Lebedev, Andrey V

Guseynov N.M., Zhukov A.A., Pogosov W.V., Lebedev A.V.

Variational quantum algorithms are a promising tool for solving partial differential equations. The standard approach for its numerical solution is finite-difference schemes, which can be reduced to the linear algebra problem. We consider three approaches to solve the heat equation on a quantum computer. Using the direct variational method we minimize the expectation value of a Hamiltonian with its ground state being the solution of the problem under study. Typically, an exponential number of Pauli products in the Hamiltonian decomposition does not allow for the quantum speedup to be achieved. The Hadamard-test-based approach solves this problem, however, the performed simulations do not evidently prove that the Ansatz circuit has a polynomial depth with respect to the number of qubits. The Ansatz tree approach exploits an explicit form of the matrix that makes it possible to achieve an advantage over classical algorithms. In our numerical simulations with up to $n=11$ qubits, this method reveals the exponential speedup.

Lebedev D.V., Shkoldin V.A., Mozharov A.M., Larin A.O., Permyakov D.V., Samusev A.K., Petukhov A.E., Golubok A.O., Arkhipov A.V., Mukhin I.S.

A micro- or nanosized electrically controlled source of optical radiation is one of the key elements in optoelectronic systems. The phenomenon of light emission via inelastic tunneling (LEIT) of electrons through potential barriers or junctions opens up new possibilities for development of such sources. In this work, we present a simple approach for fabrication of nanoscale electrically driven light sources based on LEIT. We employ STM lithography to locally modify the surface of a Si/Au film stack via heating, which is enabled by a high-density tunnel current. Using the proposed technique, hybrid Si/Au nanoantennas with a minimum diameter of 60 nm were formed. Studying both electronic and optical properties of the obtained nanoantennas, we confirm that the resulting structures can efficiently emit photons in the visible range because of inelastic scattering of electrons. The proposed approach allows for fabrication of nanosized hybrid nanoantennas and studying their properties using STM.

Shapiro D.S., Remizov S.V., Lebedev A.V., Babukhin D.V., Akzyanov R.S., Zhukov A.A., Bork L.V.

Dmitriy S. Shapiro1,2,3,∗ Sergey V. Remizov, Andrey V. Lebedev, Danila V. Babukhin, Ramil S. Akzyanov, Andrey A. Zhukov, and Leonid V. Bork Dukhov Research Institute of Automatics (VNIIA), 127055 Moscow, Russia National University of Science and Technology MISiS, 119049 Moscow, Russia Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany V. A. Kotel’nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Moscow 125009, Russia Department of Physics, National Research University Higher School of Economics, Moscow 101000, Russia Moscow Institute of Physics and Technology, 141700, Institutskii Per. 9, Dolgoprudny, Moscow Distr., Russia and Institute for Theoretical and Applied Electrodynamics, Russian Academy of Sciences, 125412 Moscow, Russia

Sultanov A., Kuzmanović M., Lebedev A.V., Paraoanu G.S.

We present a method for in situ temperature measurement of superconducting quantum circuits, by using the first three levels of a transmon device to which we apply a sequence of π gates. Our approach employs projective dispersive readout and utilizes the basic properties of the density matrix associated with thermal states. This method works with an averaging readout scheme and does not require a single-shot readout setup. We validate this protocol by performing thermometry in the range of 50 mK 200 mK, corresponding to a range of residual populations 1%− 20% for the first excited state and 0.02%− 3% for the second excited state. Superconducting qubits are one of the most promising candidates as the basic element of future quantum computers. The progress of the last decade has resulted in a significant increase of their coherence times to tens of microseconds, in a reduction of errors caused by interaction with the environment through the implementation of reset protocols and error-correction protocols, and in an enhancement in readout fidelity up to 99.6%. However, the exact mechanisms that limits further improvements in superconducting qubit systems are still not fully understood; one possibility is the spurious excitations caused by microwave noise, infrared radiation from hotter stages of the dilution refrigerators or poisoning by quasiparticles. To mitigate these effects, a range of experimental techniques have been deployed – the use of cryogenic filters and attenuators, infrared absorbers, radiation and magnetic shielding of samples, with the goal of reducing the temperature of the electromagnetic environment and the quasiparticle population. Here we introduce a protocol for evaluating the effective temperature of a superconducting qubit. Our method can be readily used as a diagnostic tool for qubit thermalization and line integrity in quantum computing applications. An important application is quantum thermodynamics, where controlling the effective temperature of the circuit can be used to drive quantum engines. The state of the electromagnetic environment of the qubit is described by an effective temperature, which characterizes the thermal equilibrium between the qubit and the environment and thus defines residual populations of former. There are several ways to estimate this effective temperature from the residual populations of qubit’s states, assuming a MaxwellBoltzmann distribution. A straightforward method is to use a single-shot readout. In this case the residual probabilities can be directly calculated from measurement statistics, provided that the states can be discriminated with sufficiently good precision. However, the implementation of a single-shot readout scheme requires a good quantum limited parametric ampliElectronic mail: sorin.paraoanu@aalto.fi fier and additional components. An alternative approach, which does not use single-shot readout, is based on the measurement of correlations between responses corresponding to the ground and excited states. Another technique uses a three level system, where the Rabi oscillation amplitude between the first and the second excited state depends on the residual population of the first excited state. However, this method is highly sensitive to the readout signal parameters. Finally, a thermometry technique for propagating waves in open-waveguides can be used to characterize the temperature of the electromagnetic field, but this method requires a dedicated sample design. Here we propose an in situ method for measuring the effective temperature, which utilizes only π pulses and requires measuring only the average responses in the dispersive readout limit. Therefore this method could be implemented without a specialized setup or sophisticated measurement techniques. In addition, determining the temperature does not rely on qubit state tomography: In our protocol, we measure the cavity responses after applying six different drive sequences that swap the populations of the three-level system, in our case defined by the first levels in a transmon device. A simple linear relationship is found between some of these responses, and the coefficient of proportionality is determined only by the thermal level occupations. Therefore, as the method does not rely on full state tomography or on the knowledge of the pure state responses, it is more resilient to noise and drifts which are commonly present in superconducting artificial atom experiments. Moreover, since only π pulses are utilized, the proposed method is robust against dephasing and, if the pulses are much shorter with respect to the relaxation time, also against decay. Consider a three-level system in thermal equilibrium with its environment at a temperature T . The density matrix reads ρ̂ = pg |g〉 〈 g|+ pe |e〉 〈e| + p f | f 〉 〈 f | , (1) where |g〉 , |e〉 , | f 〉 are respectively the ground, the first excited and the second excited state, with corresponding populations pg, pe, and p f . Thermal equilibrium means that ρ̂

