We calculate the third order out-of-time-order correlator (OTOC) of a simple harmonic oscillator with extra quartic interaction by the second quantization method. We obtain the analytic relations of spectrum, Fock space states and matrix elements of coordinate which are then used to numerically calculate the OTOC. We see that OTOC saturates to a constant value at later times, i.e. $C_T(\infty)\to 2\langle x^2\rangle_T\langle p^2\rangle_T$, which associates with quantum chaotic behavior in systems that exhibit chaos. We analyze early-time property of $C_T$ and see that the exponential growth, which diagnoses the chaos, is shown in the third-order perturbation.

We explore the application of quantum optimal control (QOC) techniques to state preparation of lattice field theories on quantum computers. As a first example, we focus on the Schwinger model, quantum electrodynamics in 1+1 dimensions. We demonstrate that QOC can significantly speed up the ground state preparation compared to gate-based methods, even for models with long-range interactions. Using classical simulations, we explore the dependence on the inter-qubit coupling strength and the device connectivity, and we study the optimization in the presence of noise. While our simulations indicate potential speedups, the results strongly depend on the device specifications. In addition, we perform exploratory studies on the preparation of thermal states. Our results motivate further studies of QOC techniques in the context of quantum simulations for fundamental physics.

In quantum computing, knowing the symmetries a given system or state obeys or disobeys is often useful. For example, Hamiltonian symmetries may limit allowed state transitions or simplify learning parameters in machine learning applications, and certain asymmetric quantum states are known to be resourceful in various applications. Symmetry testing algorithms provide a means to identify and quantify these properties with respect to a representation of a group. In this paper, we present a collection of quantum algorithms that realize projections onto the symmetric subspace, as well as the asymmetric subspace, of quantum systems. We describe how this can be modified to realize an antisymmetric projection as well, and we show how projectors can be combined in a systematic way to effectively measure various projections in a single quantum circuit. Using these constructions, we demonstrate applications such as testing for Werner-state symmetry and estimating Schmidt ranks of bipartite states, supported by experimental data from IBM Quantum systems. This work underscores the pivotal role of symmetry in simplifying quantum calculations and advancing quantum information tasks.

We show that quantum entanglement states are associated with multilinear polynomials that cannot be factored. Notice that, since multilinear polynomials have a geometric representation, we can propose a similar geometric representation for entanglement states. In particular, we show that the Bell's states are associated with non-factorable real multilinear polynomial, which can be represented geometrically by three-dimensional surfaces. Furthermore, we show that a quantum circuit can be seen as a geometric transformations of plane geometry. Notice that this phenomenon is analogous to gravity, where matter curves space-time. In addition, we show an analogy between quantum teleportation and operations involving multilinear polynomials.

We introduce regular language states, a family of quantum many-body states. They are built from a special class of formal languages, called regular, which has been thoroughly studied in the field of computer science. They can be understood as the superposition of all the words in a regular language and encompass physically relevant states such as the GHZ-, W- or Dicke-states. By leveraging the theory of regular languages, we develop a theoretical framework to describe them. First, we express them in terms of matrix product states, providing efficient criteria to recognize them. We then develop a canonical form which allows us to formulate a fundamental theorem for the equivalence of regular language states, including under local unitary operations. We also exploit the theory of tensor networks to find an efficient criterion to determine when regular languages are shift-invariant.

Kostka, Littlewood-Richardson, Plethysm and Kronecker coefficients are multiplicities of irreducible representations (irreps) of the symmetric group in restrictions and products of irreps. They play an important role in representation theory and are notoriously hard to compute. We give quantum algorithms that efficiently compute these coefficients whenever the ratio of dimensions of the representations is polynomial. Using that the Kostka numbers admit combinatorial interpretation, we show that there is an efficient classical algorithm for polynomially-bounded Kostka numbers and conjecture existence of a similar algorithm for the Littlewood-Richardson coefficients. We argue why the same classical algorithm does not straightforwardly work for the Plethysm and Kronecker coefficients, give evidence on how our quantum algorithm may avoid some hardness obstructions in their computation, and conjecture that the problem could lead to superpolynomial quantum speedups on some inputs. We finally use Frobenius reciprocity to derive another quantum algorithm that estimates these coefficients using induction and has a different cost-to-input dependence.

