We show that certain lattice gauge theories exhibiting disorder-free localization have a characteristic response in spatially averaged spectral functions: a few sharp peaks combined with vanishing response in the zero frequency limit. This reflects the discrete spectra of small clusters of kinetically active regions formed in such gauge theories when they fragment into spatially finite clusters in the localized phase due to the presence of static charges. We obtain the transverse component of the dynamic structure factor, which is probed by neutron scattering experiments, deep in this phase from a combination of analytical estimates and a numerical cluster expansion. We also show that local spectral functions of large finite clusters host discrete peaks whose positions agree with our analytical estimates. Further, information spreading, diagnosed by an unequal time commutator, halts due to real space fragmentation. Our results can be used to distinguish the disorder-free localized phase from conventional paramagnetic counterparts in those frustrated magnets which might realize such an emergent gauge theory.

This paper tests how effectively the bound states of strongly interacting gauge theories are amenable to an emergent description as a thermal ensemble. This description can be derived from a conjectured minimum free energy principle, with the entanglement entropy of two-parton subsystems playing the role of thermodynamic entropy. This allows us to calculate the ground state hadron spectrum and wavefunction over a wide range of parton masses without solving the Schr\"{o}dinger equation. We carry out this analysis for certain illustrative models in 1+1 dimensions and discuss prospects for higher dimensions.

Non-Hermitian systems have been actively studied for open and dissipative quantum systems. One of the remarkable features is the non-Hermitian skin effect, the anomalous condensation of the bulk states at the edge resulting from asymmetric hopping magnitudes. From both theoretical and experimental points of view, it has been studied based on the Hatano-Nelson argument and topological exceptional points. Beyond such non-Hermitian systems, however, different types of non-Hermiticity and their characteristics remain elusive. In this work, we focus on a non-Hermitian system where the hopping phase exists non-reciprocally and discuss the evolution of localization characteristics of the quantum states. We emphasize that the non-Hermiticity encoded in the hopping phase factor gives rise to the delocalization of the states in contrast to the non-Hermitian skin effect. Furthermore, by quantifying the localization in the spectrum via inverse participation ratio and fractal dimension, we demonstrate that the non-Hermitian hopping phase results in delicate controllability of the localization characteristics of quantum states. Our work offers new types of non-Hermitian systems which can control wave localization, and finally we also discuss the relevant experimental applications.

The exact contraction of a generic two-dimensional (2D) tensor network state (TNS) is known to be exponentially hard, making simulation of 2D systems difficult. The recently introduced class of isometric TNS (isoTNS) represents a subset of TNS that allows for efficient simulation of such systems on finite square lattices. The isoTNS ansatz requires the identification of an "orthogonality column" of tensors, within which one-dimensional matrix product state (MPS) methods can be used for calculation of observables and optimization of tensors. Here we extend isoTNS to infinitely long strip geometries and introduce an infinite version of the Moses Move algorithm for moving the orthogonality column around the network. Using this algorithm, we iteratively transform an infinite MPS representation of a 2D quantum state into a strip isoTNS and investigate the entanglement properties of the resulting state. In addition, we demonstrate that the local observables can be evaluated efficiently. Finally, we introduce an infinite time-evolving block decimation algorithm (iTEBD\textsuperscript{2}) and use it to approximate the ground state of the 2D transverse field Ising model on lattices of infinite strip geometry.

The no-broadcasting theorem is one of the most fundamental results in quantum information theory; it guarantees that the simplest attacks on any quantum protocol, based on eavesdropping and copying of quantum information, are impossible. Due to its fundamental importance, it is natural to ask whether it is an inherent quantum property or holds also for a broader class of non-classical theories. A relevant generalization is to consider non-signalling boxes. Subsequently Joshi, Grudka and Horodecki$^{\otimes 4}$ conjectured that one cannot locally broadcast nonlocal boxes. In this paper, we prove their conjecture based on fundamental properties of the relative entropy of boxes. Following a similar reasoning, we also obtain an analogous theorem for steerable assemblages.

