The design of a four-dimensional toric code is explored with the goal of finding a lattice capable of implementing a logical $\mathsf{CCCZ}$ gate transversally. The established lattice is the octaplex tessellation, which is a regular tessellation of four-dimensional Euclidean space whose underlying 4-cell is the octaplex, or hyperdiamond. This differs from the conventional 4D toric code lattice, based on the hypercubic tessellation, which is symmetric with respect to logical $X$ and $Z$ and only allows for the implementation of a transversal Clifford gate. This paper further develops the established connection between topological dimension and transversal gates in the Clifford hierarchy, generalizing the known designs for the implementation of transversal $\mathsf{CZ}$ and $\mathsf{CCZ}$ in two and three dimensions, respectively.

We present an effective field theory approach to the topological response of Floquet systems with symmetry group $G$. This is achieved by introducing a background $G$ gauge field in the Schwinger-Keldysh formalism, which is suitable for far from equilibrium systems. We carry out this program for chiral topological Floquet systems (anomalous Floquet-Anderson insulators) in two spatial dimensions and the group cohomology models of topological Floquet unitaries. These response actions serve as many-body topological invariants for topological Floquet unitaries. The effective action approach also leads us to propose topological response functions that were not considered before. For a particular family of models, we find that our response theory captures a symmetry protected version of the chiral unitary index.

Time-dependent light-matter interactions are a widespread means by which to describe controllable experimental operations. They can be viewed as an approximation in which a third system, the control system, is treated as external within the Hamiltonian. We demonstrate that this results in nonequivalence between gauges. We provide a physical example in which each different nonequivalent model coincides with a gauge-invariant description applied in a different experimental situation. The qualitative final-time predictions obtained from these models, including entanglement and photon number, depend on the gauge within which the time-dependent coupling assumption is made. This occurs whenever the interaction switching is sufficiently strong and nonadiabatic even if the coupling vanishes at the preparation and measurement stages of the protocol, at which times the subsystems are unique and experimentally addressable.

Using the Feynman-Kac formula, a work fluctuation theorem for a Brownian particle in a nonconfining potential, e.g., a potential well with finite depth, is derived. The theorem yields an inequality that puts a lower bound on the average work needed to change the potential in time. In comparison to the Jarzynski equality, which holds for confining potentials, an additional term describing a form of energy related to the never-ending diffusive expansion appears.

We investigate the phase diagrams of a one-dimensional lattice model of fermions and of a spin chain with interactions extending up to next-nearest-neighbor range. In particular, we investigate the appearance of regions with dominant pairing physics in the presence of nearest-neighbor and next-nearest-neighbor interactions. Our analysis is based on analytical calculations in the classical limit, bosonization techniques and large-scale density-matrix renormalization group numerical simulations. The phase diagram, which is investigated in all relevant filling regimes, displays a remarkably rich collection of phases, including Luttinger liquids, phase separation, charge-density waves, bond-order phases, and exotic cluster Luttinger liquids with paired particles. In relation with recent studies, we show several emergent transition lines with a central charge $c=3/2$ between the Luttinger liquid and the cluster Luttinger liquid phases. These results could be experimentally investigated using highly tunable quantum simulators.

An array of ultracold neutral atoms held in optical microtraps is a promising platform for quantum computation. One of the major bottlenecks of this platform is the weak coupling strength between adjacent atoms, which limits the speed of two-qubit gates. Here, we present a method to perform a fast universal $\sqrt{\text{SWAP}}$ gate with fermionic atoms that interact through a short-range potential. The basic idea of the gate is to release the atoms into a harmonic potential positioned in between the two atoms. By properly tailoring the interaction parameter, the collision process between the atoms generates entanglement and yields the desired gate. We prove analytically that in the limit of broad atomic wave packets, the fidelity of the gate approaches unity. We demonstrate numerically that with typical experimental parameters, our gate can operate on a microsecond timescale and achieves a fidelity higher than 0.998. Moreover, the gate duration is independent of the initial distance between the atoms. A gate with such features is an important milestone towards all-to-all connectivity and fault tolerance in quantum computation with neutral atoms.

We report an observation of magneto-oscillations in transmittance of the circularly polarized microwave radiation through the high-mobility two-dimensional electron system hosted by a GaAs quantum well. The oscillations reflect an enhanced absorption of radiation at high harmonics of the cyclotron resonance and follow simultaneously measured microwave-induced resistance oscillations (MIRO) in the DC transport. While the relative amplitude (up to 1%) of the transmittance oscillations appears to be small, they represent a significant (greater than 50%) modulation of the absorption coefficient. The analysis of obtained results demonstrates that the low-$B$ decay, magnitude, and polarization dependence of the transmittance oscillations accurately follow the theory describing photon-assisted scattering between distant disorder-broadened Landau levels. The extracted sample parameters describe reasonably well the concurrently measured MIRO. Our results provide insight into the MIRO polarization immunity problem and demonstrate that high-precision transmission measurements can be a sensitive probe of high-frequency dissipative effects in high-mobility systems.