Quantum computers promise a great computational advantage over classical computers, yet currently available quantum devices have only a limited amount of qubits and a high level of noise, limiting the size of problems that can be solved accurately with those devices. Variational Quantum Algorithms (VQAs) have emerged as a leading strategy to address these limitations by optimizing cost functions based on measurement results of shallow-depth circuits. However, the optimization process usually suffers from severe trainability issues as a result of the exponentially large search space, mainly local minima and barren plateaus. Here we propose a novel method that can improve variational quantum algorithms -- ``discretized quantum exhaustive search''. On classical computers, exhaustive search, also named brute force, solves small-size NP complete and NP hard problems. Exhaustive search and efficient partial exhaustive search help designing heuristics and exact algorithms for solving larger-size problems by finding easy subcases or good approximations. We adopt this method to the quantum domain, by relying on mutually unbiased bases for the $2^n$-dimensional Hilbert space. We define a discretized quantum exhaustive search that works well for small size problems. We provide an example of an efficient partial discretized quantum exhaustive search for larger-size problems, in order to extend classical tools to the quantum computing domain, for near future and far future goals. Our method enables obtaining intuition on NP-complete and NP-hard problems as well as on Quantum Merlin Arthur (QMA)-complete and QMA-hard problems. We demonstrate our ideas in many simple cases, providing the energy landscape for various problems and presenting two types of energy curves via VQAs.

In recent years, variational quantum circuits (VQCs) have been widely explored to advance quantum circuits against classic models on various domains, such as quantum chemistry and quantum machine learning. Similar to classic machine-learning models, VQCs can be optimized through gradient-based approaches. However, the gradient variance of VQCs may dramatically vanish as the number of qubits or layers increases. This issue, a.k.a. Barren Plateaus (BPs), seriously hinders the scaling of VQCs on large datasets. To mitigate the exponential gradient vanishing, extensive efforts have been devoted to tackling this issue through diverse strategies. In this survey, we conduct a systematic literature review of recent works from both investigation and mitigation perspectives. Besides, we propose a new taxonomy to categorize most existing mitigation strategies. At last, we provide insightful discussion for future directions of BPs.

The signaling dimension of any given physical system represents its classical simulation cost, that is, the minimum dimension of a classical system capable of reproducing all the input/output correlations of the given system. The signaling dimension landscape is vastly unexplored; the only non-trivial systems whose signaling dimension is known -- other than quantum systems -- are the octahedron and the composition of two squares. Building on previous results by Matsumoto, Kimura, and Frenkel, our first result consists of deriving bounds on the signaling dimension of any system as a function of its Minkowski measure of asymmetry. We use such bounds to prove that the signaling dimension of any two-dimensional system (i.e. with two-dimensional set of admissible states, such as polygons and the real qubit) is two if and only if such a set is centrally symmetric, and three otherwise, thus conclusively settling the problem of the signaling dimension for such systems. Guided by the relevance of symmetries in the two dimensional case, we propose a branch and bound division-free algorithm for the exact computation of the symmetries of any given polytope, in polynomial time in the number of vertices and in factorial time in the dimension of the space. Our second result then consist of providing an algorithm for the exact computation of the signaling dimension of any given system, that outperforms previous proposals by exploiting the aforementioned bounds to improve its pruning techniques and incorporating as a subroutine the aforementioned symmetries-finding algorithm. We apply our algorithm to compute the exact value of the signaling dimension for all rational Platonic, Archimedean, and Catalan solids, and for the class of hyper-octahedral systems up to dimension five.

Floquet theory and other established semiclassical approaches are widely used methods to predict the state of externally-driven quantum systems, yet, they do not allow to predict the state of the photonic driving field. To overcome this shortcoming, the photon-resolved Floquet theory (PRFT) has been developed recently [Phys. Rev. Research 6, 013116], which deploys concepts from full-counting statistics to predict the statistics of the photon flux between several coherent driving modes. In this paper, we study in detail the scaling properties of the PRFT in the semiclassical regime. We find that there is an ambiguity in the definition of the moment-generating function, such that different versions of the moment-generating function produce the same photonic probability distribution in the semiclassical limit, and generate the same leading-order terms of the moments and cumulants. Using this ambiguity, we establish a simple expression for the Kraus operators, which describe the decoherence dynamics of the driven quantum system appearing as a consequence of the light-matter interaction. The PRFT will pave the way for improved quantum sensing methods, e.g., for spectroscopic quantum sensing protocols, reflectometry in semiconductor nanostructures and other applications, where the detailed knowledge of the photonic probability distribution is necessary.

