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There are considerable obstacles against realizing practical quantum computing: a significant amount of computation errors and the restricted qubit count. As a unified method of noise-agnostic quantum error mitigation (QEM) methods, i.e., the quantum subspace expansion and virtual purification, a generalized quantum subspace expansion (GSE) has recently been proposed that is significantly robust against stochastic and coherent errors. However, GSE requires entangled measurements between copies of the quantum states, which is a significant drawback under the current situation of the restricted number of qubits and their connectivity. In this work, we propose a resource-efficient implementation of GSE, which we name "Dual-GSE", circumventing significant overheads of state copies by constructing an ansatz of error-mitigated quantum states via dual-state purification. Remarkably, Dual-GSE can further simulate larger quantum systems beyond the size of available quantum hardware with a suitable ansatz construction inspired by divide-and-conquer methods that forge entanglement classically. This also significantly reduces the measurement overhead because we only need to measure subsystems' Pauli operators. The proposed method is demonstrated by a numerical simulation of the eight-qubit transverse-field Ising model, showing that our method estimates the ground state energy with high precision under gate noise with low mitigation overhead and practical sampling cost., Comment: 26 pages, 21 figures

Analog and digital quantum simulators can efficiently simulate quantum many-body systems that appear in natural phenomena. However, experimental limitations of near-term devices still make it challenging to perform the entire process of quantum simulation. The purification-based quantum simulation methods can alleviate the limitations in experiments such as the cooling temperature and noise from the environment, while this method has the drawback that it requires global entangled measurement with a prohibitively large number of measurements that scales exponentially with the system size. In this Letter, we propose that we can overcome these problems by restricting the entangled measurements to the vicinity of the local observables to be measured, when the locality of the system can be exploited. We provide theoretical guarantees that the global purification operation can be replaced with local operations under some conditions, in particular for the task of cooling and error mitigation. We furthermore give a numerical verification that the localized purification is valid even when conditions are not satisfied. Our method bridges the fundamental concept of locality with quantum simulators, and therefore expected to open a path to unexplored quantum many-body phenomena., Comment: 31 pages, 20 figures; accepted version

This work examines the Generation and Transmission Expansion (GATE) planning problem of offshore grids under different market clearing mechanisms: a Home Market Design (HMD), a zonal cleared Offshore Bidding Zone (zOBZ) and a nodal cleared Offshore Bidding Zone (nOBZ). It aims at answering two questions. 1) Is knowing the market structure a priori necessary for effective generation and transmission expansion planning? 2) Which market mechanism results in the highest overall social welfare? To this end a multi-period, stochastic GATE planning formulation is developed for both nodal and zonal market designs. The approach considers the costs and benefits among stake-holders of Hybrid Offshore Assets (HOA) as well as gross consumer surplus (GCS). The methodology is demonstrated on a North Sea test grid based on projects from the European Network of Transmission System Operators' (ENTSO-E) Ten Year Network Development Plan (TYNDP). An upper bound on potential social welfare in zonal market designs is calculated and it is concluded that from a generation and transmission perspective, planning under the assumption of an nOBZ results in the best risk adjusted return.

This paper introduces the problem of passive control of a chain of N identical masses in which there is an identical passive connection between neighbouring masses and a similar connection to a movable point. The problem arises in the design of multi-storey buildings which are subjected to earthquake disturbances, but applies in other situations, for example vehicle platoons. The paper studies the scalar transfer functions from the disturbance to a given intermass displacement. It is shown that these transfer functions can be conveniently represented in the form of complex iterative maps and that these maps provide a method to establish boundedness in N of the H-infinity norm of these transfer functions for certain choices of interconnection impedance.