Perelshtein M.R., Kirsanov N.S., Zemlyanov V.V., Lebedev A.V., Blatter G., Vinokur V.M., Lesovik G.B.

M. R. Perelshtein,1, 2, 3, ∗ N. S. Kirsanov,1, 2, 3, 4, ∗ V. V. Zemlyanov,1, 2 A. V. Lebedev,2 G. Blatter,5 V. M. Vinokur,4, 6 and G. B. Lesovik1, 2 1Terra Quantum AG, St. Gallerstrasse 16A, 9400 Rorschach, Switzerland 2Moscow Institute of Physics and Technology, 141700, Institutskii Per. 9, Dolgoprudny, Moscow Distr., Russian Federation 3QTF Centre of Excellence, Department of Applied Physics, Aalto University School of Science, P.O. Box 15100, FI-00076 AALTO, Finland 4Consortium for Advanced Science and Engineering (CASE) University of Chicago, 5801 S Ellis Ave, Chicago, IL 60637, USA 5Theoretische Physik, Wolfgang-Pauli-Strasse 27, ETH Zürich, CH-8093 Zürich, Switzerland 6Materials Science Division, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, Illinois 60637, USA (Dated: March 25, 2021)

Popoff A., Lebedev A.V., Raymond L., Jonckheere T., Rech J., Martin T.

Abstract We consider a non-chiral Luttinger liquid in the presence of a backscattering Hamiltonian which has an extended range. Right/left moving fermions at a given location can thus be converted as left/right moving fermions at a different location, within a specific range. We perform a momentum shell renormalization group treatment which gives the evolution of the relative degrees of freedom of this Hamiltonian contribution under the renormalization flow, and we study a few realistic examples of this extended backscattering Hamiltonian. We find that, for repulsive Coulomb interaction in the Luttinger liquid, any such Hamiltonian contribution evolves into a delta-like scalar potential upon renormalization to a zero temperature cutoff. On the opposite, for attractive couplings, the amplitude of this kinetic Hamiltonian is suppressed, rendering the junction fully transparent. As the renormalization procedure may have to be stopped because of experimental constraints such as finite temperature, we predict the actual spatial shape of the kinetic Hamiltonian at different stages of the renormalization procedure, as a function of the position and the Luttinger interaction parameter, and show that it undergoes structural changes. This renormalized kinetic Hamiltonian has thus to be used as an input for the perturbative calculation of the current, for which we provide analytic expressions in imaginary time. We discuss the experimental relevance of this work by looking at one-dimensional systems consisting of carbon nanotubes or semiconductor nanowires.

Lebedev D.V., Shkoldin V.A., Mozharov A.M., Permyakov D.V., Dvoretckaia L.N., Bogdanov A.A., Samusev A.K., Golubok A.O., Mukhin I.S.

Electrically driven plasmonic nanoantennas can be integrated as a local source of the optical signal of advanced photonic schemes for on-chip data processing. The inelastic electron tunneling provides the photon generation or launch of surface plasmon waves. This process can be enhanced by the local density of optical states of nanoantennas. In this paper, we used scanning tunnel microscopy-induced light emission to probe the local optoelectronic properties of single gold nanodiscs. The electromagnetic field distribution in the vicinity of plasmonic structures was investigated with high spatial resolution. The obtained photon maps reveal the nonuniform distribution of electromagnetic near-fields, which is consistent with nanoantenna optical modes. Also, the analysis of derived I(V) curves showed a direct correlation between the nanoantenna optical states and the appearance of features on current-voltage characteristics.

Lebedev A.V., Vinokur V.M.