Using a spectrally resolved electron interferometry technique, we measure photoionization time delays between the $3s$ and $3p$ subshells of argon over a large 34-eV energy range covering the Cooper minima in both subshells. The observed strong variations of the $3s-3p$ delay difference, including a sign change, are well reproduced by theoretical calculations using the two-photon two-color random-phase approximation with exchange. Strong shake-up channels lead to photoelectrons spectrally overlapping with those emitted from the $3s$ subshell. These channels need to be included in our analysis to reproduce the experimental data. Our measurements provide a benchmark for multielectronic theoretical models aiming at an accurate description of interchannel correlation.

We present a proposal for the realization of entanglement Hamiltonians in one-dimensional critical spin systems with strongly interacting cold atoms. Our approach is based on the notion that the entanglement spectrum of such systems can be realized with a physical Hamiltonian containing a set of position-dependent couplings. We focus on reproducing the universal ratios of the entanglement spectrum for systems in two different geometries: a harmonic trap, which corresponds to a partition embedded in an infinite system, and a linear potential, which reproduces the properties of a half partition with open boundary conditions. Our results demonstrate the possibility of measuring the entanglement spectra of the Heisenberg and XX models in a realistic cold-atom experimental setting by simply using gravity and standard trapping techniques.

We propose to dynamically control the conductivity of a Josephson junction composed of two weakly coupled one-dimensional condensates of ultracold atoms. A current is induced by a periodically modulated potential difference between the condensates, giving access to the conductivity of the junction. By using parametric driving of the tunneling energy, we demonstrate that the low-frequency conductivity of the junction can be enhanced or suppressed, depending on the choice of the driving frequency. The experimental realization of this proposal provides a quantum simulation of optically enhanced superconductivity in pump-probe experiments of high-temperature superconductors.

Qubit reset is a key task in the operation of quantum devices which, for many quantum hardware platforms, presently limits device clock speed. While it is known that coupling the qubit to an ancilla on demand allows for the fastest qubit reset, the limits on reset accuracy and speed due to the choice of ancilla have not yet been identified—despite the great flexibility in device design for most quantum hardware platforms. Here, we derive bounds on qubit reset in terms of maximum fidelity and minimum time, assuming control over the qubit and no control over the ancilla. For two-level ancillas, we find a provably time-optimal protocol which consists of purity exchange between qubit and ancilla brought into resonance. The globally minimal time can only be realized for specific choices of coupling and control which we identify. When increasing the size of the ancilla Hilbert space, the maximally achievable fidelity increases, whereas the reset time remains constant. Our results translate into device design principles for realizing, in a given quantum architecture, the fastest and most accurate protocol for qubit reset.

Nonpolar materials are increasingly employed as media for electron transfer, particularly in applications related to solar energy conversion. What should be the mechanism of activation for electron tunneling in the absence of rotating permanent dipoles considered in standard theories is not clear. We suggest that compression and decompression (density) fluctuations shifting positions of polarizable molecules of the medium is the mechanism for radiationless transitions. These fluctuations affect the induction interactions between the medium induced dipoles and the localized electron (induction forces). Solvent reorganization energy must be a signature of such fluctuations, but it has never been directly measured for electron transfer in nonpolar media. Here, absorption and emission spectra of a charge-transfer complex are analyzed as functions of temperature in cyclohexane. Significant reorganization energies, 0.2–0.5 eV, are found. They strongly differ between the ground and photoexcited charge-transfer states in violation of fluctuation-dissipation relations establishing the basis for modern theories of electron transfer. The reorganization energies are decaying functions of temperature, also in violation of the macroscopic fluctuation-dissipation relations.

It is shown that measurement uncertainties can be observed directly by evaluating the feedback compensation of the decoherence induced by the measured system on a probe qubit in a weak interaction occurring between state preparation and measurement. The uncompensated decoherence is described by the measurement uncertainties introduced by Ozawa in Phys. Rev. A 67, 042105 (2003), confirming the empirical validity of measurement theories that combine the initial information of the input state with the additional information provided by each measurement outcome.

Experimental results and simulation models show that crystals might play a relevant role for the development of new generations of high-energy and high-intensity particle accelerators and might disclose innovative possibilities at existing ones. In this paper we describe the most advanced manufacturing techniques of crystals suitable for operations at ultrahigh energy and ultrahigh intensity particle accelerators, reporting as an example of potential application the collimation of the particle beams circulating in the Large Hadron Collider at CERN, which will be upgraded through the addition of bent crystals in the frame of the High Luminosity Large Hadron Collider project.