This paper studies the problem of signal tracking and disturbance rejection for sampled-data control systems, where the pertinent signals can reside beyond the so-called Nyquist frequency. In light of the sampling theorem, it is generally understood that manipulating signals beyond the Nyquist frequency is either impossible or at least very difficult. On the other hand, such control objectives often arise in practice, and control of such signals is much desired. This paper examines the basic underlying assumptions in the sampling theorem and pertinent sampled-data control schemes, and shows that the limitation above can be removed by assuming a suitable analog signal generator model. Detailed analysis of multirate closed-loop systems, zeros and poles are given, which gives rise to tracking or rejection conditions. Robustness of the new scheme is fully characterized; it is shown that there is a close relationship between tracking/rejection frequencies and the delay length introduced for allowing better performance. Examples are discussed to illustrate the effectiveness of the proposed method here.

The rotation symmetric bosonic code (RSBC) is a unified framework of practical bosonic codes that have rotation symmetries, such as cat codes and binomial codes. While cat codes achieve the break-even point in which the coherence time of the encoded qubits exceeds that of unencoded qubits, with binomial codes nearly approaching that point, the state preparation fidelity needs to be still improved for practical quantum computing. Concerning this problem, we investigate the framework of symmetry expansion, a class of quantum error mitigation that virtually projects the state onto the noise-free symmetric subspace by exploiting the system's intrinsic symmetries and post-processing of measurement outcomes. Although symmetry expansion has been limited to error mitigation of quantum states immediately before measurement, we successfully generalize symmetry expansion for state preparation. To implement our method, we use an ancilla qubit and only two controlled-rotation gates via dispersive interactions between the bosonic code states and the ancilla qubit. Interestingly, this method also allows us to virtually prepare the RSBC states only from easy-to-prepare states, e.g., coherent states. We also discuss that the conventional symmetry expansion protocol can be applied to improve the computation fidelity when the symmetries of rotation bosonic codes are unavailable due to low measurement fidelity. By giving comprehensive analytical and numerical arguments regarding the trace distance between the error-mitigated state and the ideal state and the sampling cost of quantum error mitigation, we show that symmetry expansion dramatically suppresses the effect of photon loss. Our novel error mitigation method will significantly enhance computation accuracy in the near-term bosonic quantum computing paradigm.

This paper studies the relation between node deletion and algebraic connectivity for graphs with a hierarchical structure represented by layers. To capture this structure, the concepts of layered path graph and its (sub)graph cone are introduced. The problem is motivated by a mobile robot formation control guided by a leader. In particular, we consider a scenario in which robots may leave the network resulting in the removal of the nodes and the associated edges. We show that the existence of at least one neighbor in the upper layer is crucial for the algebraic connectivity not to deteriorate by node deletion.

We propose a model predictive control (MPC) based approach to a flock control problem with obstacle avoidance capability in a leader-follower framework, utilizing the future trajectory prediction computed by each agent. We employ the traditional Reynolds' flocking rules (cohesion, separation, and alignment) as a basis, and tailor the model to fit a navigation (as opposed to formation) purpose. In particular, we introduce several concepts such as the credibility and the importance of the gathered information from neighbors, and dynamic trade-offs between references. They are based on the observations that near-future predictions are more reliable, agents closer to leaders are implicit carriers of more educated information, and the predominance of either cohesion or alignment is dictated by the distance between the agent and its neighbors. These features are incorporated in the MPC formulation, and their advantages are discussed through numerical simulations.

Quantum metrology with entangled resources aims to achieve sensitivity beyond the standard quantum limit by harnessing quantum effects even in the presence of environmental noise. So far, sensitivity has been mainly discussed from the viewpoint of reducing statistical errors under the assumption of perfect knowledge of a noise model. However, we cannot always obtain complete information about a noise model due to coherence time fluctuations, which are frequently observed in experiments. Such unknown fluctuating noise leads to systematic errors and nullifies the quantum advantages. Here, we propose an error-mitigated quantum metrology that can filter out unknown fluctuating noise with the aid of purification-based quantum error mitigation. We demonstrate that our protocol mitigates systematic errors and recovers superclassical scaling in a practical situation with time-inhomogeneous bias-inducing noise. Our results reveal the usefulness of purification-based error mitigation for unknown fluctuating noise, thus paving the way not only for practical quantum metrology but also for quantum computation affected by such noise., Comment: 6+11 pages, 3+4 figures, close to the published version