Anderson's orthogonality catastrophe (AOC) theorem establishes that the ground state of the many-body fermion system is asymptotically orthogonal to the ground state of the same system perturbed by a scattering potential, so that the overlap between the original and new ground states decays to zero with the system size. We adopt the AOC for a description of heat production in a complementary metal-oxide-semiconductor (CMOS) transistor. We find that the heat released in the transistor comprises two distinct components, contribution from the dissipation accompanying electron transmission under the applied voltage and purely quantum-mechanical AOC part due to the change in scattering matrix for electrons upon switching between high and low conductance regimes. We calculate the AOC-induced heat production, which we call switching heat.

Lebedev A.V., Vinokur V.M.

AbstractFor decades, researchers have sought to understand how the irreversibility of the surrounding world emerges from the seemingly time-symmetric, fundamental laws of physics. Quantum mechanics conjectured a clue that final irreversibility is set by the measurement procedure and that the time-reversal requires complex conjugation of the wave function, which is overly complex to spontaneously appear in nature. Building on this Landau-Wigner conjecture, it became possible to demonstrate that time-reversal is exponentially improbable in a virgin nature and to design an algorithm artificially reversing a time arrow for a given quantum state on the IBM quantum computer. However, the implemented arrow-of-time reversal embraced only the known states initially disentangled from the thermodynamic reservoir. Here we develop a procedure for reversing the temporal evolution of an arbitrary unknown quantum state. This opens the route for general universal algorithms sending temporal evolution of an arbitrary system backward in time.

Pakhomchik A.I., Feshchenko I., Glatz A., Vinokur V.M., Lebedev A.V., Filippov S.N., Lesovik G.B.

We realize the Landau–Streater (LS) and Werner–Holevo (WH) quantum channels for qutrits on IBM quantum computers. These channels correspond to the interaction between a qutrit and its environment that results in the globally unitarily covariant qutrit transformation violating the multiplicativity of the maximal p-norm. Our realization of the LS and WH channels is based on embedding the qutrit states into states of two qubits and using the single-qubit and two-qubit CNOT gates to implement the specific interaction. We employ the standard quantum gates, hence the developed algorithm suits any quantum computer. We run our algorithm on a 5-qubit computer and a 20-qubit computer, as well as on a simulator. We quantify the quality of the implemented channels comparing their action on different input states with theoretical predictions. The overall efficiency is quantified by the fidelity between the theoretical and experimental Choi states implemented on the 20-qubit computer.

Lebedev A.V., Lesovik G.B.

H-theorem gives necessary conditions for a system to evolve in time with a non-diminishing entropy. In a quantum case the role of H-theorem plays the unitality criteria of a quantum channel transformation describing the evolution of the system’s density matrix under the presence of the interaction with an environment. Here, we show that if diagonal elements of the system’s density matrix are robust to the presence of interaction the corresponding quantum channel is unital.

Lesovik G.B., Sadovskyy I.A., Suslov M.V., Lebedev A.V., Vinokur V.M.

AbstractUncovering the origin of the “arrow of time” remains a fundamental scientific challenge. Within the framework of statistical physics, this problem was inextricably associated with the Second Law of Thermodynamics, which declares that entropy growth proceeds from the system’s entanglement with the environment. This poses a question of whether it is possible to develop protocols for circumventing the irreversibility of time and if so to practically implement these protocols. Here we show that, while in nature the complex conjugation needed for time reversal may appear exponentially improbable, one can design a quantum algorithm that includes complex conjugation and thus reverses a given quantum state. Using this algorithm on an IBM quantum computer enables us to experimentally demonstrate a backward time dynamics for an electron scattered on a two-level impurity.

Lebedev A.V., Lesovik G.B., Vinokur V.M., Blatter G.

A quantum Maxwell demon is a device that can lower the entropy of a quantum system by providing it with purity. The functionality of such a quantum demon is rooted in a quantum mechanical SWAP operation exchanging mixed and pure states. We describe the setup and performance of a quantum Maxwell demon that purifies an energy-isolated system from a distance. Our cQED-based design involves two transmon qubits, where the mixed-state target qubit is purified by a pure-state demon qubit connected via an off-resonant transmission line; this configuration naturally generates an iSWAP gate. Although less powerful than a full SWAP gate, we show that assuming present-day performance characteristics of a cQED implementation, such an extended quantum Maxwell demon can purify the target qubit over macroscopic distances on the order of meters and tolerates elevated temperatures of the order of a few Kelvin in the transmission line.

Danilin S., Lebedev A.V., Vepsäläinen A., Lesovik G.B., Blatter G., Paraoanu G.S.

Phase estimation algorithms are key protocols in quantum information processing. Besides applications in quantum computing, they can also be employed in metrology as they allow for fast extraction of information stored in the quantum state of a system. Here, we implement two suitably modified phase estimation procedures, the Kitaev and the semiclassical Fourier-transform algorithms, using an artificial atom realized with a superconducting transmon circuit. We demonstrate that both algorithms yield a flux sensitivity exceeding the classical shot-noise limit of the device, allowing one to approach the Heisenberg limit. Our experiment paves the way for the use of superconducting qubits as metrological devices which are potentially able to outperform the best existing flux sensors with a sensitivity enhanced by few orders of magnitude. Quantum computing algorithms can improve the performance of a superconducting magnetic field sensor beyond the classical limit. A qubit’s time evolution is often influenced by environmental factors like magnetic fields; measuring this evolution allows the magnetic field strength to be determined. Using classical methods, improvements in measurement performance can only scale with the square root of the total measurement time. However, by exploiting quantum coherence to use so-called phase estimation algorithms during the measurements, the scaling with measurement time can be driven beyond the classical limits. Andrey Lebedev at ETH Zurich and colleagues in Finland, Switzerland and Russia have applied this approach to superconducting qubits. They demonstrate both superior performance and improved scaling compared to the classical approach, and show that in principle superconducting qubits can become the highest-performing magnetic flux sensors.