Neural avalanches are collective firings of neurons that exhibit emergent scale-free behavior. Understanding the nature and distribution of these avalanches is an important element in understanding how the brain functions. We study a model of neural avalanches for which the dynamics are governed by neutral theory. The neural avalanches are defined using causal connections between the firing neurons. We analyze the scaling of causal neural avalanches as the critical point is approached from the absorbing phase. By using cluster analysis tools from percolation theory, we characterize the critical properties of the neural avalanches. We identify the tuning parameters consistent with experiments. The scaling hypothesis provides a unified explanation of the power laws which characterize the critical point. The critical exponents characterizing the avalanche distributions and divergence of the response functions are consistent with the predictions of the scaling hypothesis. We use a universal scaling function for the avalanche profile to find that the firing rates for avalanches of different durations show data collapse after appropriate rescaling. We also find data collapse for the avalanche distribution functions, which is stronger evidence of criticality than just the existence of power laws. Critical slowing-down and power-law relaxation of avalanches is observed as the system is tuned to its critical point. We discuss how our results motivate future empirical studies of criticality in the brain.

The violation of the Floquet version of the eigenstate thermalization hypothesis is rigorously discussed with realistic Hamiltonians. Our model is based on the PXP-type interactions without disorder. We rigorously prove the existence of many-body scar states in the Floquet eigenstates that appear only at specific periods of driving by showing the explicit expressions of the wave functions. This is equivalently the first rigorous proof of the breakdown of the Floquet eigenstate thermalization hypothesis. Through the exact expression of the scar states, the underlying physical mechanism is clarified. Using the underlying mechanism, various driven Hamiltonians with Floquet-scar states can be systematically engineered. We then discuss Floquet-scar states that can be checked through time evolution of observables in a chain of Rydberg atoms.

In $d>2$ dimensional, homogeneous threshold models discontinuous transition occur, but the mean-field solution provides $1/t$ power-law activity decay and other power laws, and thus it is called mixed-order or hybrid type. It has recently been shown that the introduction of quenched disorder rounds the discontinuity and second-order phase transition and Griffiths phases appear. Here we provide numerical evidence that even in case of high graph dimensional hierarchical modular networks a Griffiths phase in the $K=2$ threshold model is present below the hybrid phase transition. This is due to the fragmentation of the activity propagation by modules, which are connected via single links. This provides a widespread mechanism in the case of the threshold type of heterogeneous systems, modeling the brain, or epidemics for the occurrence of dynamical criticality in extended Griffiths phase parameter spaces. We investigate this in synthetic modular networks with and without inhibitory links as well as in the presence of refractory states.

We studied the ferrimagnet ${\mathrm{La}}_5{\mathrm{Mo}}_4{\mathrm{O}}_{16}$ with Mo ions on quasisquare lattices both experimentally and theoretically. We found that in addition to the antiferromagnetic ordering at $T_N=200$ K, a magnetic phase transition into a ferrimagnetic phase occurs at $T_{s1}=60$ K, which is caused by the orbital ordering of the Mo $4d$ states. We also found that the relatively small size of ferrimagnetic domains despite the large Ising anisotropy of the Mo spins are formed below $T_{s1}$, which are responsible for the relaxation behavior and the memory effect in the magnetization. Nonvolatile positive magnetoresistance observed in this compound below $T_{s1}$ can be attributed to the fact that such magnetic domains and the electrical conduction along the domain walls disappear with the applied magnetic field.

We propose to use a quantum adiabatic and simulated-annealing framework to compute the ground state of small molecules. The initial Hamiltonian of our algorithms is taken to be the maximum commuting Hamiltonian that consists of a maximal set of commuting terms in the full Hamiltonian of molecules in the Pauli basis. We consider two variants. In the first method, we perform the adiabatic evolution on the obtained time- or path-dependent Hamiltonian with the initial state as the ground state of the maximum commuting Hamiltonian. However, this method does suffer from the usual problems of adiabatic quantum computation due to degeneracy and energy-level crossings along the Hamiltonian path. This problem is mitigated by a Zeno method, i.e., via a series of eigenstate projections used in the quantum simulated annealing, with the path-dependent Hamiltonian augmented by a sum of Pauli X terms, whose contribution vanishes at the beginning and the end of the path. In addition to the ground state, the low lying excited states can be obtained using this quantum Zeno approach with equal accuracy to that of the ground state.

We consider the time-reversal odd dynamics of the bilayer graphene at low energies in the quantum Hall regime. A generating functional for the effective action that captures the electromagnetic response to all orders in momentum and frequency is presented and evaluated to the third order in the space-time gradient $\mathcal{O}\left({\partial }^3\right)$. In addition, we calculate the Hall viscosity and derive an explicit relationship with the $q^2$ coefficient of the Hall conductivity. It is reminiscent of the Hoyos-Son relation in Galilean invariant systems, which can be recovered in the limit of large filling factor $N$.