When subject to a non-local unitary evolution, qubits in a quantum circuit become increasingly entangled. Conversely, measurements applied to individual qubits lead to their disentanglement from the collective system. The extent of entanglement reduction depends on the frequency of local projective measurements. A delicate balance emerges between unitary evolution, which enhances entanglement, and measurements which diminish it. In the thermodynamic limit, there is a phase transition from volume law entanglement to area law entanglement at a critical value of measurement frequency. This phenomenon, occurring in hybrid quantum circuits with both unitary gates and measurements, is termed as measurement-induced phase transition (MIPT). We study the behavior of MIPT in circuits comprising of two qubit unitary gates parameterized by Cartan decomposition. We show that the entangling power and gate typicality of the two-qubit local unitaries employed in the circuit can be used to explain the behavior of global bipartite entanglement the circuit can sustain. When the two qubit gate throughout the circuit is the identity and measurements are the sole driver of the entanglement behavior, we obtain analytical estimate for the entanglement entropy that shows remarkable agreement with numerical simulations. We also find that the entangling power and gate typicality enable the classification of the two-qubit unitaries by different universality classes of phase transitions that can occur in the hybrid circuit. For all unitaries in a particular universality class, the transition from volume to area law of entanglement occurs with same exponent that characterizes the phase transition.

Combinatorial optimization problems are one of the areas where near-term noisy quantum computers may have practical advantage against classical computers. Recently a novel feedback-based quantum optimization algorithm has been proposed by Magann \textit{et al}. The method explicitly determines quantum circuit parameters by feeding back measurement results thus avoids classical parameter optimization that is known to cause significant trouble in quantum approximate optimization algorithm, the well-studied near-term algorithm. Meanwhile, a significant drawback of the feedback-based quantum optimization is that it requires deep circuits, rendering the method unsuitable to noisy quantum devices. In this study we propose a new feedback law for parameter determination by introducing the second-order approximation with respect to time interval, a hyperparameter in the feedback-based quantum optimization. This allows one to take larger time interval, leading to acceleration of convergence to solutions. In numerical simulations on the maximum cut problem we demonstrate that our proposal significantly reduces circuit depth, with its linear scaling with the problem size smaller by more than an order of magnitude. We expect that the new feedback law proposed in this work may pave the way for feedback-based quantum optimization with near-term noisy quantum computers.

Interactions of molecules with their environment influence the course and outcome of almost all chemical reactions. However, classical computers struggle to accurately simulate complicated molecule-environment interactions because of the steep growth of computational resources with both molecule size and environment complexity. Therefore, many quantum-chemical simulations are restricted to isolated molecules, whose dynamics can dramatically differ from what happens in an environment. Here, we show that analog quantum simulators can simulate open molecular systems by using the native dissipation of the simulator and injecting additional controllable dissipation. By exploiting the native dissipation to simulate the molecular dissipation -- rather than seeing it as a limitation -- our approach enables longer simulations of open systems than are possible for closed systems. In particular, we show that trapped-ion simulators using a mixed qudit-boson (MQB) encoding could simulate molecules in a wide range of condensed phases by implementing widely used dissipative processes within the Lindblad formalism, including pure dephasing and both electronic and vibrational relaxation. The MQB open-system simulations require significantly fewer additional quantum resources compared to both classical and digital quantum approaches.