Kirsanov N.S., Lebedev A.V., Sadovskyy I.A., Suslov M.V., Vinokur V.M., Blatter G., Lesovik G.B.

The Second Law of Thermodynamics states that temporal evolution of an isolated system occurs with non-diminishing entropy. In quantum realm, this holds for energy-isolated systems the evolution of which is described by the so-called unital quantum channel. The entropy of a system evolving in a non-unital quantum channel can, in principle, decrease. We formulate a general criterion of unitality for the evolution of a quantum system, enabling a simple and rigorous approach for finding and identifying the processes accompanied by decreasing entropy in energy-isolated systems. We discuss two examples illustrating our findings, the quantum Maxwell demon and heating-cooling process within a two-qubit system.

Singh H., Majumder S., Mishra S.

Quantum computing is finding increasingly more applications in quantum chemistry, particularly to simulate electronic structure and molecular properties of simple systems. The transformation of a molecular Hamiltonian from the fermionic space to the qubit space results in a series of Pauli strings. Calculating the energy then involves evaluating the expectation values of each of these strings, which presents a significant bottleneck for applying variational quantum eigensolvers (VQEs) in quantum chemistry. Unlike fermionic Hamiltonians, the terms in a qubit Hamiltonian are additive. This work leverages this property to introduce a novel method for extracting information from the partial qubit Hamiltonian, thereby enhancing the efficiency of VQEs. This work introduces the SHARC-VQE (Simplified Hamiltonian Approximation, Refinement, and Correction-VQE) method, where the full molecular Hamiltonian is partitioned into two parts based on the ease of quantum execution. The easy-to-execute part constitutes the partial Hamiltonian, and the remaining part, while more complex to execute, is generally less significant. The latter is approximated by a refined operator and added up as a correction into the partial Hamiltonian. SHARC-VQE significantly reduces computational costs for molecular simulations. The cost of a single energy measurement can be reduced from O(N4ϵ2) to O(1ϵ2) for a system of N qubits and accuracy ϵ, while the overall cost of VQE can be reduced from O(N7ϵ2) to O(N3ϵ2). Furthermore, measurement outcomes using SHARC-VQE are less prone to errors induced by noise from quantum circuits, reducing the errors from 20%–40% to 5%–10% without any additional error correction or mitigation technique. In addition, the SHARC-VQE is demonstrated as an initialization technique, where the simplified partial Hamiltonian is used to identify an optimal starting point for a complex problem. Overall, this method improves the efficiency of VQEs and enhances the accuracy and reliability of quantum simulations by mitigating noise and overcoming computational challenges.

Linehan R., Hernandez I., Temples D.J., Dang S.Q., Baxter D., Hsu L., Figueroa-Feliciano E., Khatiwada R., Anyang K., Bowring D., Bratrud G., Cancelo G., Chou A., Gualtieri R., Stifter K., et. al.

Mukhopadhyay C., Montenegro V., Bayat A.

Abstract Quantum sensors are now universally acknowledged as one of the most promising near-term quantum technologies. The traditional formulation of quantum sensing introduces a concrete bound on ultimate precision through the so-called local sensing framework, in which a significant knowledge of prior information about the unknown parameter value is implicitly assumed. Moreover, the framework provides a systematic approach for optimizing the sensing protocol. In contrast, the paradigm of global sensing aims to find a precision bound for parameter estimation in the absence of such prior information. In recent years, vigorous research has been pursued to describe the contours of global quantum estimation. Here, we review some of these emerging developments. These developments are both in the realm of finding ultimate precision bounds with respect to appropriate figures of merit in the global sensing paradigm, as well as in the search for algorithms that achieve these bounds. We categorize these developments into two largely mutually exclusive camps; one employing Bayesian updating and the other seeking to generalize the frequentist picture of local sensing towards the global paradigm. In the first approach, in order to achieve the best performance, one has to optimize the measurement settings adaptively. In the second approach, the measurement setting is fixed, however the challenge is to identify this fixed measurement optimally.

Ojha V.K., Radhakrishnan R., Ughradar M.

Over P., Bengoechea S., Rung T., Clerici F., Scandurra L., de Villiers E., Jaksch D.

Larin A.O., Bruyere S., Nomine A., Maragkakis G., Psilodimitrakopoulos S., Permyakov D.V., Belmonte T., Stratakis E., Zuev D.A.

Slepnev V., Gubaydullin A., Vinokur V.

Samajdar R., McCulloch E., Khemani V., Vasseur R., Gopalakrishnan S.

Pausch L., Damanet F., Bastin T., Martin J.

