## Quantum Physics (quant-ph) updates on the arXiv.org e-print archive



We describe the class (semigroup) of quantum channels mapping states with finite entropy into states with finite entropy. We show, in particular, that this class is naturally decomposed into three convex subclasses, two of them are closed under concatenations and tensor products. We obtain asymptotically tight universal continuity bounds for the output entropy of two types of quantum channels: channels with finite output entropy and energy-constrained channels preserving finiteness of the entropy.

One of the important characteristics of topological phases of matter is the topology of the underlying manifold on which they are defined. In this paper, we present the sensitivity of such phases of matter to the underlying topology, by studying the phase transitions induced due to the change in the boundary conditions. We claim that these phase transitions are accompanied by broken symmetries in the excitation space and to gain further insight we analyze various signatures like the ground state degeneracy, topological entanglement entropy while introducing the open-loop operator whose expectation value effectively captures the phase transition. Further, we extend the analysis to an open quantum setup by defining effective collapse operators, the dynamics of which cool the system to different topologically ordered steady states. We show that the phase transition between such steady states is effectively captured by the expectation value of the open-loop operator.

A good qubit must have a coherence time long enough for gate operations to be performed. Avoided level crossings allow for clock transitions in which coherence is enhanced by the insensitivity of the transition to fluctuations in external fields. Because of this insensitivity, it is not obvious how to effectively couple qubits together while retaining clock-transition behavior. Here we present a scheme for using a heterodimer of two coupled molecular nanomagnets, each with a clock transition at zero magnetic field, in which all of the gate operations needed to implement one- and two-qubit gates can be implemented with pulsed radio-frequency radiation. We show that given realistic coupling strengths between the nanomagnets in the dimer, good gate fidelities ($\sim$99.4\%) can be achieved. We identify the primary sources of error in implementing gates and discuss how these may be mitigated, and investigate the range of coherence times necessary for such a system to be a viable platform for implementing quantum computing protocols.

Gauge-invariance is a fundamental concept in Physics---known to provide mathematical justification for the fundamental forces. In this paper, we provide discrete counterparts to the main gauge theoretical concepts directly in terms of Cellular Automata. More precisely, the notions of gauge-invariance and gauge-equivalence in Cellular Automata are formalized. A step-by-step gauging procedure to enforce this symmetry upon a given Cellular Automaton is developed, and three examples of gauge-invariant Cellular Automata are examined.

Modern challenges arising in the fields of theoretical and experimental physics require new powerful tools for high-precision electronic structure modelling; one of the most perspective tools is the relativistic Fock space coupled cluster method (FS-RCC). Here we present a new extensible implementation of the FS-RCC method designed for modern parallel computers. The underlying theoretical model, algorithms and data structures are discussed. The performance and scaling features of the implementation are analyzed. The software developed allows to achieve a completely new level of accuracy for prediction of properties of atoms and molecules containing heavy and superheavy nuclei.

Non-Hermiticity and decoherence are two different effects of the open systems. Each of them has triggered many interesting phenomena. In this work, we rewrite the non-Hermitian Lindblad master equation into a linear one, under which the eigenvalues and eigenmatrices are easy to be obtained. Based on this, we consider an open system including both non-Hermitian and decoherence effects, which can be realized in the system of linearly coupled active and passive resonators. We find that there are new-style exceptional points and steady-states without PT-symmetry or pseudo-Hermiticity in this system. And we demonstrate that they in the presented system have different properties from the cases of the normal open quantum systems. Our work opens a new way to further explore the open systems.

Current density distributions in active integrated circuits (ICs) result in patterns of magnetic fields that contain structural and functional information about the IC. Magnetic fields pass through standard materials used by the semiconductor industry and provide a powerful means to fingerprint IC activity for security and failure analysis applications. Here, we demonstrate high spatial resolution, wide field-of-view, vector magnetic field imaging of static (DC) magnetic field emanations from an IC in different active states using a Quantum Diamond Microscope (QDM). The QDM employs a dense layer of fluorescent nitrogen-vacancy (NV) quantum defects near the surface of a transparent diamond substrate placed on the IC to image magnetic fields. We show that QDM imaging achieves simultaneous $\sim10$ $\mu$m resolution of all three vector magnetic field components over the 3.7 mm $\times$ 3.7 mm field-of-view of the diamond. We study activity arising from spatially-dependent current flow in both intact and decapsulated field-programmable gate arrays (FPGAs); and find that QDM images can determine pre-programmed IC active states with high fidelity using machine-learning classification methods.

We introduce a measure of non-Markovianity based on the minimal amount of extra Markovian noise we have to add to the process via incoherent mixing, in order to make the resulting transformation Markovian too at all times. We show how to evaluate this measure by considering the set of depolarizing evolutions in arbitrary dimension and the set of dephasing evolutions for qubits.

Multiphoton entanglement, as a quantum resource, plays an essential role in linear optical quantum information processing. Krenn et al. (Phys. Rev. Lett. 118, 080401 2017) proposed an innovative scheme that generating entanglement by path identity, in which two-photon interference (called Hong-Ou-Mandel effect) is not necessary in experiment. However, the experiments in this scheme have strict requirements in stability and scalability, which is difficult to be realized in bulk optics. To solve this problem, in this paper we first propose an on-chip scheme to generate multi-photon polarization entangled states, including Greenberger-Horne-Zeilinger (GHZ) states and W states. Moreover, we also present a class of generalized graphs for W states (odd-number-photon) by path identity in theory. The on-chip scheme can be implemented in existing integrated optical technology which is meaningful for multi-party entanglement distribution in quantum communication networks.