We provide a comprehensive study of the capabilities of modulated electron wavefunctions for the preparation and readout of the quantum state of the quantum emitters (QEs) they interact with. First, we consider perfectly periodic electron combs, which do not produce QE-electron entanglement, preserving the purity of the QE while inducing Rabi-like dynamics in it. We extend our findings to realistic, non-ideally modulated electron wavepackets, showing that the phenomenology persists, and exploring their use to prepare the emitter in a desired quantum state. Thus, we establish the balance that electron comb size, emitter radiative decay, and electron-emitter coupling strength must fulfil in order to implement our ideas in experimentally feasible platforms. Finally, moving into the limit of small electron combs, we reveal that these wavefunctions allow for quantum state tomography of their target, providing access not only to the populations, but also the coherences of the QE density matrix. We believe that our theoretical results showcase modulated free-electrons as very promising tools for quantum technologies based on light-matter coupling.

The treatment of quantum thermodynamic systems beyond weak coupling is of increasing relevance, yet extremely challenging. The evaluation of thermodynamic quantities in strong-coupling regimes requires a nonperturbative knowledge of the bath dynamics, which in turn relies on heavy numerical simulations. To tame these difficulties, considering thermal bosonic baths linearly coupled to the open system, we derive expressions for heat, work, and average system-bath interaction energy that only involve the autocorrelation function of the bath and two-time expectation values of system operators. We then exploit the pseudomode approach, which replaces the physical continuous bosonic bath with a small finite number of damped, possibly interacting, modes, to numerically evaluate these relevant thermodynamic quantities. We show in particular that this method allows for an efficient numerical evaluation of thermodynamic quantities in terms of one-time expectation values of the open system and the pseudomodes. We apply this framework to the investigation of two paradigmatic situations. In the first instance, we study the entropy production for a two-level system coupled to an ohmic bath, simulated via interacting pseudomodes, allowing for the presence of time-dependent driving. Secondly, we consider a quantum thermal machine composed of a two-level system interacting with two thermal baths at different temperatures, showing that an appropriate sinusoidal modulation of the coupling with the cold bath only is enough to obtain work extraction.

We study a mechanical oscillator coupled to a two-level system driven by a blue-detuned coherent source in the resolved sideband regime. For weak mechanical damping, we find dynamical instabilities leading to limit cycles. They are signaled by strong fluctuations in the number of emitted photons, with a large Fano factor. The phonon-number fluctuations exhibit a strikingly similar behavior. When the coupling strength becomes comparable to the mechanical frequency, non-classical mechanical states appear. We discuss the relation with cavity optomechanical systems. Candidates for observing these effects include superconducting qubits, NV centers, and single molecules coupled to oscillators.

The one-dimensional spin-$s$ ${\rm SU}(2)$ ferromagnetic Heisenberg model, as a paradigmatic example for spontaneous symmetry breaking (SSB) with type-B Goldstone modes (GMs), is expected to exhibit an abstract fractal underlying the ground state subspace. This intrinsic abstract fractal is here revealed from a systematic investigation into the entanglement entropy for a linear combination of factorized (unentangled) ground states on a fractal decomposable into a set of the Cantor sets. The entanglement entropy scales logarithmically with the block size, with the prefactor being half the fractal dimension of a fractal, as long as the norm for the linear combination scales as the square root of the number of the self-similar building blocks kept at each step $k$ for a fractal, under an assumption that the maximum absolute value of the coefficients in the linear combination is chosen to be around one, and the coefficients in the linear combination are almost constants within the building blocks. Actually, the set of the fractal dimensions for all the Cantor sets forms a {\it dense} subset in the interval $[0,1]$. As a consequence, the ground state subspace is separated into a disjoint union of countably infinitely many regions, each of which is labeled by a decomposable fractal. Hence, the interpretation of the prefactor as half the fractal dimension is valid for any support beyond a fractal, which in turn leads to the identification of the fractal dimension with the number of type-B GMs for the orthonormal basis states. Our argument may be extended to any quantum many-body systems undergoing SSB with type-B GMs.

We argue by example that conditionally clean ancillae, recently described by [NZS24], should become a standard tool in the quantum circuit design kit. We use conditionally clean ancillae to reduce the gate counts and depths of several circuit constructions. In particular, we present: (a) n-controlled NOT using 2n Toffolis and O(log n) depth given 2 clean ancillae. (b) n-qubit incrementer using 3n Toffolis given log*(n) clean ancillae. (c) n-qubit quantum-classical comparator using 3n Toffolis given log*(n) clean ancillae. (d) unary iteration over [0, N) using 2.5N Toffolis given 2 clean ancillae. (e) unary iteration via skew tree over [0, N) using 1.25 N Toffolis given n dirty ancillae. We also describe a technique for laddered toggle detection to replace clean ancillae with dirty ancillae in all our constructions with a 2x Toffoli overhead. Our constructions achieve the lowest gate counts to date with sublinear ancilla requirements and should be useful building blocks to optimize circuits in the low-qubit regime of Early Fault Tolerance.