Rodríguez-García M.A., de Matos Filho R.L., Barberis-Blostein P.

We investigate strategies for reaching the ultimate limit on the precision of frequency estimation when the number of probes used in each run of the experiment is fixed. That limit is set by the quantum Cramér-Rao bound (QCRB), which predicts that the use of maximally entangled probes enhances the estimation precision, when compared with the use of independent probes. However, the bound is only achievable if the statistical model used in the estimation remains identifiable throughout the procedure. This in turn sets different limits on the maximal sensing time used in each run of the estimation procedure, when entangled and independent probes are used. When those constraints are taken into account, one can show that, when the total number of probes and the total duration of the estimation process are counted as fixed resources, the use of entangled probes is, in fact, disadvantageous when compared with the use of independent probes. In order to counteract the limitations imposed on the sensing time by the requirement of identifiability of the statistical model, we propose a time-adaptive strategy, in which the sensing time is adequately increased at each step of the estimation process, calculate an attainable error bound for the strategy, and discuss how to optimally choose its parameters in order to minimize that bound. We show that the proposed strategy leads to much better scaling of the estimation uncertainty with the total number of probes and the total sensing time than the traditional fixed-sensing-time strategy. We also show that, when the total number of probes and the total sensing time are counted as resources, independent probes and maximally entangled ones have now the same performance, in contrast to the nonadaptive strategy, where the use of independent is more advantageous than the use of maximally entangled ones. Published by the American Physical Society 2024

Wright L., Mc Keever C., First J.T., Johnston R., Tillay J., Chaney S., Rosenkranz M., Lubasch M.

We design and implement quantum circuits for the simulation of the one-dimensional wave equation on the Quantinuum H1-1 quantum computer. The circuit depth of our approach scales as O(n2) for n qubits representing the solution on 2n grid points, and leads to infidelities of O(2−4nt2) for simulation time t assuming smooth initial conditions. By varying the qubit count we study the interplay between the algorithmic and physical gate errors to identify the optimal working point of minimum total error. Our approach to simulating the wave equation can be used with appropriate state preparation algorithms across different quantum processors and serve as an application-oriented benchmark. Published by the American Physical Society 2024

Krause J., Marchegiani G., Janssen L.M., Catelani G., Ando Y., Dickel C.

Goel R., Chakraborty S., Awasthi V., Bhardwaj V., Kumar Dubey S.

Surface-enhanced Raman scattering (SERS), a variant of Raman spectroscopy, is a powerful analytical technique that uses plasmonics to obtain detailed chemical information of molecules or molecular assemblies adsorbed or attached to nanostructured metallic surfaces. It is being considered for numerous sensing applications including health, food, environmental monitoring, safety etc. Plasmonics, exploits the interaction between light and metallic nanostructures at the metal-dielectric interface. The metal-dielectric interfaces are engineered to optimize for high enhancement factors and molecular specificity with high accuracy and sensitivity. In this review we have focused on the basics of plasmonics, fundamentals of SERS, different methods adopted for fabrication of various types of SERS substrates, applications of SERS in bio-medicine, a brief description of different variants of Raman spectroscopy and a concise introduction on quantum sensing. Fundamental mechanisms of SERS and factors contributing to SERS enhancement have also been reviewed in this article. Latest developments in the field of novel SERS substrates have been explored including different kinds of plasmonic/non-plasmonic materials, different sizes, shapes, and architectures of SERS substrate to achieve high sensitivity and specificity as well as tunability or flexibility. Different forms of Raman spectroscopy have been discussed in terms of advantages and challenges of each technique. With artificial intelligence and machine learning expanding its dominance in almost every field, it is inevitable to discuss the importance of signal detection schemes and data analytics, and its implementation in the detection/quantification of analytes using SERS-based point-of-care technologies. The objective of this review is to provide a comprehensive overview of SERS by highlighting challenges and shortfalls in implementing it and providing a deeper insight of its principle, mechanism, advantages, and limitations of current technology. Different fundamental approaches are discussed, such as label-free and functional assays. We have also reviewed the main advantages and challenges of SERS-based biosensing and presented a brief outlook.

Danilin S., Nugent N., Weides M.

Abstract Sensing and metrology are crucial in both fundamental science and practical applications. They meet the constant demand for precise data, enabling more dependable assessments of theoretical models’ validity. Sensors, now a common feature in many fields, play a vital role in applications like gravity imaging, geology, navigation, security, timekeeping, spectroscopy, chemistry, magnetometry, healthcare, and medicine. The advancements in quantum technologies have sparked interest in employing quantum systems as sensors, offering enhanced capabilities and new possibilities. This article describes the optimization of the quantum-enhanced sensing of magnetic fluxes with a Kitaev phase estimation algorithm based on frequency tunable transmon qubits. It provides the optimal flux biasing point for sensors with different qubit transition frequencies and gives an estimation of decoherence rates and achievable sensitivity. The use of 2- and 3-qubit entangled states are compared in simulation with the single-qubit case. The flux sensing accuracy reaches 10 − 8 ⋅ Φ 0 and scales inversely with time, which proves the speed-up of sensing with high ultimate accuracy.

Rodríguez-García M.A., Becerra F.E.