All elementary particles in nature can be classified as fermions with half-integer spin and bosons with integer spin. Within quantum electrodynamics (QED), even though the spin of the Dirac particle is well defined, there exist open questions on the quantized description of the spin of the gauge field particle - the photon. Here, we discover the quantum operators for the spin angular momentum (SAM) $\boldsymbol{S}_{M}=(1/c)\int d^{3}x\boldsymbol{\pi}\times\boldsymbol{A}$ and orbital angular momentum (OAM) $\boldsymbol{L}_{M}=-(1/c)\int d^{3}x\pi^{\mu}\boldsymbol{x}\times\boldsymbol{\nabla}A_{\mu}$ of the photon, where $\pi^{\mu}$ is the the conjugate canonical momentum of the gauge field $A_{\mu}$. Using relativistic field theory, we show that these physical quantities obey the canonical commutation relations for angular momenta. Importantly, we reveal a fundamental gauge-hiding mechanism that identifies the missing link between the complete photon spin operator and helicity, an experimental observable. Our work resolves the long-standing issues on the decomposition of the orbital and spin angular momentum of the photon with applications in quantum optics, topological photonics as well as nanophotonics and also has important ramifications for the spin structure of nucleons.

Minor embedding heuristics have become an indispensable tool for compiling problems in quadratically unconstrained binary optimization (QUBO) into the hardware graphs of quantum and CMOS annealing processors. While recent embedding heuristics have been developed for annealers of moderate size (about 2000 nodes) the size of the latest CMOS annealing processor (with 102,400 nodes) poses entirely new demands on the embedding heuristic. This raises the question, if recent embedding heuristics can maintain meaningful embedding performance on hardware graphs of increasing size. Here, we develop an improved version of the probabilistic-swap-shift-annealing (PSSA) embedding heuristic [which has recently been demonstrated to outperform the standard embedding heuristic by D-Wave Systems (Cai et al., 2014)] and evaluate its embedding performance on hardware graphs of increasing size. For random-cubic and Barabasi-Albert graphs we find the embedding performance of improved PSSA to consistently exceed the threshold of the best known complete graph embedding by a factor of 3.2 and 2.8, respectively, up to hardware graphs with 102,400 nodes. On the other hand, for random graphs with constant edge density not even improved PSSA can overcome the deterministic threshold guaranteed by the existence of the best known complete graph embedding. Finally, we prove a new upper bound on the maximal embeddable size of complete graphs into hardware graphs of CMOS annealers and show that the embedding performance of its currently best known complete graph embedding has optimal order for hardware graphs with fixed coordination number.

We theoretically analyse the equation of topological solitons in a chain of particles interacting via a repulsive power-law potential and confined by a periodic lattice. Starting from the discrete model, we perform a gradient expansion which delivers the kink equation in the continuum limit. The power-law interaction modifies the sine-Gordon equation, giving rise to a rescaling of the coefficient in from of the second derivative (the kink width) and to an additional integral term. We argue that the integral term does not affect the local properties of the kink, but it governs the behaviour at the asymptotics. The kink behaviour at the center is dominated by a sine-Gordon equation, where the kink width tends to increase with the power law exponent. When the interaction is the Coulomb repulsion, in particular, the kink width depends logarithmically on the chain size. We define an appropriate thermodynamic limit and compare our results with existing studies performed for infinite chains. Our formalism allows one to systematically take into account the finite-size effects and also slowly varying external potentials, such as for instance the curvature in an ion trap.

In this document it is shown that the chemical shift, spin-spin couplings and return to equilibrium observed in Nuclear Magnetic Resonance (NMR) are naturally contained in the realtime nuclear spin dynamics, if the dynamics is calculated directly from molecular Quantum Electrodynamics at finite temperatures. Thus, no effective NMR parameters or relaxation superoperators are used for the calculation of \textit{continuous} NMR spectra. This provides a basis for the repeal of Ramsey's theory from the 1950s, NMR relaxation theory and later developments which form the current basis for NMR theory. The presented approach replaces the discrete spectrum of the effective spin model by a continuous spectrum, whose numerical calculation is enabled by the usage of the mathematical structure of algebraic Quantum Field Theory. While the findings are demonstrated for the hydrogen atom, it is outlined that the approach can be applied to any molecular system for which the electronic structure can be calculated by using a common quantum chemical method. Thus, the presented approach has potential for an improved NMR data analysis and more accurate predictions for hyperpolarized Magnetic Resonance Imaging.

Population transfer in quantum systems has always been an interesting area in physics since the introduction of quantum mechanics. In this paper, transition probabilities for a coupled system consisting of four two - level particles are studied by solving Landau - Zener Hamiltonian. The effects of the first and second nearest neighbors interactions are investigated. Presented results indicate that the second nearest neighbors interactions will decrease the transition probability when the coupling strength for each neighborhood has the same sign. The fast sweep effect on transition probability is also studied here.