We develop a statistical framework, based on a manifold learning embedding, to extract relevant features of multipartite entanglement structures of mixed quantum states from the measurable correlation data of a quantum computer. We show that the statistics of the measured correlators contains sufficient information to characterise the entanglement, and to quantify the mixedness of the state of the computer's register. The transition to the maximally mixed regime, in the embedding space, displays a sharp boundary between entangled and separable states. Away from this boundary, the multipartite entanglement structure is robust to finite noise.

As quantum machine learning continues to develop at a rapid pace, the importance of ensuring the robustness and efficiency of quantum algorithms cannot be overstated. Our research presents an analysis of quantum randomized smoothing, how data encoding and perturbation modeling approaches can be matched to achieve meaningful robustness certificates. By utilizing an innovative approach integrating Grover's algorithm, a quadratic sampling advantage over classical randomized smoothing is achieved. This strategy necessitates a basis state encoding, thus restricting the space of meaningful perturbations. We show how constrained $k$-distant Hamming weight perturbations are a suitable noise distribution here, and elucidate how they can be constructed on a quantum computer. The efficacy of the proposed framework is demonstrated on a time series classification task employing a Bag-of-Words pre-processing solution. The advantage of quadratic sample reduction is recovered especially in the regime with large number of samples. This may allow quantum computers to efficiently scale randomized smoothing to more complex tasks beyond the reach of classical methods.

Quantum computing has the potential to solve many complex algorithms in the domains of optimization, arithmetics, structural search, financial risk analysis, machine learning, image processing, and others. Quantum circuits built to implement these algorithms usually require multi-controlled gates as fundamental building blocks, where the multi-controlled Toffoli stands out as the primary example. For implementation in quantum hardware, these gates should be decomposed into many elementary gates, which results in a large depth of the final quantum circuit. However, even moderately deep quantum circuits have low fidelity due to decoherence effects and, thus, may return an almost perfectly uniform distribution of the output results. This paper proposes a different approach for efficient cost multi-controlled gates implementation using the quantum Fourier transform. We show how the depth of the circuit can be significantly reduced using only a few ancilla qubits, making our approach viable for application to noisy intermediate-scale quantum computers. This quantum arithmetic-based approach can be efficiently used to implement many complex quantum gates.

Critical systems represent a valuable resource in quantum sensing and metrology. Critical quantum sensing (CQS) protocols can be realized using finite-component phase transitions, where criticality is not due to the thermodynamic limit but rather to the rescaling of the system parameters. In particular, the second-order phase transitions of parametric Kerr resonators are of high experimental relevance, as they can be implemented and controlled with various quantum technologies currently available. Here, we show that collective quantum advantage can be achieved with a multipartite critical quantum sensor based on a parametrically coupled Kerr resonators chain in the weak-nonlinearity limit. We derive analytical solutions for the low-energy spectrum of this unconventional quantum many-body system, which is composed of \emph{locally} critical elements. We then assess the performance of an adiabatic CQS protocol, comparing the coupled-resonator chain with an equivalent ensemble of independent critical sensors. We evaluate the scaling of the quantum Fisher information with respect to fundamental resources, and find that the critical chain achieves a quadratic enhancement in the number of resonators. Beyond the advantage found in the case of zero Kerr, we find that there is a collective enhancement even in the scenario of finite Kerr nonlinearity.

