Quantum Counterpart Research Articles

Physics-Inspired Optimization in the QUBO Framework: Key Concepts and Approaches

Quantum computing promises to have a tremendous advantage over its classical counterpart for solving computationally hard problems, yet remains in a relatively early stage for practical applications owing to the limited capabilities of today’s quantum computers. The approach to the special purposes of quantum computers by exploiting the special-purpose physics-inspired or quantum-inspired computers is emerging as a novel alternative to its quantum counterpart in tackling hard problems in high-performance computing. Inspired by physics, the Ising machine — a type of special-purpose computer that implements or emulates physics or quantum effects of the Ising model to speed up finding solutions to optimization problems — has recently become an active research area in the field of combinatorial optimization. This paper is to address the key enabling software and hardware technology underlying physics-inspired optimization using Ising machines in the unified quadratic unconstrained binary optimization (QUBO) framework for modeling and solving computationally hard combinatorial optimization problems, and with an aim to shed some light on the challenges and opportunities associated with the ever-growing landscape of this novel high-performance computing.

Energy efficient half-flux-quantum circuit aiming at milli-kelvin stage operation

Half-flux-quantum (HFQ) circuits are based on 0–π superconducting quantum interference devices (SQUIDs) and is one of the energy-efficient superconductor digital circuits. The bit energy is determined by the critical current I cn of 0–π SQUID, which can be easily tuned with the loop inductance and junction critical current. In this work, an alternative π–π–π SQUID is adopted to demonstrate HFQ circuits to simplify the fabrication process and enhance circuit energy efficiency. The properties of superconductor/ferromagnet/insulator/superconductor Josephson junctions (π-JJs) are measured with temperature dependence from 4.2 K down to 10 mK. HFQ toggle flip-flops (TFFs) are successfully demonstrated at frequencies of up to 6.7 GHz and 44.5 GHz at temperatures of 4.2 K and 10 mK, respectively. Comparing the HFQ TFF with its rapid single-flux quantum counterpart under the same fabrication process, it is anticipated that the HFQ TFF will exhibit approximately 70% reduction in both static and dynamic energy dissipation. This research establishes the foundation for developing cryogenic interface control and readout circuits for large-scale quantum computing in the future.

Ultimate Limits for Quickest Quantum Change-Point Detection.

Detecting abrupt changes in data streams is crucial because they are often triggered by events that have important consequences if left unattended. Quickest change-point detection has become a vital sequential analysis primitive that aims at designing procedures that minimize the expected detection delay of a change subject to a bounded expected false alarm time. We put forward the quantum counterpart of this fundamental primitive on streams of quantum data. We give a lower bound on the mean minimum delay when the expected time of a false alarm is asymptotically large, under the most general quantum detection strategy, which is given by a sequence of adaptive collective (potentially weak) measurements on the growing string of quantum data. In addition, we give particular strategies based on repeated measurements on independent blocks of samples that asymptotically attain the lower bound and thereby establish the ultimate quantum limit for quickest change-point detection. Finally, we discuss online change-point detection in quantum channels.

Mean and variance of the cardinality of particles in infinite true polyanalytic Ginibre processes via a coherent states quantization method

We discuss the mean and variance of the number ‘point-particles’ inside a disk D R centered at the origin of the complex plane and of radius R > 0 with respect to an infinite true polyanalytic process of index by quantizing the phase space via a set of generalized coherent states (CSs) of the harmonic oscillator on . By this procedure, the spectrum of the quantum observable representing the indicator function ofD R (viewed as a classical observable) allows to compute the mean value of . The variance of is obtained as a special eigenvalue of a quantum observable involving the auto-convolution of . By adopting a CSs quantization approach, we seek to identify classical observables on whose quantum counterparts may encode the first cumulants of through spectral properties.

Quintom fields from chiral anisotropic cosmology

In this paper we present an analysis of a chiral anisotropic cosmological scenario from the perspective of quintom fields. In this setup quintessence and phantom fields interact in a non-standard (chiral) way within an anisotropic Bianchi type I background. We present our examination from two fronts: classical and quantum approaches. In the classical program we find analytical solutions given by a particular choice of the emerged relevant parameters. Remarkably, we present an explanation of the “big-bang” singularity by means of a “big-bounce”. Moreover, isotropization is in fact reached as the time evolves. On the quantum counterpart the Wheeler–DeWitt equation is analytically solved for various instances given by the same parameter space from the classical study, and we also include the factor ordering $$\mathrm Q$$ . Having solutions in this scheme we compute the probability density, which is in effect damped as the volume function and the scalar fields evolve; and it also tends towards a flat FLRW framework when the factor ordering constant $$\textrm{Q}\ll 0$$ . This result might indicate that for a fixed set of parameters, the anisotropies quantum-mechanically vanish for very small values of the parameter $$\mathrm Q$$ . Finally, classical and quantum solutions reduce to their flat FLRW counterparts when the anisotropies vanish.