The purpose of this paper is to present a comprehensive study of a coherent feedback network where the main component consists of two distant double quantum dot (DQD) qubits which are directly coupled to a cavity. This main component has recently been physically realized (van Woerkom, {\it et al.}, Microwave photon-mediated interactions between semiconductor qubits, Physical Review X, 8(4):041018, 2018). The feedback loop is closed by cascading this main component with a beamsplitter. The dynamics of this coherent feedback network is studied from three perspectives. First, an analytic form of the output single-photon state of the network driven by a single-photon state is derived; in particular, it is observed that coherent feedback elongates considerably the interaction between the input single photon and the network. Second, excitation probabilities of DQD qubits are computed when the network is driven by a single-photon input state. Moreover, if the input is vacuum but one of the two DQD qubits is initialized in its excited state, the explicit expression of the state of the network is derived, in particular, it is shown that the output field and the two DQD qubits can form an entangled state if the transition frequencies of two DQD qubits are equal. Finally, the exact form of the pulse shape is obtained by which the single-photon input can fully excite one of these two DQD qubits at any controllable time, which may be useful in the construction of $2$-qubit quantum gates.

Ultraviolet (UV) diode lasers are widely used in many photonics applications. But their frequency stabilization schemes are not as mature as frequency-doubling lasers, mainly due to some limitations in the UV spectral region. Here we developed a high-performance UV frequency stabilization technique implemented directly on UV diode lasers by combining the dichroic atomic vapor laser lock and the resonant transfer cavity lock. As an example, we demonstrate a stable locking with frequency standard deviations of approximately 200 KHz and 300 KHz for 399nm and 370nm diode lasers in 20 minutes. We achieve a long-term frequency drift of no more than 1 MHz for the target 370nm laser within an hour, which was further verified with fluorescence counts rates of a single trapped $^{171}$Yb$^+$ ion. We also find strong linear correlations between lock points and environmental factors such as temperature and atmospheric pressure.

Quantum or classical mechanical systems symmetric under $SU(2)$ are called spin systems. A $SU(2)$-equivariant map from $(n+1)$-square matrices to functions on the $2$-sphere, satisfying some basic properties, is called a spin-$j$ symbol correspondence ($n=2j\in\mathbb N$). Given a spin-$j$ symbol correspondence, the matrix algebra induces a twisted $j$-algebra of symbols. In this paper, we establish a new, more intuitive criterion for when the Poisson algebra of smooth functions on the $2$-sphere emerges asymptotically ($n\to\infty$) from the sequence of twisted $j$-algebras of symbols. This new, more geometric criterion, which in many cases is equivalent to the numerical criterion obtained in [Rios&Straume], is now given in terms of a classical (asymptotic) localization of the symbols of projectors (quantum pure states). For some important kinds of symbol correspondence sequences, classical localization of all projector-symbols is equivalent to asymptotic emergence of the Poisson algebra. But in general, such a classical localization condition is stronger than Poisson emergence. We thus also consider some weaker notions of asymptotic localization of projector-symbols. Finally, we obtain some relations between asymptotic localization of a symbol correspondence sequence and its quantizations of the classical spin system.

A novel quantum-classical hybrid scheme is proposed to efficiently solve large-scale combinatorial optimization problems. The key concept is to introduce a Hamiltonian dynamics of the classical flux variables associated with the quantum spins of the transverse-field Ising model. Molecular dynamics of the classical fluxes can be used as a powerful preconditioner to sort out the frozen and ambivalent spins for quantum annealers. The performance and accuracy of our smooth hybridization in comparison to the standard classical algorithms (the tabu search and the simulated annealing) are demonstrated by employing the MAX-CUT and Ising spin-glass problems.

It is commonly known that the Fokker-Planck equation is exactly solvable only for some particular systems, usually with time-independent drift coefficients. To extend the class of solvable problems, we use the intertwining relations of SUSY Quantum Mechanics but in new - asymmetric - form. It turns out that this form is just useful for solution of Fokker-Planck equation. As usual, intertwining provides a partnership between two different systems both described by Fokker-Planck equation. Due to the use of an asymmetric kind of intertwining relations with a suitable ansatz, we managed to obtain a new class of analytically solvable models. What is important, this approach allows us to deal with the drift coefficients depending on both variables, $x,$ and $t.$ An illustrating example of the proposed construction is given explicitly.

We establish a kind of resource conversion relationship between quantum coherence and entanglement in multipartite systems, where the operational measures of resource cost and distillation are focused on. The coherence cost of single-party system bounds the maximal amounts of entanglement cost and entanglement of formation generated via multipartite incoherent operations. The converted entanglement in multipartite systems can be further transferred to subsystems or restored to coherence of single party by means of local incoherent operations and classical communications. The similar relations also hold for distillable coherence and entanglement. As an example, we present a scheme for cyclic interconversion between coherence and entanglement in three-qubit systems under full incoherent operations scenario. Moreover, we also analyze the property of genuine multi-level entanglement by the initial coherence and investigate resource dynamics in the conversion.