We introduce a novel reservoir engineering approach for stabilizing multi-component Schr\"odinger's cat manifolds. The fundamental principle of the method lies in the destructive interference at crossings of gain and loss Hamiltonian terms in the coupling of an oscillator to a zero-temperature auxiliary system, which are nonlinear with respect to the oscillator's energy. The nature of these gain and loss terms is found to determine the rotational symmetry, energy distributions, and degeneracy of the resulting stabilized manifolds. Considering these systems as bosonic error-correction codes, we analyze their properties with respect to a variety of errors, including both autonomous and passive error correction, where we find that our formalism gives straightforward insights into the nature of the correction. We give example implementations using the anharmonic laser-ion coupling of a trapped ion outside the Lamb-Dicke regime as well as nonlinear superconducting circuits. Beyond the dissipative stabilization of standard cat manifolds and novel rotation symmetric codes, we demonstrate that our formalism allows for the stabilization of bosonic codes linked to cat states through unitary transformations, such as quadrature-squeezed cats. Our work establishes a design approach for creating and utilizing codes using nonlinearity, providing access to novel quantum states and processes across a range of physical systems.

Quantum correlations are at the core of the power of quantum information and are necessary to reach a quantum computational advantage. In the context of continuous-variable quantum systems, another necessary ressource for quantum advantages is non-Gaussianity. In this work, we propose a witness, based on previously known relations between metrological power and quantum correlations, to detect a strong form of entanglement that only non-Gaussian states possess and that cannot be undone by passive optical operations, i.e., entanglement in all mode bases. The strength of our witness is two-fold: it only requires measurements in one basis to check entanglement in any arbitrary mode basis; it can be made applicable experimentally using homodyne measurements and without requiring a full tomography of the state.

We seek a systematic tightening method to represent the monogamy relation for some measure in multipartite quantum systems. By introducing a family of parametrized bounds, we obtain tighter lowering bounds for the monogamy relation compared with the most recently discovered relations. We provide detailed examples to illustrate why our bounds are better.

In the fast-paced field of quantum computing, identifying the architectural characteristics that will enable quantum processors to achieve high performance across a diverse range of quantum algorithms continues to pose a significant challenge. Given the extensive and costly nature of experimentally testing different designs, this paper introduces the first Design Space Exploration (DSE) for quantum-dot spin-qubit architectures. Utilizing the upgraded SpinQ compilation framework, this study explores a substantial design space comprising 29,312 spin-qubit-based architectures and applies an innovative optimization tool, ArtA (Artificial Architect), to speed up the design space traversal. ArtA can leverage seventeen optimization method configurations, significantly reducing exploration times by up to 99.1% compared to a traditional brute force approach while maintaining the same result quality. After a comprehensive evaluation of best-matching optimization configurations per quantum circuit, ArtA suggests universal architectural features that perform optimally across all examined circuits, emphasizing the importance of maximizing quantum gate parallelization at the expense of more crosstalk interference.

All quantum harmonic oscillators possess an ontological variable, which implies that they may be interpreted in terms of classical logic. Since many quantum models are based on quantum harmonic oscillators, this observation may open pathways towards a better understanding of how to interpret quantum mechanics.

An observer with a finite lifetime $\mathcal{T}$ perceives the Minkowski vacuum as a thermal state at temperature $T_D = 2 \hbar/(\pi \mathcal{T})$, as a result of being constrained to a double-coned-shaped region known as a causal diamond. In this paper, we explore the emergence of thermality in causal diamonds due to the role played by the symmetries of conformal quantum mechanics (CQM) as a (0+1)-dimensional conformal field theory, within the de Alfaro-Fubini-Furlan model and generalizations. In this context, the hyperbolic operator $S$ of the SO(2,1) symmetry of CQM is the generator of the time evolution of a diamond observer, and its dynamical behavior leads to the predicted thermal nature. Our approach is based on a comprehensive framework of path-integral representations of the CQM generators in canonical and microcanonical forms, supplemented by semiclassical arguments. The properties of the operator $S$ are studied with emphasis on an operator duality with the corresponding elliptic operator $R$, using a representation in terms of an effective scale-invariant inverse square potential combined with inverted and ordinary harmonic oscillator potentials.