A proof-of-concept application of a quantum algorithm to multiloop Feynman integrals in the Loop-Tree Duality (LTD) framework is applied to a representative four-loop topology. Bootstrapping causality in the LTD formalism, is a suitable problem to address with quantum computers given the straightforward possibility to encode the two on-shell states of a propagator on the two states of a qubit. A modification of Grover's quantum search algorithm is developed and the quantum algorithm is successfully implemented on IBM Quantum and QUTE simulators.

We investigate the quantum irreversibility and quantum diffusion in a non-Hermitian kicked rotor model for which the kicking strength is complex. Our results show that the exponential decay of Loschmidt echo gradually disappears with increasing the strength of the imaginary part of non-Hermitian driven potential, demonstrating the suppress of the exponential instability by non-Hermiticity. The quantum diffusion exhibits the dynamical localization in momentum space, namely, the mean square of momentum increases to saturation with time evolution, which decreases with the increase of the strength of the imaginary part of the kicking. This clearly reveals the enhancement of dynamical localization by non-Hermiticity. We find, both analytically and numerically, that the quantum state are mainly populated on a very few quasieigenstates with significantly large value of the imaginary part of quasienergies. Interestingly, the average value of the inverse participation ratio of quasieigenstates decreases with the increase of the strength of the imaginary part of the kicking potential, which implies that the feature of quasieigenstates determines the stability of wavepacket's dynamics and the dynamical localization of energy diffusion.

Polymer self-consistent field theory techniques are used to derive quantum density functional theory without the use of the theorems of density functional theory. Instead, a free energy is obtained from a partition function that is constructed directly from a Hamiltonian, so that the results are, in principle, valid at finite temperatures. The main governing equations are found to be a set of modified diffusion equations, and the set of self-consistent equations are essentially identical to those of a ring polymer system. The equations are shown to be equivalent to Kohn-Sham density functional theory, and to reduce to classical density functional theory, each under appropriate conditions. The obtained non-interacting kinetic energy functional is, in principle, exact, but suffers from the usual orbital-free approximation of the Pauli exclusion principle in additional to the exchange-correlation approximation. The equations are solved using the spectral method of polymer self-consistent field theory, which allows the set of modified diffusion equations to be evaluated for the same computational cost as solving a single diffusion equation. A simple exchange-correlation functional is chosen, together with a shell-structure-based Pauli potential, in order to compare the ensemble average electron densities of several isolated atom systems to known literature results. The agreement is excellent, justifying the alternative formalism and numerical method. Some speculation is provided on considering the time-like parameter in the diffusion equations, which is related to temperature, as having dimensional significance, and thus picturing point-like quantum particles instead as non-local, polymer-like, threads in a higher dimensional thermal-space. A consideration of the double-slit experiment from this point of view is speculated to provide results equivalent to the Copenhagen interpretation.

Optomechanical sensors are capable of transducing external perturbations to resolvable optical signals. A particular regime of interest is that of high-bandwidth force detection, where an impulse is delivered to the system over a short period of time. Exceedingly sensitive impulse detection has been proposed to observe very weak signals like those for long range interactions with dark matter requiring much higher sensitivities than current sensors can provide. Quantum resources to go beyond the standard quantum limit of noise in these sensors include squeezing of the light used to transduce the signal, backaction evasion by measuring the optimum quadrature, and quantum nondemolition (QND) measurements which reduce backaction directly. However, it has been extremely difficult to determine a scheme where all these quantum resources contribute to noise reduction thereby exceeding the benefit of using only one quantum resource alone. We provide the theoretical limits to noise reduction while combining quantum enhanced readout techniques such as squeezing and QND measurements for these optomechanical sensors. We demonstrate that backaction evasion through QND techniques dramatically reduces the technical challenges presented when using squeezed light for broadband force detection, paving the way for combining multiple quantum noise reduction techniques for enhanced sensitivity in the context of impulse metrology.

One of the ultimate missions of lattice QCD is to simulate atomic nuclei from the first principle of the strong interaction. This is an extremely hard task for the current computational technology, but might be reachable in coming quantum computing era. In this paper, we discuss the computational complexities of classical and quantum simulations of lattice QCD. It is shown that the quantum simulation scales better as a function of a nucleon number and thus will outperform for large nuclei.