Periodically driven quantum systems manifest various non-equilibrium features which are absent at equilibrium. For example, discrete time-translation symmetry can be broken in periodically driven quantum systems leading to an exotic phase of matter, called discrete time crystal(DTC). For open quantum systems, previous studies showed that DTC can be found only when there exists a meta-stable state in the undriven system. However, by investigating the simplest Bose-Hubbard model with dissipation and time periodically tunneling, we find in this paper that a $2T$ DTC can appear even when the meta-stable state is absent in the undriven system. This observation extends the understanding of DTC and shed more light on the physics behind the DTC. Besides, by the detailed analysis of simplest two-sites model, we show further that the two-sites model can be used as basic building blocks to construct large rings in which a $nT$ DTC might appear. These results might find applications into engineering exotic phases in driven open quantum systems.

The development of spin qubits for quantum technologies requires their protection from the main source of finite-temperature decoherence: atomic vibrations. Here we eliminate one of the main barriers to the progress in this field by providing a complete first-principles picture of spin relaxation that includes up to two-phonon processes. Our method is based on machine learning and electronic structure theory and makes the prediction of spin lifetime in realistic systems feasible. We study a prototypical vanadium-based molecular qubit and reveal that the spin lifetime at high temperature is limited by Raman processes due to a small number of THz intra-molecular vibrations. These findings effectively change the conventional understanding of spin relaxation in this class of materials and open new avenues for the rational design of long-living spin systems.

This paper presents a non-Hermitian PT-symmetric extension of the Nambu--Jona-Lasinio (NJL) model of quantum chromodynamics in 3+1 and 1+1 dimensions. In 3+1 dimensions, the SU(2)-symmetric NJL Hamiltonian $H_{\textrm{NJL}} = \bar\psi (-i \gamma^k \partial_k + m_0) \psi - G [ (\bar\psi \psi)^2 + (\bar\psi i \gamma_5 \vec{\tau} \psi)^2 ]$ is extended by the non-Hermitian, PT- and chiral-symmetric bilinear term $ig\bar\psi \gamma_5 B_{\mu} \gamma^{\mu} \psi$; in 1+1 dimensions, where $H_{\textrm{NJL}}$ is a form of the Gross-Neveu model, it is extended by the non-Hermitian PT-symmetric but chiral symmetry breaking term $g \bar\psi \gamma_5 \psi$. In each case, the gap equation is derived and the effects of the non-Hermitian terms on the generated mass are studied. We have several findings: in previous calculations for the free Dirac equation modified to include non-Hermitian bilinear terms, contrary to expectation, no real mass spectrum can be obtained in the chiral limit; in these cases a nonzero bare fermion mass is essential for the realization of PT symmetry in the unbroken regime. Here, in the NJL model, in which four-point interactions are present, we {\it do} find real values for the mass spectrum also in the limit of vanishing bare masses in both 3+1 and 1+1 dimensions, at least for certain specific values of the non-Hermitian couplings $g$. Thus, the four-point interaction overrides the effects leading to PT symmetry-breaking for these parameter values. Further, we find that in both cases, in 3+1 and in 1+1 dimensions, the inclusion of a non-Hermitian bilinear term can contribute to the generated mass. In both models, this contribution can be tuned to be small; we thus fix the fermion mass to its value when $m_0=0$ in the absence of the non-Hermitian term, and then determine the value of the coupling required so as to generate a bare fermion mass.

The left-to-right motion of a free quantum Gaussian wave packet can be accompanied by the right-to-left flow of the probability density, the effect recently studied by Villanueva [Am. J. Phys. 88, 325 (2020)]. Using the Wigner representation of the wave packet, we analyze the effect in phase space, and demonstrate that its physical origin is rooted in classical mechanics.

In this paper we develop the Hellmann-Feynman theorem in statistical mechanics without resorting to the eigenvalues and eigenvectors of the Hamiltonian operator. Present approach does not require the quantum-mechanical version of the theorem at $T=0$.

We simulate various topological phenomena in condense matter, such as formation of different edge states and topological phases, through two types of quantum walk with step-dependent coins in one- and two-dimensional position space. Particularly, we show that quantum walk with step-dependent coin simulates all types of topological phases and edge states. In addition, we show that step-dependent coins provide the number of steps as a controlling factor over the simulations. In fact, with tuning number of steps, we can determine the occurrences of edge states or topological phases, the type of edge state or topological phases and where they should be located. These two features make quantum walks versatile and highly controllable simulators of topological phases, edge states and topological phase transitions. We also report on emergences of cell-like structures for simulated topological phases and edge states. Each cell contains all types of edge states and topological phases.

The Generalized Uncertainty Principle (GUP) has been directly applied to the motion of (macroscopic) test bodies on a given space-time in order to compute corrections to the classical orbits predicted in Newtonian Mechanics or General Relativity. These corrections generically violate the Equivalence Principle. The GUP has also been indirectly applied to the gravitational source by relating the GUP modified Hawking temperature to a deformation of the background metric. Such a deformed background metric determines new geodesic motions without violating the Equivalence Principle. We point out here that the two effects are mutually exclusive when compared with experimental bounds. Moreover, the former stems from modified Poisson brackets obtained from a wrong classical limit of the deformed canonical commutators.

We re-visit Unclonable Encryption as introduced by Gottesman in 2003. We introduce two slightly different qubit-based prepare-and-measure Unclonable Encryption schemes with re-usable keys. We aim for low communication complexity and high rate. Our first scheme has low complexity but a sub-optimal rate. Our second scheme needs more rounds but has the advantage that it achieves the same rate as Quantum Key Distribution. We provide security proofs for both our schemes, based on the diamond norm distance, taking noise into account.