Quantum magnetic field sensing is an important technology for material science and biology. Although experimental imperfections affect the sensitivity, repetitions of the measurements decrease the estimation uncertainty by a square root of the total number of the measurements if there are only statistical errors. However, it is difficult to precisely characterize the coherence time of the system because it fluctuates in time in realistic conditions, which induces systematic errors. In this case, due to residual bias of the measured values, estimation uncertainty cannot be lowered than a finite value even in the limit of the infinite number of measurements. On the basis of the fact that the decoherence dynamics in the so-called Zeno regime are not significant compared to other regimes, we propose a novel but very simple protocol to use measurements in the Zeno regime for reducing systematic errors. Our scheme allows the estimation uncertainty $\delta ^2 \omega$ to scale as $L^{1/4}$ where $L$ denotes the number of the measurements even when we cannot precisely characterize the coherence time.

We phenomenologically calculate the performance of the recently-observed Seebeck-driven transverse thermoelectric generation (STTG) for various systems in terms of the thermopower, power factor, and figure of merit to demonstrate the usefulness of STTG. The STTG system consists of a closed circuit comprising thermoelectric and magnetic materials which exhibit the Seebeck and anomalous Hall effects, respectively. When a temperature gradient is applied to the hybrid system, the Seebeck effect in the thermoelectric material layer generates a longitudinal charge current in the closed circuit and the charge current subsequently drives the anomalous Hall effect in the magnetic material layer. The anomalous Hall voltage driven by the Seebeck effect has a similar symmetry to the transverse thermoelectric conversion based on the anomalous Nernst effect. We find that the thermoelectric properties of STTG can be much better than those of the anomalous Nernst effect by increasing the Seebeck coefficient and anomalous Hall angle of the thermoelectric and magnetic materials, respectively, as well as by optimizing their dimensions. We also formulate the electronic cooling performance in the STTG system, confirming the reciprocal relation for the hybrid transverse thermoelectric conversion., Comment: 7 pages, 4 figures

Thermal switching provides an effective way for active heat flow control, which has recently attracted increasing attention in terms of nanoscale thermal management technologies. In magnetic and spintronic materials, the thermal conductivity depends on the magnetization configuration: this is the magneto-thermal resistance effect. Here we show that an epitaxial Cu/Co$_{50}$Fe$_{50}$ multilayer film exhibits giant magnetic-field-induced modulation of the cross-plane thermal conductivity. The magneto-thermal resistance ratio for the Cu/Co$_{50}$Fe$_{50}$ multilayer reaches 150% at room temperature, which is much larger than the previous record high. Although the ratio decreases with increasing the temperature, the giant magneto-thermal resistance effect of ~100% still appears up to 400 K. The magnetic field dependence of the thermal conductivity of the Cu/Co$_{50}$Fe$_{50}$ multilayer was observed to be about twice greater than that of the cross-plane electrical conductivity. The observation of the giant magneto-thermal resistance effect clarifies a potential of spintronic multilayers as thermal switching devices., Comment: 23 pages, 3 figures, 5 supplemental figures

Through Bayesian optimization and the least absolute shrinkage and selection operator (LASSO) technique combined with first-principles calculations, we investigated the tunnel magnetoresistance (TMR) effect of Fe/disordered-MgAl2O4(MAO)/Fe(001) magnetic tunnel junctions (MTJs) to determine structures of disordered-MAO that give large TMR ratios. The optimal structure with the largest TMR ratio was obtained by Bayesian optimization with 1728 structural candidates, where the convergence was reached within 300 structure calculations. Characterization of the obtained structures suggested that the in-plane distance between two Al atoms plays an important role in determining the TMR ratio. Since the Al-Al distance of disordered MAO significantly affects the imaginary part of complex band structures, the majority-spin conductance of the {\Delta}1 state in Fe/disordered-MAO/Fe MTJs increases with increasing in-plane Al-Al distance, leading to larger TMR ratios. Furthermore, we found that the TMR ratio tended to be large when the ratio of the number of Al, Mg, and vacancies in the [001] plane was 2:1:1, indicating that the control of Al atomic positions is essential to enhancing the TMR ratio in MTJs with disordered MAO. The present work reveals the effectiveness and advantage of material informatics combined with first-principles transport calculations in designing high-performance spintronic devices based on MTJs., Comment: 26 pages, 8 figures and 1 table