The quantum speed limit provides a fundamental bound on how fast a quantum system can evolve between the initial and the final states under any physical operation. The celebrated Mandelstam-Tamm (MT) bound has been widely studied for various quantum systems undergoing unitary time evolution. Here, we prove a new quantum speed limit using the tighter uncertainty relations for pure quantum systems undergoing arbitrary unitary evolution. We also derive a tighter uncertainty relation for mixed quantum states and then derive a new quantum speed limit for mixed quantum states from it such that it reduces to that of the pure quantum states derived from tighter uncertainty relations. We show that the MT bound is a special case of the tighter quantum speed limit derived here. We also show that this bound can be improved when optimized over many different sets of basis vectors. We illustrate the tighter speed limit for pure states with examples using random Hamiltonians and show that the new quantum speed limit outperforms the MT bound.

Quantum simulation is one of the most promising near term applications of quantum computing. Especially, systems with a large Hilbert space are hard to solve for classical computers and thus ideal targets for a simulation with quantum hardware. In this work, we study experimentally the transient dynamics in the multistate Landau-Zener model as a function of the Landau-Zener velocity. The underlying Hamiltonian is emulated by superconducting quantum circuit, where a tunable transmon qubit is coupled to a bosonic mode ensemble comprising four lumped element microwave resonators. We investigate the model for different initial states: Due to our circuit design, we are not limited to merely exciting the qubit, but can also pump the harmonic modes via a dedicated drive line. Here, the nature of the transient dynamics depends on the average photon number in the excited resonator. The greater effective coupling strength between qubit and higher Fock states results in a quasi-adiabatic transition, where coherent quantum oscillations are suppressed without the introduction of additional loss channels. Our experiments pave the way for more complex simulations with qubits coupled to an engineered bosonic mode spectrum.

Quantum noise suppression and phase-sensitive modulation of continuously variable in vacuum and squeezed fields in a hybrid resonant cavity system are investigated theoretically. Multiple dark windows similar to electromagnetic induction transparency (EIT) are observed in quantum noise fluctuation curve. The effects of pumping light on both suppression of quantum noise and control the widths of dark windows are carefully analyzed, and the saturation point of pumping light for nonlinear crystal conversion is obtained. We find that the noise suppression effect is strongly sensitive to the pumping light power. The degree of noise suppression can be up to 13.9 dB when the pumping light power is 6.5 Beta_th. Moreover, a phase-sensitive modulation scheme is demonstrated, which well fills the gap that multi-channel quantum noise suppression is difficult to realize at the quadrature amplitude of squeezed field. Our result is meaningful for various applications in precise measurement physics, quantum information processing and quantum communications of system-on-a-chip.

Deep neural networks (NN) suffer from scaling issues when considering a large number of neurons, in turn limiting also the accessible number of layers. To overcome this, here we propose the integration of tensor networks (TN) into NNs, in combination with variational DMRG-like optimization. This results in a scalable tensor neural network (TNN) architecture that can be efficiently trained for a large number of neurons and layers. The variational algorithm relies on a local gradient-descent technique, with tensor gradients being computable either manually or by automatic differentiation, in turn allowing for hybrid TNN models combining dense and tensor layers. Our training algorithm provides insight into the entanglement structure of the tensorized trainable weights, as well as clarify the expressive power as a quantum neural state. We benchmark the accuracy and efficiency of our algorithm by designing TNN models for regression and classification on different datasets. In addition, we also discuss the expressive power of our algorithm based on the entanglement structure of the neural network.

We consider quantum state transfer on finite graphs which are attached to infinite paths. The finite graph represents an operational quantum system for performing useful quantum information tasks. In contrast, the infinite paths represent external infinite-dimensional systems which have limited (but nontrivial) interaction with the finite quantum system. We show that {\em perfect} state transfer can surprisingly still occur on the finite graph even in the presence of the infinite tails. Our techniques are based on a decoupling theorem for eventually-free Jacobi matrices, equitable partitions, and standard Lie theoretic arguments. Through these methods, we rehabilitate the notion of a dark subspace which had been so far viewed in an unflattering light.