Extended versions of the Lambek Calculus currently used in computational linguistics rely on unary modalities to allow for the controlled application of structural rules affecting word order and phrase structure. These controlled structural operations give rise to derivational ambiguities that are missed by the original Lambek Calculus or its pregroup simplification. Proposals for compositional interpretation of extended Lambek Calculus in the compact closed category of FVect and linear maps have been made, but in these proposals the syntax-semantics mapping ignores the control modalities, effectively restricting their role to the syntax. Our aim is to turn the modalities into first-class citizens of the vectorial interpretation. Building on the density matrix semantics of (Correia et al, 2019), we extend the interpretation of the type system with an extra spin density matrix space. The interpretation of proofs then results in ambiguous derivations being tensored with orthogonal spin states. Our method introduces a way of simultaneously representing co-existing interpretations of ambiguous utterances, and provides a uniform framework for the integration of lexical and derivational ambiguity.

The ability to simulate a fermionic system on a quantum computer is expected to revolutionize chemical engineering, materials design, nuclear physics, to name a few. Thus, optimizing the simulation circuits is of significance in harnessing the power of quantum computers. Here, we address this problem in two aspects. In the fault-tolerant regime, we optimize the $\rzgate$ gate counts and depths, assuming the use of a product-formula algorithm for implementation. In the pre-fault tolerant regime, we optimize the two-qubit gate counts, assuming the use of variational quantum eigensolver (VQE) approach. Specifically to the latter, we present a framework that enables bootstrapping the VQE progression towards the convergence of the ground-state energy of the fermionic system. This framework, based on perturbation theory, also improves the energy estimate at each cycle of the VQE progression dramatically, resulting in significant savings of quantum resources required to be within a pre-specified tolerance from the known ground-state energy in the test-bed, classically-accessible system of the water molecule. We also explore a suite of generalized transformations of fermion to qubit operators and show that resource-requirement savings of up to nearly $20\%$ is possible.

Quantum enhanced sensing promises to improve the performance of sensing tasks using non-classical probes and measurements using far less scene-modulated photons than possible by the best classical scheme, thereby gaining previously-inaccessible quantitative information about a wide range of physical systems. We propose a generalized distributed sensing framework that uses an entangled quantum probe to estimate a scene-parameter that is encoded within an array of phases, with a functional dependence on that parameter determined by the physics of the actual system. The receiver uses a laser light source enhanced by quantum-entangled multi-partite squeezed-vacuum light to probe the phases, to estimate the desired scene parameter. The entanglement suppresses the collective quantum vacuum noise across the phase array. We show our approach enables Heisenberg limited sensitivity in estimating the scene parameter with respect to total probe energy, as well as with respect to the number of modulated phases, and saturates the quantum Cram\'er Rao bound. We apply our approach to examples as diverse as radio-frequency phased-array directional radar, fiber-based temperature gradiometer, and beam-displacement tracking for atomic-force microscopy.

An important task in quantum physics is the estimation of local quantities for ground states of local Hamiltonians. Recently, [Ambainis, CCC 2014] defined the complexity class P^QMA[log], and motivated its study by showing that the physical task of estimating the expectation value of a local observable against the ground state of a local Hamiltonian is P^QMA[log]-complete. In this paper, we continue the study of P^QMA[log], obtaining the following lower and upper bounds.

Lower bounds (hardness results): (1) The P^QMA[log]-completeness result of [Ambainis, CCC 2014] requires O(log n)-local observables and Hamiltonians. We show that simulating even a single qubit measurement on ground states of 5-local Hamiltonians is P^QMA[log]-complete, resolving an open question of Ambainis. (2) We formalize the complexity theoretic study of estimating two-point correlation functions against ground states, and show that this task is similarly P^QMA[log]-complete. (3) We identify a flaw in [Ambainis, CCC 2014] regarding a P^UQMA[log]-hardness proof for estimating spectral gaps of local Hamiltonians. By introducing a "query validation" technique, we build on [Ambainis, CCC 2014] to obtain P^UQMA[log]-hardness for estimating spectral gaps under polynomial-time Turing reductions.

Upper bounds (containment in complexity classes): P^QMA[log] is thought of as "slightly harder" than QMA. We justify this formally by exploiting the hierarchical voting technique of [Beigel, Hemachandra, Wechsung, SCT 1989] to show P^QMA[log] is in PP. This improves the containment QMA is in PP [Kitaev, Watrous, STOC 2000].

This work contributes a rigorous treatment of the subtlety involved in studying oracle classes in which the oracle solves a promise problem. This is particularly relevant for quantum complexity theory, where most natural classes such as BQP and QMA are defined as promise classes.