Optimizing Quantum Classification Algorithms on Classical Benchmark Datasets.

The discovery of quantum algorithms offering provable advantages over the best known classical alternatives, together with the parallel ongoing revolution brought about by classical artificial intelligence, motivates a search for applications of quantum information processing methods to machine learning. Among several proposals in this domain, quantum kernel methods have emerged as particularly promising candidates. However, while some rigorous speedups on certain highly specific problems have been formally proven, only empirical proof-of-principle results have been reported so far for real-world datasets. Moreover, no systematic procedure is known, in general, to fine tune and optimize the performances of kernel-based quantum classification algorithms. At the same time, certain limitations such as kernel concentration effects-hindering the trainability of quantum classifiers-have also been recently pointed out. In this work, we propose several general-purpose optimization methods and best practices designed to enhance the practical usefulness of fidelity-based quantum classification algorithms. Specifically, we first describe a data pre-processing strategy that, by preserving the relevant relationships between data points when processed through quantum feature maps, substantially alleviates the effect of kernel concentration on structured datasets. We also introduce a classical post-processing method that, based on standard fidelity measures estimated on a quantum processor, yields non-linear decision boundaries in the feature Hilbert space, thus achieving the quantum counterpart of the radial basis functions technique that is widely employed in classical kernel methods. Finally, we apply the so-called quantum metric learning protocol to engineer and adjust trainable quantum embeddings, demonstrating substantial performance improvements on several paradigmatic real-world classification tasks.

Reaction-Limited Quantum Reaction-Diffusion Dynamics.

We consider the quantum nonequilibrium dynamics of systems where fermionic particles coherently hop on a one-dimensional lattice and are subject to dissipative processes analogous to those of classical reaction-diffusion models. Particles can either annihilate in pairs, A+A→0, or coagulate upon contact, A+A→A, and possibly also branch, A→A+A. In classical settings, the interplay between these processes and particle diffusion leads to critical dynamics as well as to absorbing-state phase transitions. Here, we analyze the impact of coherent hopping and of quantum superposition, focusing on the so-called reaction-limited regime. Here, spatial density fluctuations are quickly smoothed out due to fast hopping, which for classical systems is described by a mean-field approach. By exploiting the time-dependent generalized Gibbs ensemble method, we demonstrate that quantum coherence and destructive interference play a crucial role in these systems and are responsible for the emergence of locally protected dark states and collective behavior beyond mean field. This can manifest both at stationarity and during the relaxation dynamics. Our analytical results highlight fundamental differences between classical nonequilibrium dynamics and their quantum counterpart and show that quantum effects indeed change collective universal behavior.

Symplectic and inverse spectral geometry of integrable systems: A glimpse and open problems

We first give a glimpse of finite dimensional classical integrable Hamiltonian systems from the point of view of symplectic geometry and briefly discuss their quantum counterparts, with an emphasis on recent progress on inverse spectral geometry. Then we propose several open problems about the geometry, topology and dynamics of these systems. The problems are largely motivated by the works of a number of authors, including Arnold, Atiyah, Colin de Verdière, Delzant, Duistermaat, Eliasson, Fomenko, Guillemin, Kolmogorov, Kostant, Moser and Sternberg.

Senses along Which the Entropy Sq Is Unique.

The Boltzmann-Gibbs-von Neumann-Shannon additive entropy SBG=-k∑ipilnpi as well as its continuous and quantum counterparts, constitute the grounding concept on which the BG statistical mechanics is constructed. This magnificent theory has produced, and will most probably keep producing in the future, successes in vast classes of classical and quantum systems. However, recent decades have seen a proliferation of natural, artificial and social complex systems which defy its bases and make it inapplicable. This paradigmatic theory has been generalized in 1988 into the nonextensive statistical mechanics-as currently referred to-grounded on the nonadditive entropy Sq=k1-∑ipiqq-1 as well as its corresponding continuous and quantum counterparts. In the literature, there exist nowadays over fifty mathematically well defined entropic functionals. Sq plays a special role among them. Indeed, it constitutes the pillar of a great variety of theoretical, experimental, observational and computational validations in the area of complexity-plectics, as Murray Gell-Mann used to call it. Then, a question emerges naturally, namely In what senses is entropy Sq unique? The present effort is dedicated to a-surely non exhaustive-mathematical answer to this basic question.

Stochastic strong zero modes and their dynamical manifestations.