Causal diamonds are known to have thermal behavior that can be probed by finite-lifetime observers equipped with energy-scaled detectors. This thermality can be attributed to the time evolution of observers within the causal diamond, governed by one of the conformal quantum mechanics (CQM) symmetry generators: the noncompact hyperbolic operator $S$. In this paper, we show that the unbounded nature of $S$ endows it with a quantum instability, which is a generalization of a similar property exhibited by the inverted harmonic oscillator potential. Our analysis is semiclassical, including a detailed phase-space study of the classical dynamics of $S$ and its dual operator $R$, and a general semiclassical framework yielding basic instability and thermality properties that play a crucial role in the quantum behavior of the theory. For an observer with a finite lifetime $\mathcal{T}$, the detected temperature $T_D = 2 \hbar/(\pi \mathcal{T})$ is associated with a Lyapunov exponent $\lambda_L = \pi T_D/\hbar$, which is half the upper saturation bound of the information scrambling rate.

The emergence of quantum reinforcement learning (QRL) is propelled by advancements in quantum computing (QC) and machine learning (ML), particularly through quantum neural networks (QNN) built on variational quantum circuits (VQC). These advancements have proven successful in addressing sequential decision-making tasks. However, constructing effective QRL models demands significant expertise due to challenges in designing quantum circuit architectures, including data encoding and parameterized circuits, which profoundly influence model performance. In this paper, we propose addressing this challenge with differentiable quantum architecture search (DiffQAS), enabling trainable circuit parameters and structure weights using gradient-based optimization. Furthermore, we enhance training efficiency through asynchronous reinforcement learning (RL) methods facilitating parallel training. Through numerical simulations, we demonstrate that our proposed DiffQAS-QRL approach achieves performance comparable to manually-crafted circuit architectures across considered environments, showcasing stability across diverse scenarios. This methodology offers a pathway for designing QRL models without extensive quantum knowledge, ensuring robust performance and fostering broader application of QRL.

We present a tight inequality to test the dynamical nature of spacetime. A general-relativistic violation of that inequality certifies change of curvature, in the same sense as a quantum-mechanical violation of a Bell inequality certifies a source of entanglement. The inequality arises from a minimal generalization of the Bell setup. It represents a limit on the winning chance of a collaborative multi-agent game played on the M\"obius graph. A long version of this Letter including other games and how these games certify the dynamical character of the celebrated quantum switch is accessible as arXiv:2309.15752 [gr-qc].

We construct $\mathbb{Z}_N$ orbifolds of the ten-dimensional heterotic string theories appropriate for implementing the stringy replica method for the calculation of quantum entanglement entropy. A novel feature for the heterotic string is that the gauge symmetry must be broken by a Wilson line to ensure modular invariance. We completely classify the patterns of symmetry breaking. We show that the tachyonic contributions in all cases can be analytically continued, with a finite answer in the domain $0<N \leq 1$, relevant for calculating entanglement entropy across the Rindler horizon. We discuss the physical implications of our results.

Neutral atoms become strongly interacting when their electrons are excited to loosely bound Rydberg states. We investigate the strongly correlated quantum phases of matter that emerge in two-dimensional atom arrays where three Rydberg levels are used to encode an effective spin-1 degree of freedom. Dipolar exchange between such spin-1 Rydberg atoms naturally yields two distinct models: (i) a two-species hardcore boson model, and (ii) upon tuning near a F\"orster resonance, a dipolar spin-1 XY model. Through extensive, large-scale infinite density matrix renormalization group calculations, we provide a broad roadmap predicting the quantum phases that emerge from these models on a variety of lattice geometries: square, triangular, kagome, and ruby. We identify a wealth of correlated states, including lattice supersolids and simplex phases, all of which can be naturally realized in near-term experiments.

Superfluidity describes the ability of quantum matter to flow without friction. Due to its fundamental role in many transport phenomena, it is crucial to understand the robustness of superfluid properties to external perturbations. Here, we theoretically study the effects of speckle disorder on the propagation of sound waves in a two-dimensional Bose-Einstein condensate at zero temperature. We numerically solve the Gross-Pitaevskii equation in the presence of disorder and employ a superfluid hydrodynamic approach to elucidate the role of the compressibility and superfluid fraction on the propagation of sound. A key result is that disorder reduces the superfluid fraction and hence the speed of sound; it also introduces damping and mode coupling. In the limit of weak disorder, the predictions for the speed of sound and its damping rate are well reproduced by a quadratic perturbation theory. The hydrodynamic description is valid over a wide range of parameters, while discrepancies become evident if the disorder becomes too strong, the effect being more significant for disorder applied in only one spatial direction. Our predictions are well within the reach of state-of-the-art cold-atom experiments and carry over to more general disorder potentials.