Quantum Darwinism extends the traditional formalism of decoherence to explain the emergence of classicality in a quantum universe. A classical description emerges when the environment tends to redundantly acquire information about the pointer states of an open system. In light of recent interest, we apply the theoretical tools of the framework to a qubit coupled with many bosonic sub-environments. We examine the degree to which the same classical information is encoded across collections of: (i) complete sub-environments, and (ii) residual "pseudomode" components of each sub-environment, the conception of which provides a dynamic representation of the reservoir memory. Overall, significant redundancy of information is found as a typical result of the decoherence process. However, by examining its decomposition in terms of classical and quantum correlations, we discover classical information to be non-redundant in both cases (i) and (ii). Moreover, with the full collection of pseudomodes, certain dynamical regimes realize opposite effects, where either the total classical or quantum correlations predominantly decay over time. Finally, when the dynamics are non-Markovian, we find that redundant information is suppressed in line with information back-flow to the qubit. By quantifying redundancy, we concretely show it to act as a witness to non-Markovianity in the same way as the trace distance does for nondivisible dynamical maps.

We still do not have perfect decoders for topological codes that can satisfy all needs of different experimental setups. Recently, a few neural network based decoders have been studied, with the motivation that they can adapt to a wide range of noise models, and can easily run on dedicated chips without a full-fledged computer. The later feature might lead to fast speed and the ability to operate at low temperatures. However, a question which has not been addressed in previous works is whether neural network decoders can handle 2D topological codes with large distances. In this work, we provide a positive answer for the toric code. The structure of our neural network decoder is inspired by the renormalization group decoder. With a fairly strict policy on training time, when the bit-flip error rate is lower than $9\%$ and syndrome extraction is perfect, the neural network decoder performs better when code distance increases. With a less strict policy, we find it is not hard for the neural decoder to achieve a performance close to the minimum-weight perfect matching algorithm. The numerical simulation is done up to code distance $d=64$. Last but not least, we describe and analyze a few failed approaches. They guide us to the final design of our neural decoder, but also serve as a caution when we gauge the versatility of stock deep neural networks. The source code of our neural decoder can be found at https://github.com/XiaotongNi/toric-code-neural-decoder .

We investigate whether entanglement can survive the thermalization of subsystems. We present two equivalent formulations of this problem: (1) Can two isolated agents, accessing only pre-shared randomness, locally thermalize arbitrary input states while maintaining some entanglement? (2) Can thermalization with local heat baths, which may be classically correlated but do not exchange information, locally thermalize arbitrary input states while maintaining some entanglement? We answer these questions in the positive at every nonzero temperature and provide bounds on the amount of preserved entanglement. We provide explicit protocols and discuss their thermodynamic interpretation: we suggest that the underlying mechanism is a speed-up of the subsystem thermalization process. We also present extensions to multipartite systems. Our findings show that entanglement can survive locally performed thermalization processes accessing only classical correlations as a resource. They also suggest a broader study of the channel's ability to preserve resources and of the compatibility between global and local dynamics.

Estimating multiple parameters simultaneously is of great importance to measurement science and application. For a single parameter, atomic Ramsey interferometry (or equivalently optical Mach-Zehnder interferometry) is capable of providing the precision at the standard quantum limit (SQL) using unentangled probe states as input. In such an interferometer, the first beam splitter represented by unitary transformation $U$ generates a quantum phase sensing superposition state, while the second beam splitter $U^{-1}$ recombines the phase encoded paths to realize interferometric sensing in terms of population measurements. We prove that such an interferometric scheme can be directly generalized to estimation of multiple parameters (associated with commuting generators) to the SQL precision using multi-mode unentangled states, if (but not iff) $U$ is orthogonal, i.e. a unitary transformation with only real matrix elements. We show that such a $U$ can always be constructed experimentally in a simple and scalable manner. The effects of particle number fluctuation and detection noise on such multi-mode interferometry are considered. Our findings offer a simple solution for estimating multiple parameters corresponding to mutually commuting generators.

We provide evidence that, alongside topologically protected edge states, two-dimensional Chern insulators also support localised bulk states deep in their valance and conduction bands. These states manifest when local potential gradients are applied to the bulk, while all parts of the system remain adiabatically connected to the same phase. In turn, the bulk states produce bulk current transverse to the strain. This occurs even when the potential is always below the energy gap, where one expects only edge currents to appear. Bulk currents are topologically protected and behave like edge currents under external influence, such as temperature or local disorder. Detecting topologically resilient bulk currents offers a direct means to probe the localised bulk states.

Charge qubits can be created and manipulated in solid-state double-quantum-dot (DQD) platforms. Typically, these systems are strongly affected by quantum noise stemming from coupling to substrate phonons. This is usually assumed to lead to decoherence towards steady states that are diagonal in the energy eigenbasis. In this article we show, to the contrary, that due to the presence of phonons the equilibrium steady state of the DQD charge qubit spontaneously exhibits coherence in the energy eigenbasis with high purity. The magnitude and phase of the coherence can be controlled by tuning the Hamiltonian parameters of the qubit. The coherence is also robust to presence of fermionic leads. In addition, we show that this steady-state coherence can be used to drive an auxiliary cavity mode coupled to the DQD.

Entanglement is a fundamental resource for quantum information science. However, bipartite entanglement is destroyed when one particle is observed via projective (sharp) measurements, as it is typically the case in most experiments. Here we experimentally show that, if instead of sharp measurements, one performs many sequential unsharp measurements on one particle which are suitably chosen depending on the previous outcomes, then entanglement is preserved and it is possible to reveal quantum correlations through measurements on the second particle at any step of the sequence. Specifically, we observe that pairs of photons entangled in polarization maintain their entanglement when one particle undergoes three sequential measurements, and each of these can be used to violate a CHSH inequality. This proof-of-principle experiment demonstrates the possibility of repeatedly harnessing two crucial resources, entanglement and Bell nonlocality, that, in most quantum protocols, are destroyed after a single measurement. The protocol we use, which in principle works for an unbounded sequence of measurements, can be useful for randomness extraction.