Strong zero modes (SZMs) are conserved operators localized at the edges of certain quantum spin chains, which give rise to long coherence times of edge spins. Here we define and analyze analogous operators in one-dimensional classical stochastic systems. For concreteness, we focus on chains with single occupancy and nearest-neighbor transitions, in particular particle hopping and pair creation and annihilation. For integrable choices of parameters we find the exact form of the SZM operators. Being in general nondiagonal in the classical basis, the dynamical consequences of stochastic SZMs are very different from those of their quantum counterparts. We show that the presence of a stochastic SZM is manifested through a class of exact relations between time-correlation functions, absent in the same system with periodic boundaries.

MAQA: a quantum framework for supervised learning

Quantum machine learning has the potential to improve traditional machine learning methods and overcome some of the main limitations imposed by the classical computing paradigm. However, the practical advantages of using quantum resources to solve pattern recognition tasks are still to be demonstrated. This work proposes a universal, efficient framework that can reproduce the output of a plethora of classical supervised machine learning algorithms exploiting quantum computation’s advantages. The proposed framework is named Multiple Aggregator Quantum Algorithm (MAQA) due to its capability to combine multiple and diverse functions to solve typical supervised learning problems. In its general formulation, MAQA can be potentially adopted as the quantum counterpart of all those models falling into the scheme of aggregation of multiple functions, such as ensemble algorithms and neural networks. From a computational point of view, the proposed framework allows generating an exponentially large number of different transformations of the input at the cost of increasing the depth of the corresponding quantum circuit linearly. Thus, MAQA produces a model with substantial descriptive power to broaden the horizon of possible applications of quantum machine learning with a computational advantage over classical methods. As a second meaningful addition, we discuss the adoption of the proposed framework as hybrid quantum–classical and fault-tolerant quantum algorithm.

Quantum fingerprinting for heterogeneous devices localization

In this paper, we present QHFP, a device-independent quantum fingerprint matching algorithm that addresses two of the issues for realizing worldwide ubiquitous large-scale location tracking systems: scalability of storage space and running time as well as devices heterogeneity. In particular, we present a quantum algorithm with a complexity that is exponentially better than the classical techniques, both in space and running time. QHFP also has provisions for handling the inherent localization error due to building the large-scale fingerprint using heterogeneous devices. We give the details of the entire system starting from extracting device-independent features from the raw received signal strength, mapping the classical feature vectors to their quantum counterparts, and showing a quantum cosine similarity algorithm for fingerprint matching.We implement our quantum algorithm and deploy it in a real testbed using the IBM Quantum machine simulator. We also study the effect of the different quantum error sources, such as quantum gates error and quantum measurement error, on the system accuracy. Based on this, we discuss the suitable provisions to mitigate the effect of the quantum error sources on the localization accuracy.Results confirm the ability of QHFP to obtain the correct estimated location with an exponential improvement in space and running time compared to the traditional classical counterparts. In addition, the proposed device-independent features lead to more than 20% better accuracy in median error. This highlights the promise of our algorithm for future ubiquitous large-scale worldwide device-independent fingerprinting localization systems.

Using Quantum Nodes Connected via the Quantum Cloud to Perform IoT Quantum Network

Computer networks consist of millions of nodes that need constant protection because of their continued vulnerability to attacks. Classical security methods for protecting such networks will not be effective enough if quantum computers become widespread. On the other hand, we can exploit the capabilities of quantum computing and communications to build a new quantum communication network. In this paper, we focused on enhancing the performance of the classical client–server Internet application. For this sake, we introduced a novel Internet of Things (IoT) quantum network that provides high security and Quality of Service (QoS) compared with the traditional IoT network. This can be achieved by adding quantum components to the traditional IoT network. Quantum counterpart nodes, channels, and servers are used. In order to establish a secure communication between the quantum nodes and the quantum server, we defined a new Communication Procedure (CP) for the suggested IoT quantum network. The currently available quantum computer has a small qubit size (from 50 to 433 qubits). The proposed IoT quantum network allows us to overcome this problem by concatenating the computation efforts of multiple quantum nodes (quantum processors).

Generalized Toffoli Gate Decomposition Using Ququints: Towards Realizing Grover's Algorithm with Qudits.