We investigate the thermoelectric properties of Fe/MgO/Fe(001) magnetic tunnel junctions (MTJs) by means of the linear-response theory combined with a first-principles-based Landauer-B\"uttiker approach. We find that the Seebeck coefficient of Fe/MgO/Fe(001) MTJs strongly depends on the barrier thickness and the tetragonal distortion. A compressive tetragonal distortion of the in-plane lattice parameter in the MTJs provides interface resonant states just above the Fermi energy. This causes resonant tunneling in the MTJs and significantly enhances the Seebeck coefficient when the thickness of the MgO barrier is around 1 nm (four or five atomic layers of MgO). Moreover, an extensive tetragonal distortion of the in-plane lattice parameter pushes the interface states away from the Fermi energy, leading to a reduction of the Seebeck coefficient. Furthermore, we find that the interface resonant tunneling enhances the power factor of the MTJs for the compressive distortion. These results indicate that control of the barrier thickness and the tetragonal distortion will be effective for maximizing the thermoelectric properties of MTJs., Comment: 9 pages, 10 figures, published version

We present two sensitivity function trade-offs that apply to a class of networks with a string topology. In particular we show that a lower bound on the H-infinity norm and a Bode sensitivity relation hold for an entire family of sensitivity functions associated with growing the network. The trade-offs we identify are a direct consequence of growing the network, and can be used to explain why poorly regulated low frequency behaviours emerge in long vehicle platoons even when using dynamic feedback.

We give a method for designing a mechanical impedance to suppress the propagation of disturbances along a chain of masses. The key feature of our method is that it is scale free. This means that it can be used to give a single, fixed, design, with provable performance guarantees in mass chains of any length. We illustrate the approach by designing a bidirectional control law in a vehicle platoon in a manner that is independent of the number of vehicles in the platoon.

The electronic thermoelectric coefficients are analyzed in the vicinity of one and two Anderson localization thresholds in three dimensions. For a single mobility edge, we correct and extend previous studies, and find universal approximants which allow to deduce the critical exponent for the zero-temperature conductivity from thermoelectric measurements. In particular, we find that at non-zero low temperatures the Seebeck coefficient and the thermoelectric efficiency can be very large on the "insulating" side, for chemical potentials below the (zero-temperature) localization threshold. Corrections to the leading power-law singularity in the zero-temperature conductivity are shown to introduce non-universal temperature-dependent corrections to the otherwise universal functions which describe the Seebeck coefficient, the figure of merit and the Wiedemann-Franz ratio. Next, the thermoelectric coefficients are shown to have interesting dependences on the system size. While the Seebeck coefficient decreases with decreasing size, the figure of merit first decreases but then increases, while the Wiedemann-Franz ratio first increases but then decreases as the size decreases. Small (but finite) samples may thus have larger thermoelectric efficiencies. In the last part we study thermoelectricity in systems with a pair of localization edges, the ubiquitous situation in random systems near the centers of electronic energy bands. As the disorder increases, the two thresholds approach each other, and then the Seebeck coefficient and the figure of merit increase significantly, as expected from the general arguments of Mahan and Sofo [J. D. Mahan and J. O. Sofo, Proc. Natl. Acad. Sci. U.S.A. 93, 7436 (1996)] for a narrow energy-range of the zero-temperature metallic behavior., Comment: 16 pages, 11 figures, close to the published version

We present an efficient algorithm for recent generalizations of optimal mass transport theory to matrix-valued and vector-valued densities. These generalizations lead to several applications including diffusion tensor imaging, color images processing, and multi-modality imaging. The algorithm is based on sequential quadratic programming (SQP). By approximating the Hessian of the cost and solving each iteration in an inexact manner, we are able to solve each iteration with relatively low cost while still maintaining a fast convergent rate. The core of the algorithm is solving a weighted Poisson equation, where different efficient preconditioners may be employed. We utilize incomplete Cholesky factorization, which yields an efficient and straightforward solver for our problem. Several illustrative examples are presented for both the matrix and vector-valued cases., Comment: 18 pages, 4 figures