Phase estimation plays a central role in communications, sensing, and information processing. Quantum correlated states, such as squeezed states, enable phase estimation beyond the shot-noise limit, and in principle approach the ultimate quantum limit in precision, when paired with optimal quantum measurements. However, physical realizations of optimal quantum measurements for optical phase estimation with quantum-correlated states are still unknown. Here we address this problem by introducing an adaptive Gaussian measurement strategy for optical phase estimation with squeezed vacuum states that, by construction, approaches the quantum limit in precision. This strategy builds from a comprehensive set of locally optimal POVMs through rotations and homodyne measurements and uses the Adaptive Quantum State Estimation framework for optimizing the adaptive measurement process, which, under certain regularity conditions, guarantees asymptotic optimality for this quantum parameter estimation problem. As a result, the adaptive phase estimation strategy based on locally-optimal homodyne measurements achieves the quantum limit within the phase interval of [0,π/2). Furthermore, we generalize this strategy by including heterodyne measurements, enabling phase estimation across the full range of phases from [0,π), where squeezed vacuum allows for unambiguous phase encoding. Remarkably, for this phase interval, which is the maximum range of phases that can be encoded in squeezed vacuum, this estimation strategy maintains an asymptotic quantum-optimal performance, representing a significant advancement in quantum metrology.

Alghassi H., Deshmukh A., Ibrahim N., Robles N., Woerner S., Zoufal C.

We propose an algorithm based on variational quantum imaginary time evolution for solving the Feynman-Kac partial differential equation resulting from a multidimensional system of stochastic differential equations. We utilize the correspondence between the Feynman-Kac partial differential equation (PDE) and the Wick-rotated Schrödinger equation for this purpose. The results for a (2+1) dimensional Feynman-Kac system obtained through the variational quantum algorithm are then compared against classical ODE solvers and Monte Carlo simulation. We see a remarkable agreement between the classical methods and the quantum variational method for an illustrative example on six and eight qubits. In the non-trivial case of PDEs which are preserving probability distributions – rather than preserving the ℓ2-norm – we introduce a proxy norm which is efficient in keeping the solution approximately normalized throughout the evolution. The algorithmic complexity and costs associated to this methodology, in particular for the extraction of properties of the solution, are investigated. Future research topics in the areas of quantitative finance and other types of PDEs are also discussed.

Zhukov A., Pogosov W.

Deep neural networks (DNN) can be applied at the post-processing stage for the improvement of the results of quantum computations on noisy intermediate-scale quantum (NISQ) processors. Here, we propose a method based on this idea, which is most suitable for digital quantum simulation characterized by the periodic structure of quantum circuits consisting of Trotter steps. A key ingredient of our approach is that it does not require any data from a classical simulator at the training stage. The network is trained to transform data obtained from quantum hardware with artificially increased Trotter steps number (noise level) toward the data obtained without such an increase. The additional Trotter steps are fictitious, i.e., they contain negligibly small rotations and, in the absence of hardware imperfections, reduce essentially to the identity gates. This preserves, at the training stage, information about relevant quantum circuit features. Two particular examples are considered that are the dynamics of the transverse-field Ising chain and XY spin chain, which were implemented on two real five-qubit IBM Q processors. A significant error reduction is demonstrated as a result of the DNN application that allows us to effectively increase quantum circuit depth in terms of Trotter steps.

Holmes Z., Sharma K., Cerezo M., Coles P.J.

A fundamental relationship between expressibility and trainability of an ansatz is derived, providing designing strategies that help to avoid barren plateaus.

Wang S., Fontana E., Cerezo M., Sharma K., Sone A., Cincio L., Coles P.J.

Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers. A natural question is whether noise on NISQ devices places fundamental limitations on VQA performance. We rigorously prove a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau (i.e., vanishing gradient). Specifically, for the local Pauli noise considered, we prove that the gradient vanishes exponentially in the number of qubits n if the depth of the ansatz grows linearly with n. These noise-induced barren plateaus (NIBPs) are conceptually different from noise-free barren plateaus, which are linked to random parameter initialization. Our result is formulated for a generic ansatz that includes as special cases the Quantum Alternating Operator Ansatz and the Unitary Coupled Cluster Ansatz, among others. For the former, our numerical heuristics demonstrate the NIBP phenomenon for a realistic hardware noise model. Variational quantum algorithms (VQAs) are a leading candidate for useful applications of near-term quantum computing, but limitations due to unavoidable noise have not been clearly characterized. Here, the authors prove that local Pauli noise can cause vanishing gradients rendering VQAs untrainable.

Sato Y., Kondo R., Koide S., Takamatsu H., Imoto N.

Computer-aided engineering techniques are indispensable in modern engineering developments. In particular, partial differential equations are commonly used to simulate the dynamics of physical phenomena, but very large systems are often intractable within a reasonable computation time, even when using supercomputers. To overcome the inherent limit of classical computing, we present a variational quantum algorithm for solving the Poisson equation that can be implemented in noisy intermediate-scale quantum devices. The proposed method defines the total potential energy of the Poisson equation as a Hamiltonian, which is decomposed into a linear combination of Pauli operators and simple observables. The expectation value of the Hamiltonian is then minimized with respect to a parameterized quantum state. Because the number of decomposed terms is independent of the size of the problem, this method requires relatively few quantum measurements. Numerical experiments demonstrate the faster computing speed of this method compared with classical computing methods and a previous variational quantum approach. We believe that our approach brings quantum computer-aided techniques closer to future applications in engineering developments. Code is available at https://github.com/ToyotaCRDL/VQAPoisson.

