-Heine theorem. Finally, we interpret the supports of these quasiprobability distributions in terms of repeated thought experiments.

We present an iterative optimal control method of quantum systems, aimed at an implementation of a desired operation with optimal fidelity. The update step of the method is based on the linear response of the fidelity to the control operators, and its projection onto the mode functions of the corresponding operator. Our method extends methods such as gradient-ascent pulse engineering (GRAPE) and variational quantum algorithms, by determining the fidelity gradient in a hyperparameter-free manner, and using it for a multiparameter update, capitalizing on the multimode overlap of the perturbation and the mode functions. This directly reduces the number of dynamical trajectories that need to be evaluated in order to update a set of parameters. We demonstrate this approach, and compare it to the standard GRAPE algorithm, for the example of a quantum gate on two qubits, demonstrating a clear improvement in convergence and optimal fidelity of the generated protocol.

We investigate the prospect of using ultracold alkali diatomic molecules to implement many-body quantum systems with $\mathrm{SU}\left(N\right)$ symmetry. Experimentally accessible molecules offer large $N$ for both bosonic and fermionic systems, with both attractive and repulsive interactions. We carry out coupled-channel scattering calculations on pairs of NaK, NaRb, and NaCs molecules that are shielded from destructive collisions with static electric fields. We develop new methods to handle the very large basis sets required to include nuclear spins. We show that all the molecules studied have the properties required for $\mathrm{SU}\left(N\right)$ symmetry: the collisions are principally elastic, and the scattering lengths depend only weakly on the spin states of the molecules. The rates of spin-changing inelastic collisions are very low. We develop and test a semiclassical model of the spin dependence and find that it performs well.