Initialization of composite quantum systems into highly entangled states is usually a must to allow their use for quantum technologies. However, the presence of unavoidable noise in the preparation stage makes the system state mixed, thus limiting the possibility of achieving this goal. Here we address this problem in the context of identical particle systems. We define the entanglement of formation for an arbitrary state of two identical qubits within the operational framework of spatially localized operations and classical communication (sLOCC). We then introduce an entropic measure of spatial indistinguishability under sLOCC as an information resource. We show that spatial indistinguishability, even partial, may shield entanglement from noise, guaranteeing Bell inequality violations. These results prove the fundamental role of particle identity as a control for efficient noise-protected entanglement generation.

The Quantum Approximate Optimization Algorithm (QAOA) is a standard method for combinatorial optimization with a gate-based quantum computer. The QAOA consists of a particular ansatz for the quantum circuit architecture, together with a prescription for choosing the variational parameters of the circuit. We propose modifications to both. First, we define the Gibbs objective function and show that it is superior to the energy expectation value for use as an objective function in tuning the variational parameters. Second, we describe an Ansatz Architecture Search (AAS) algorithm for searching the discrete space of quantum circuit architectures near the QAOA to find a better ansatz. Applying these modifications for a complete graph Ising model results in a $244.7\%$ median relative improvement in the probability of finding a low-energy state while using $33.3\%$ fewer two-qubit gates. For Ising models on a 2d grid we similarly find $44.4\%$ median improvement in the probability with a $20.8\%$ reduction in the number of two-qubit gates. This opens a new research field of quantum circuit architecture design for quantum optimization algorithms.

Resource theory is a general, model-independent approach aiming to understand the qualitative notion of resource quantitatively. In a given resource theory, free operations are physical processes that do not create the resource and are considered zero-cost. This brings the following natural question: For a given free operation, what is its ability to preserve a resource? We axiomatically formulate this ability as the resource preservability, which is constructed as a channel resource theory induced by a state resource theory. We provide two general classes of resource preservability monotones: One is based on state resource monotones, and another is based on channel distance measures. Specifically, the latter gives the robustness monotone, which has been recently found to have an operational interpretation. As examples, we show that athermality preservability of a Gibbs-preserving channel can be related to the smallest bath size needed to thermalize all its outputs, and it also bounds the capacity of a classical communication scenario under certain thermodynamic constraints. We further apply our theory to the study of entanglement preserving local thermalization (EPLT) and provide a new family of EPLT which admits arbitrarily small nonzero entanglement preservability and free entanglement preservation at the same time. Our results give the first systematic and general formulation of the resource preservation character of free operations.

We discuss the effects of many-body coherence on the speed of evolution of ultracold atomic gases and the relation to quantum speed limits. Our approach is focused on two related systems, spinless fermions and the bosonic Tonks-Girardeau gas, which possess equivalent density dynamics but very different coherence properties. To illustrate the effect of the coherence on the dynamics we consider squeezing an anharmonic potential which confines the particles and find that the speed of the evolution exhibits subtle, but fundamental differences between the two systems. Furthermore, we explore the difference in the driven dynamics by implementing a shortcut to adiabaticity designed to reduce spurious excitations. We show that collisions between the strongly interacting bosons can lead to changes in the coherence which results in different evolution speeds and therefore different fidelities of the final states.

Function inversion is the problem that given a random function $f: [M] \to [N]$, we want to find pre-image of any image $f^{-1}(y)$ in time $T$. In this work, we revisit this problem under the preprocessing model where we can compute some auxiliary information or advice of size $S$ that only depends on $f$ but not on $y$. It is a well-studied problem in the classical settings, however, it is not clear how quantum algorithms can solve this task any better besides invoking Grover's algorithm, which does not leverage the power of preprocessing.

Nayebi et al. proved a lower bound $ST^2 \ge \tilde\Omega(N)$ for quantum algorithms inverting permutations, however, they only consider algorithms with classical advice. Hhan et al. subsequently extended this lower bound to fully quantum algorithms for inverting permutations. In this work, we give the same asymptotic lower bound to fully quantum algorithms for inverting functions for fully quantum algorithms under the regime where $M = O(N)$.

In order to prove these bounds, we generalize the notion of quantum random access code, originally introduced by Ambainis et al., to the setting where we are given a list of (not necessarily independent) random variables, and we wish to compress them into a variable-length encoding such that we can retrieve a random element just using the encoding with high probability. As our main technical contribution, we give a nearly tight lower bound (for a wide parameter range) for this generalized notion of quantum random access codes, which may be of independent interest.