Wang F., Liu Y., Hoang T.X., Chu H., Chua S., Nijhuis C.A.

To develop methods to generate, manipulate, and detect plasmonic signals by electrical means with complementary metal-oxide-semiconductor (CMOS)-compatible materials is essential to realize on-chip electronic-plasmonic transduction. Here, electrically driven, CMOS-compatible electronic-plasmonic transducers with Al-AlOX -Cu tunnel junctions as the excitation source of surface plasmon polaritons (SPPs) and Si-Cu Schottky diodes as the detector of SPPs, connected via plasmonic strip waveguides of Cu, are demonstrated. Remarkably, the electronic-plasmonic transducers exhibit overall transduction efficiency of 1.85 ± 0.03%, five times higher than previously reported transducers with two tunnel junctions (metal-insulator-metal (MIM)-MIM transducers) where SPPs are detected based on optical rectification. The result establishes a new platform to convert electronic signals to plasmonic signals via electrical means, paving the way toward CMOS-compatible plasmonic components.

Huang H., Bharti K., Rebentrost P.

Abstract Solving linear systems of equations is essential for many problems in science and technology, including problems in machine learning. Existing quantum algorithms have demonstrated the potential for large speedups, but the required quantum resources are not immediately available on near-term quantum devices. In this work, we study near-term quantum algorithms for linear systems of equations, with a focus on the two-norm and Tikhonov regression settings. We investigate the use of variational algorithms and analyze their optimization landscapes. There exist types of linear systems for which variational algorithms designed to avoid barren plateaus, such as properly-initialized imaginary time evolution and adiabatic-inspired optimization, suffer from a different plateau problem. To circumvent this issue, we design near-term algorithms based on a core idea: the classical combination of variational quantum states (CQS). We exhibit several provable guarantees for these algorithms, supported by the representation of the linear system on a so-called ansatz tree. The CQS approach and the ansatz tree also admit the systematic application of heuristic approaches, including a gradient-based search. We have conducted numerical experiments solving linear systems as large as 2300 × 2300 by considering cases where we can simulate the quantum algorithm efficiently on a classical computer. Our methods may provide benefits for solving linear systems within the reach of near-term quantum devices.

Xu X., Sun J., Endo S., Li Y., Benjamin S.C., Yuan X.

Quantum algorithms have been developed for efficiently solving linear algebra tasks. However, they generally require deep circuits and hence universal fault-tolerant quantum computers. In this work, we propose variational algorithms for linear algebra tasks that are compatible with noisy intermediate-scale quantum devices. We show that the solutions of linear systems of equations and matrix-vector multiplications can be translated as the ground states of the constructed Hamiltonians. Based on the variational quantum algorithms, we introduce Hamiltonian morphing together with an adaptive ansätz for efficiently finding the ground state, and show the solution verification. Our algorithms are especially suitable for linear algebra problems with sparse matrices, and have wide applications in machine learning and optimisation problems. The algorithm for matrix multiplications can be also used for Hamiltonian simulation and open system simulation. We evaluate the cost and effectiveness of our algorithm through numerical simulations for solving linear systems of equations. We implement the algorithm on the IBM quantum cloud device with a high solution fidelity of 99.95%.

Fontanela F., Jacquier A., Oumgari M.

We propose a hybrid quantum-classical algorithm, which originated from quantum chemistry, to price European and Asian options in the Black--Scholes model. Our approach is based on the equivalence b...

Egan L., Debroy D.M., Noel C., Risinger A., Zhu D., Biswas D., Newman M., Li M., Brown K.R., Cetina M., Monroe C.

Quantum error correction protects fragile quantum information by encoding it into a larger quantum system1,2. These extra degrees of freedom enable the detection and correction of errors, but also increase the control complexity of the encoded logical qubit. Fault-tolerant circuits contain the spread of errors while controlling the logical qubit, and are essential for realizing error suppression in practice3–6. Although fault-tolerant design works in principle, it has not previously been demonstrated in an error-corrected physical system with native noise characteristics. Here we experimentally demonstrate fault-tolerant circuits for the preparation, measurement, rotation and stabilizer measurement of a Bacon–Shor logical qubit using 13 trapped ion qubits. When we compare these fault-tolerant protocols to non-fault-tolerant protocols, we see significant reductions in the error rates of the logical primitives in the presence of noise. The result of fault-tolerant design is an average state preparation and measurement error of 0.6 per cent and a Clifford gate error of 0.3 per cent after offline error correction. In addition, we prepare magic states with fidelities that exceed the distillation threshold7, demonstrating all of the key single-qubit ingredients required for universal fault-tolerant control. These results demonstrate that fault-tolerant circuits enable highly accurate logical primitives in current quantum systems. With improved two-qubit gates and the use of intermediate measurements, a stabilized logical qubit can be achieved. Fault-tolerant circuits for the control of a logical qubit encoded in 13 trapped ion qubits through a Bacon–Shor quantum error correction code are demonstrated.