This work treats few-body systems consisting of neutrons interacting with a $^{4}{\mathrm{He}}$ nucleus. The adiabatic hyperspherical representation is utilized to solve the $N$-body Schr$\ddot{\mathrm{o}}$dinger equation for the three- and four-body systems, treating both $^{6}{\mathrm{He}}$ and $^{7}{\mathrm{He}}$ nuclei. A simplified central potential model for the $^{4}{\mathrm{He}}-n$ interaction is used in conjunction with a spin-dependent three-body interaction to reproduce $^{6}{\mathrm{He}}$ bound-state and resonance properties as well as properties for the $^{8}{\mathrm{He}}$ nucleus in its ground-state. With this Hamiltonian, the adiabatic hyperspherical representation is used to compute bound and scattering states for both $^{6}{\mathrm{He}}$ and $^{7}{\mathrm{He}}$ nuclei. For the $^{6}{\mathrm{He}}$ system, the electric quadrupole transition between the $0^{+}$ and $2^{+}$ state is investigated. For the $^{7}{\mathrm{He}}$ system, $^{6}{\mathrm{He}}+n$ elastic scattering is investigated along with the four-body recombination process $^{4}{\mathrm{He}}+n+n+n\rightarrow$$^{6}{\mathrm{He}}+n$ and breakup process $^{6}{\mathrm{He}}+n\rightarrow$$^{4}{\mathrm{He}}+n+n+n$.

Quantum cosmology aims at elucidating the beginning of our Universe. Back in early 80's, Vilenkin and Hartle-Hawking put forward the "tunneling from nothing'' and "no boundary'' proposals. Recently there has been renewed interest in this subject from the viewpoint of defining the oscillating path integral for Lorentzian quantum gravity using the Picard-Lefschetz theory. Aiming at going beyond the mini-superspace and saddle-point approximations, we perform Monte Carlo calculations using the generalized Lefschetz thimble method to overcome the sign problem. In particular, we confirm that either Vilenkin or Hartle-Hawking saddle point becomes relevant if one uses the Robin boundary condition depending on its parameter. We also clarify some fundamental issues in quantum cosmology, such as an issue related to the integration domain of the lapse function and an issue related to reading off the real geometry from the complex geometry obtained at the saddle point.

We study a model of networked atoms or molecules oscillating around their equilibrium positions. The model assumes the harmonic approximation of the interactions. We provide bounds for the total number of phonons, and for the specific heat, in terms of the average Wiener capacity, or resistance, of the network. Thanks to such bounds, we can distinguish qualitatively different behaviours in terms of the network structure alone.

In present work, we present a couple-channel formalism for the description of tunneling time of a quantum particle through a composite compound with multiple energy levels or a complex structure that can be reduced to a quasi-one-dimensional multiple-channel system.

The finding that electronic conductance across ultra-thin protein films between metallic electrodes remains nearly constant from room temperature to just a few degrees Kelvin has posed a challenge. We show that a model based on a generalized Landauer formula explains the nearly constant conductance and predicts an Arrhenius-like dependence for low temperatures. A critical aspect of the model is that the relevant activation energy for conductance is either the difference between the HOMO and HOMO-1 or the LUMO+1 and LUMO energies instead of the HOMO-LUMO gap of the proteins. Analysis of experimental data confirm the Arrhenius-like law and allows us to extract the activation energies. We then calculate the energy differences with advanced DFT methods for proteins used in the experiments. Our main result is that the experimental and theoretical activation energies for these three different proteins and three differently prepared solid-state junctions match nearly perfectly, implying the mechanism's validity.

This paper looks at the intersection of algorithmic information theory and physics, namely quantum mechanics, thermodynamics, and black holes. We discuss theorems which characterize the barrier between the quantum world and the classical realm. The notion of a "semi-classical subspace" is introduced. The No Synchronization Law is detailed, which says separate and isolated physical systems evolving over time cannot have thermodynamic algorithmic entropies that are in synch. We look at future work involving the Kolmogorov complexity of black holes.