We propose and investigate a pump-probe spectroscopy scheme to unveil the time-resolved dynamics of fermionic or bosonic impurities immersed in a harmonically trapped Bose-Einstein condensate. In this scheme a pump pulse initially transfers the impurities from a noninteracting to a resonantly interacting spin-state and, after a finite time in which the system evolves freely, the probe pulse reverses this transition. This directly allows to monitor the nonequilibrium dynamics of the impurities as the dynamical formation of coherent attractive or repulsive Bose polarons and signatures of their induced-interactions are imprinted in the probe spectra. We show that for interspecies repulsions exceeding the intraspecies ones a temporal orthogonality catastrophe occurs, followed by enhanced energy redistribution processes, independently of the impurity's flavor. This phenomenon takes place for the characteristic trap timescales. For much longer timescales a steady state is reached characterized by substantial losses of coherence of the impurities. This steady state is related to eigenstate thermalization and it is demonstrated to be independent of the system's characteristics.

To analyze quantum many-body Hamiltonians, recently, machine learning techniques have been shown to be quite useful and powerful. However, the applicability of such machine learning solvers is still limited. Here, we propose schemes that make it possible to apply machine learning techniques to analyze fermion-boson coupled Hamiltonians and to calculate excited states. As for the extension to fermion-boson coupled systems, we study the Holstein model as a representative of the fermion-boson coupled Hamiltonians. We show that the machine-learning solver achieves highly accurate ground-state energy, improving the accuracy substantially compared to that obtained by the variational Monte Carlo method. As for the calculations of excited states, we propose a different approach than that proposed in K. Choo et al., Phys. Rev. Lett. 121 (2018) 167204. We discuss the difference in detail and compare the accuracy of two methods using the one-dimensional $S=1/2$ Heisenberg chain. We also show the benchmark for the frustrated two-dimensional $S=1/2$ $J_1$-$J_2$ Heisenberg model and show an excellent agreement with the results obtained by the exact diagonalization. The extensions shown here open a way to analyze general quantum many-body problems using machine learning techniques.

We have developed an trapped ion system for producing two-dimensional (2D) ion crystals for applications in scalable quantum computing, quantum simulations, and 2D crystal phase transition and defect studies. The trap is a modification of a Paul trap with its ring electrode flattened and split into eight identical sectors, and its two endcap electrodes shaped as truncated hollow cones for laser and imaging optics access. All ten trap electrodes can be independently DC-biased to create various aspect ratio trap geometries. We trap and Doppler cool 2D crystals of up to 30 Ba+ ions and demonstrate the tunability of the trapping potential both in the plane of the crystal and in the transverse direction.

We introduce the post-processing preorder and equivalence relations for general measurements on a possibly infinite-dimensional general probabilistic theory described by an order unit Banach space $E$ with a Banach predual. We define the measurement space $\mathfrak{M}(E)$ as the set of post-processing equivalence classes of continuous measurements on $E .$ We define the weak topology on $\mathfrak{M} (E)$ as the weakest topology in which the state discrimination probabilities for any finite-label ensembles are continuous and show that $\mathfrak{M}(E)$ equipped with the convex operation corresponding to the probabilistic mixture of measurements can be regarded as a compact convex set regularly embedded in a locally convex Hausdorff space. We also prove that the measurement space $\mathfrak{M}(E)$ is infinite-dimensional except when the system is $1$-dimensional and give a characterization of the post-processing monotone affine functional. We apply these general results to the problems of simulability and incompatibility of measurements. We show that the robustness measures of unsimulability and incompatibility coincide with the optimal ratio of the state discrimination probability of measurement(s) relative to that of simulable or compatible measurements, respectively. The latter result for incompatible measurements generalizes the recent result for finite-dimensional quantum measurements. Throughout the paper, the fact that any weakly$\ast$ continuous measurement can be arbitrarily approximated in the weak topology by a post-processing increasing net of finite-outcome measurements is systematically used to reduce the discussions to finite-outcome cases.

We propose a design of topological quantum computer device through a hybrid of the 1-, 2- and 7-layers of chiral topological superconductor ($\chi$TSC) thin films. Based on the $SO(7)_1/(G_2)_1$ coset construction, interacting Majorana fermion edge modes on the 7-layers of $\chi$TSC are factorized into Fibonacci $\tau$-anyon modes and $\varepsilon$-anyon modes in the tricritical Ising model. Furthermore, the deconfinment of the factorization via the interacting potential gives the braiding of either $\tau$ or $\varepsilon$. By braiding $\tau$ and $\varepsilon$ in turn, a topological phase gate for Majorana edge states is assembled. With the help of the topological phase gate, a set of universal quantum gates of the Ising-type quantum computation becomes topological. Owing to the tensor product structure of the Hilbert space, encoding quantum information is more efficient and substantial than that with Fibonacci anyons and the computation results is easier to be read out by electric signals.

Stark deceleration enables the production of cold and dense molecular beams with applications in trapping, collisional studies, and precision measurement. Improving the efficiency of Stark deceleration, and hence the achievable molecular densities, is central to unlock the full potential of such studies. One of the chief limitations arises from the transverse focusing properties of Stark decelerators. We introduce a new operation strategy that circumvents this limit without any hardware modifications, and experimentally verify our results for hydroxyl radicals. Notably, improved focusing results in significant gains in molecule yield with increased operating voltage, formerly limited by transverse-longitudinal coupling. At final velocities sufficiently small for trapping, molecule flux improves by a factor of four, and potentially more with increased voltage. The improvement is more significant for less readily polarized species, thereby expanding the class of candidate molecules for Stark deceleration.