Historically, Kennard was the first to choose the standard deviation as a quantitative measure of uncertainty, and neither he nor Heisenberg explicitly explained why this choice should be appropriate from the experimental physical point of view. If a particle is prepared by a single slit of spatial width $\Delta x$, it has been shown that a finite standard deviation $\sigma_p<\infty$ can only be ensured if the wave-function is zero at the edge of $\Delta x$, otherwise it does not exist. Under this circumstances the corresponding sharp inequality is $\sigma_p\Delta x\geq \pi\hbar$. This bound will be reconsidered from the mathematical point of view in terms of a variational problem in Hilbert space and will furthermore be tested in a 4f-single slit diffraction experiment of a laser beam. Our results will be compared with a laser-experiment recently given by M. F. Guasti (2022).

In this work, using the noncommutative integration method of linear differential equations, we obtain a complete set of solutions to the Schrodinger equation for a quantum asymmetric top in Euler angles. It is shown that the noncommutative reduction of the Schrodinger equation leads to the Lame equation. The resulting set of solutions is determined by the Lame polynomials in a complex parameter, which is related to the geometry of the orbits of the coadjoint representation of the rotation group. The spectrum of an asymmetric top is obtained from the condition that the solutions are invariant with respect to a special irreducible $\lambda$-representation of the rotation group.

The decoherence of a fast quantum particle in a gas is studied by applying the Kramers-Moyal expansion to the quantum master equation for the reduced density matrix of the particle. This expansion leads to a general form of the Caldeira-Leggett master equation accounting for the angular variation of the differential cross section. The equation describes the decoherence in both the longitudinal and transverse directions with respect to the particle motion. It is shown that, when the differential cross section is concentrated in the forward direction, transverse decoherence dominates. The coherence region off the diagonal of the density matrix is characterized by coherence lengths, which can be deduced, for Gaussian states, from the momentum covariance matrix according to a Heisenberg-type uncertainty relation. Finally, the longitudinal-to-transverse ratio of the coherence lengths is estimated for an alpha particle of a few MeVs. This ratio indicates that the coherence region looks like an ellipsoid elongated in the direction of motion.

Non-Hermitian quantum systems have recently attracted considerable attentions due to their exotic properties. Though many experimental realizations of non-Hermitian systems have been reported, the non-Hermiticity usually resorts to the hard-to-control environments. An alternative approach is to use quantum simulation with the closed system, whereas how to simulate general non-Hermitian Hamiltonian dynamics remains a great challenge. To tackle this problem, we propose a protocol by combining a dilation method with the variational quantum algorithm. The dilation method is used to transform a non-Hermitian Hamiltonian into a Hermitian one through an exquisite quantum circuit, while the variational quantum algorithm is for efficiently approximating the complex entangled gates in this circuit. As a demonstration, we apply our protocol to simulate the dynamics of an Ising chain with nonlocal non-Hermitian perturbations, which is an important model to study quantum phase transition at nonzero temperatures. The numerical simulation results are highly consistent with the theoretical predictions, revealing the effectiveness of our protocol. The presented protocol paves the way for practically simulating general non-Hermitian dynamics in the multi-qubit case.

A common situation in quantum many-body physics is that the underlying theories are known but too complicated to solve efficiently. In such cases, one usually builds simpler effective theories as low-energy or large-scale alternatives to the original theories. Here the central tasks are finding the optimal effective theories among a large number of candidates and proving their equivalence to the original theories. Recently quantum computing has shown the potential of solving quantum many-body systems by exploiting its inherent parallelism. It is thus an interesting topic to discuss the emergence of effective theories and design efficient tools for finding them based on the results from quantum computing. As the first step towards this direction, in this paper, we propose two approaches that apply quantum computing to find the optimal effective theory of a quantum many-body system given its full Hamiltonian. The first algorithm searches the space of effective Hamiltonians by quantum phase estimation and amplitude amplification. The second algorithm is based on a variational approach that is promising for near-future applications.