We consider certain matricial analogues of optimal mass transport of positive definite matrices of equal trace. The framework is motivated by the need to devise a suitable geometry for interpolating positive definite matrices in ways that allow controlling the apparent tradeoff between "aligning up their eigenstructure" and "scaling the corresponding eigenvalues". Indeed, motivation for this work is provided by power spectral analysis of multivariate time series where, linear interpolation between matrix-valued power spectra generates push-pop artifacts. Push-pop of power distribuion is objectionable as it corresponds to unrealistic response of scatterers., Comment: 4 pages, 6 figures

We examine the efficiency of an effective two-terminal thermoelectric device under broken time-reversal symmetry. The setup is derived from a three-terminal thermoelectric device comprising a thermal terminal and two electronic contacts, under a magnetic field. We find that breaking time-reversal symmetry in the presence of the inelastic electron-phonon processes can significantly enhance the figure of merit for delivering electric power by supplying heat from a phonon bath, beyond the one for producing the electric power by investing thermal power from the electronic heat current. The efficiency of such a device is bounded by the non-negativity of the entropy production of the original three-terminal junction. The efficiency at maximal power can be quite close to the Carnot efficiency, but then the electric power vanishes., Comment: 6 pages, 3 figures, published version

Dynamical localization, i.e., reduction of the intersite electronic transfer integral t by an alternating electric field, E(omega) , is a promising strategy for controlling strongly correlated systems with a competing energy balance between t and the Coulomb repulsion energy. Here we describe a charge localization induced by the 9.3 MV/cm instantaneous electric field of a 1.5 cycle (7 fs) infrared pulse in an organic conductor alpha-(bis[ethylenedithio]-tetrathiafulvelene)_2I_3. A large reflectivity change of > 25% and a coherent charge oscillation along the time axis reflect the opening of the charge ordering gap in the metallic phase. This optical freezing of charges, which is the reverse of the photoinduced melting of electronic orders, is attributed to the 10% reduction of t driven by the strong, high-frequency (omega>t/h_bar) electric field., Comment: 20 pages, 6 figure

Mesoscopic thermoelectric heat engine is much anticipated as a device that allows us to utilize with high efficiency wasted heat inaccessible by conventional heat engines. However, the derivation of the heat current in this engine seems to be either not general or described too briefly, even inappropriate in some cases. In this paper, we give a clear-cut derivation of the heat current of the engine with suitable assumptions beyond the linear-response regime. It resolves the confusion in the definition of the heat current in the linear-response regime. After verifying that we can construct the same formalism as that of the cyclic engine, we find the following two interesting results within the Landauer-B\"uttiker formalism: the efficiency of the mesoscopic thermoelectric engine reaches the Carnot efficiency if and only if the transmission probability is finite at a specific energy and zero otherwise; the unitarity of the transmission probability guarantees the second law of thermodynamics, invalidating Benenti et al.'s argument in the linear-response regime that one could obtain a finite power with the Carnot efficiency under a broken time-reversal symmetry. These results demonstrate how quantum mechanics constraints thermodynamics., Comment: 8 pages, 3 figures, close to publish version

In the present thesis, we study the heat flow in mesoscopic one-dimensional transport systems. Using the analysis of full counting statistics, we calculate the cumulant generating function of the particle and heat flows and prove its symmetry. The symmetry produces the relations among transport coefficients of the particle and heat flows when we expand these flows with respect to the appropriate affinities. Moreover, we consider the generalized flows which are superpositions of the particle and energy flows. We show that we can choose the appropriate affinities of the generalized flows and derive the relations among their transport coefficients when we expand the generalized flows with respect to their affinities., Comment: 62pages, Master Thesis, Department of Physics, The University of Tokyo