Qubits, which are the quantum counterparts of classical bits, are used as basic information units for quantum information processing, whereas underlying physical information carriers, e.g., (artificial) atoms or ions, admit encoding of more complex multilevel states-qudits. Recently, significant attention has been paid to the idea of using qudit encoding as a way for further scaling quantum processors. In this work, we present an efficient decomposition of the generalized Toffoli gate on five-level quantum systems-so-called ququints-that use ququints' space as the space of two qubits with a joint ancillary state. The basic two-qubit operation we use is a version of the controlled-phase gate. The proposed N-qubit Toffoli gate decomposition has O(N) asymptotic depth and does not use ancillary qubits. We then apply our results for Grover's algorithm, where we indicate on the sizable advantage of using the qudit-based approach with the proposed decomposition in comparison to the standard qubit case. We expect that our results are applicable for quantum processors based on various physical platforms, such as trapped ions, neutral atoms, protonic systems, superconducting circuits, and others.

Coherent backscattering of entangled photon pairs

Correlations between entangled photons are a key ingredient for testing fundamental aspects of quantum mechanics and an invaluable resource for quantum technologies. However, scattering from a dynamic medium typically scrambles and averages out such correlations. Here we show that multiply scattered entangled photons reflected from a dynamic complex medium remain partially correlated. In experiments and full-wave simulations we observe enhanced correlations, within an angular range determined by the transport mean free path, which prevail over disorder averaging. Theoretical analysis reveals that this enhancement arises from the interference between scattering trajectories, in which the photons leave the sample and are then virtually reinjected back into it. These paths are the quantum counterpart of the paths that lead to the coherent backscattering of classical light. This work points to opportunities for entanglement transport despite dynamic multiple scattering in complex systems. Dynamic and disordered media destroy the correlations that underlie many quantum measurement protocols and applications. However, coherently backscattered photons can remain partially correlated due to interference between scattering trajectories.

Out-of-time-order correlations and quantum chaos

Quantum Chaos has originally emerged as the field which studies how the properties of classical chaotic systems arise in their quantum counterparts. The growing interest in quantum many-body systems, with no obvious classical meaning has led to consider time-dependent quantities that can help to characterize and redefine Quantum Chaos. This article reviews the prominent role that the out of time ordered correlator (OTOC) plays to achieve such goal.

Advantage of Classical Approximate Analytical Methods for Studying Rydberg States Over the Quantum Counterparts

Advantage of Classical Approximate Analytical Methods for Studying Rydberg States Over the Quantum Counterparts

Singularities in the Loschmidt echo of quenched topological superconductors

We study the Loschmidt echo in the quenched two-dimensional $p$-wave topological superconductor. We find that if this superconductor is quenched out of the critical point separating its topological and nontopological phases into either of the two gapful phases, its Loschmidt echo features singularities occurring periodically in time where the second derivative of the Loschmidt echo over time diverges logarithmically. Conversely, we give arguments towards $s$-wave superconductors not having singularities in their Loschmidt echo regardless of the quench. We also demonstrate that the conventional mean-field theory calculates classical echo instead of its quantum counterpart, and show how it should be modified to capture the full quantum Loschmidt echo.

Characterization of nonsignaling bipartite correlations corresponding to quantum states

Characterizing quantum correlations from physical principles is a central problem in the field of quantum information theory. Entanglement breaks bounds on correlations put forth by Bell's theorem, thus challenging the notion of local causality as a physical principle. A natural relaxation is to study no-signalling as a constraint on joint probability distributions. It was shown that, when considered with respect to so-called locally quantum observables, bipartite nonsignalling correlations never exceed their quantum counterparts; still, such correlations generally do not derive from quantum states. This leaves open the search for additional principles which identify quantum states within the larger set of (collections of) nonsignalling joint probability distributions over locally quantum observables. Here, we suggest a natural generalization of no-signalling in the form of no-disturbance to dilated systems. We prove that nonsignalling joint probability distributions satisfying this extension correspond with bipartite quantum states up to a choice of time orientation in subsystems.

Classical versus quantum: Comparing tensor-network-based quantum circuits on Large Hadron Collider data

Tensor networks (TN) are approximations of high-dimensional tensors designed to represent locally entangled quantum many-body systems efficiently. This paper provides a comprehensive comparison between classical TNs and TN-inspired quantum circuits in the context of machine learning on highly complex, simulated Large Hadron Collider data. We show that classical TNs require exponentially large bond dimensions and higher Hilbert-space mapping to perform comparably to their quantum counterparts. While such an expansion in the dimensionality allows better performance, we observe that, with increased dimensionality, classical TNs lead to a highly flat loss landscape, rendering the usage of gradient-based optimization methods highly challenging. Furthermore, by employing quantitative metrics, such as the Fisher information and effective dimensions, we show that classical TNs require a more extensive training sample to represent the data as efficiently as TN-inspired quantum circuits. We also engage with the idea of hybrid classical-quantum TNs and show possible architectures to employ a larger phase space from the data. We offer our results using three main TN Ans\"atze: Tree tensor networks, matrix product states, and multiscale entanglement renormalization Ans\"atze.