Cattaneo M., Paraoanu G.S.

The importance of dissipation engineering ranges from universal quantum computation to non‐equilibrium quantum thermodynamics. In recent years, more and more theoretical and experimental studies have shown the relevance of this topic for circuit quantum electrodynamics, one of the major platforms in the race for a quantum computer. This article discusses how to simulate thermal baths by inserting resistive elements in networks of superconducting qubits. Apart from pedagogically reviewing the phenomenological and microscopic models of a resistor as thermal bath with Johnson–Nyquist noise, the paper introduces some new results in the weak coupling limit, showing that the most common examples of open quantum systems can be simulated through capacitively coupled superconducting qubits and resistors. The aim of the manuscript, written with a broad audience in mind, is to be both an instructive tutorial about how to derive and characterize the Hamiltonian of general dissipative superconducting circuits with capacitive coupling, and a review of the most relevant and topical theoretical and experimental works focused on resistive elements and dissipation engineering.

Darmawan A.S., Brown B.J., Grimsmo A.L., Tuckett D.K., Puri S.

The development of robust architectures capable of large-scale fault-tolerant quantum computation should consider both their quantum error-correcting codes, and the underlying physical qubits upon which they are built, in tandem. Following this design principle we demonstrate remarkable error correction performance by concatenating the XZZX surface code with Kerr-cat qubits. We contrast several variants of fault-tolerant systems undergoing different circuit noise models that reflect the physics of Kerr-cat qubits. Our simulations show that our system is scalable below a threshold gate infidelity of $p_\mathrm{CX} \sim 6.5\%$ within a physically reasonable parameter regime, where $p_\mathrm{CX}$ is the infidelity of the noisiest gate of our system; the controlled-not gate. This threshold can be reached in a superconducting circuit architecture with a Kerr-nonlinearity of $10$MHz, a $\sim 6.25$ photon cat qubit, single-photon lifetime of $\gtrsim 64\mu$s, and thermal photon population $\lesssim 8\%$. Such parameters are routinely achieved in superconducting circuits.

McRae C.R., Stiehl G.M., Wang H., Lin S., Caldwell S.A., Pappas D.P., Mutus J., Combes J.

Superconducting Quantum Devices Corey Rae H. McRae,1, 2, 3, a) Gregory M. Stiehl,4 Haozhi Wang,5 Sheng-Xiang Lin,1, 2, 3 Shane A. Caldwell,4 David P. Pappas,2 Josh Mutus,4 and Joshua Combes6 1)Department of Physics, University of Colorado, Boulder, Colorado 80309, USA 2)National Institute of Standards and Technology, Boulder, Colorado 80305, USA 3)Boulder Cryogenic Quantum Testbed, University of Colorado, Boulder, Colorado 80309, USA 4)Rigetti Computing, Berkeley, California 94710, USA 5)Laboratory for Physical Sciences, University of Maryland College Park, College Park, MD 20740, USA 6)Department of Electrical, Computer, and Energy Engineering, University of Colorado, Boulder, Colorado 80309, USA

Liu Y., Chua S., Gao S., Hu W., Guo Y.

Abstract A compact electrical source capable of generating surface plasmon polaritons would represent a crucial step for on-chip plasmonic circuitry. The device fabrication of plasmonic actuator based on Au/SiO2/n++Si tunnel junction and performance have been reported in [ACS photonics, 2021, 8, 7, 1951–1960]. This work focuses on the underlying mechanisms of electroluminescence. The n-type Si samples were doped with concentrations ranging from 1.6 × 1015 cm−3 to 1.0 × 1020 cm−3. A low voltage of 1.4 V for intense light emission was achieved at the highest concentration. The electrical/spectral characteristics and energy band diagrams calculation show two distinct behaviors indicating two distinct mechanisms of light emission are at work in the heavily doped versus the lightly doped Si. In the heavily doped case, the light output is correlated to tunneling current and the subsequent conversion of surface plasmons to photons, while that for the lightly doped case is due to indirect band-to-band recombination in silicon. The results are validated by numerical simulation which indicates that the heavy doping of the n++-Si is necessary to achieve surface plasmon generation via electron tunneling due to the presence of band tail states and their effect on lowering the barrier height.

Liu H., Wu Y., Wan L., Pan S., Qin S., Gao F., Wen Q.

The Poisson equation has wide applications in many areas of science and engineering. Although there are some quantum algorithms that can efficiently solve the Poisson equation, they generally require a fault-tolerant quantum computer, which is beyond the current technology. We propose a variational quantum algorithm (VQA) to solve the Poisson equation, which can be executed on noisy intermediate-scale quantum devices. In detail, we first adopt the finite-difference method to transform the Poisson equation into a linear system. Then, according to the special structure of the linear system, we find an explicit tensor product decomposition, with only $(2{log}_{2}n+1)$ items, of its coefficient matrix under a specific set of simple operators, where $n$ is the dimension of the coefficient matrix. This implies that the proposed VQA needs fewer quantum measurements, which dramatically reduces the required quantum resources. Additionally, we design observables to efficiently evaluate the expectation values of the simple operators on a quantum computer. Numerical experiments demonstrate that our algorithm can solve the Poisson equation.