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Post-quantum cryptosystems based on QC-MDPC codes are designed to mitigate the security threat posed by quantum computers to traditional public-key cryptography. The polynomial inversion is the core operation of key generation in such cryptosystems and the adoption of ephemeral keys imposes the execution of key generation for each session. To this end, there is a need for efficient and scalable hardware implementations of the binary polynomial inversion operation to support the key generation primitive across a wide range of computational platforms. This manuscript proposes an efficient and scalable architecture implementing the binary polynomial inversion at the hardware level. Our solution can deliver a performance-optimized implementation for the large polynomials used in post-quantum code-based cryptosystems and for each FPGA of the mid-range Xilinx Artix-7 family. The effectiveness of the proposed solution was validated by means of the BIKE and LEDAcrypt post-quantum QC-MDPC cryptosystems as representative use cases. Compared to the C11- and the optimized AVX2-based software implementations of LEDAcrypt, instances of the proposed architecture targeting the Artix-7 200 FPGA show an average performance improvement of 31.7 and 2.2 times, respectively. Moreover, the proposed architecture delivers a performance improvement up to 18.1 and 21.5 times for AES-128 and AES-192 security levels, respectively, compared to the BIKE hardware implementation. [ABSTRACT FROM AUTHOR]

The design of decoding algorithms is a significant technological component in the development of fault-tolerant quantum computers. Often design of quantum decoders is inspired by classical decoding algorithms, but there are no general principles for building quantum decoders from classical decoders. Given any pair of classical codes, we can build a quantum code using the hypergraph product, yielding a hypergraph product code. Here we show we can also lift the decoders for these classical codes. That is, given oracle access to a minimum weight decoder for the relevant classical codes, the corresponding $[[n,k,d]]$ quantum code can be efficiently decoded for any error of weight smaller than $(d-1)/2$. The quantum decoder requires only $O(k)$ oracle calls to the classical decoder and $O(n^{2})$ classical resources. The lift and the correctness proof of the decoder have a purely algebraic nature that draws on the discovery of some novel homological invariants of the hypergraph product codespace. While the decoder works perfectly for adversarial errors, that is errors of weight up to half the code distance, it is not suitable for more realistic stochastic noise models and therefore can not be used to establish an error correcting threshold. [ABSTRACT FROM AUTHOR]

Future communication networks will require increased flexibility, scalability, and data computation capabilities to adequately respond to the growing number of service demands. Advanced mixed-integer network resource optimization models and algorithms are required to meet these requirements. The purpose of this article is to introduce a hybrid quantum-classical computing framework for addressing future network resource optimization issues. We begin by discussing the fundamentals of quantum computing and its parallelism. Following that, we discuss in detail the hybrid quantum-classical computing paradigm. Then, we discuss the potential applications of the proposed paradigm for network resource optimization, including network function virtualization (NFV), multi-access edge computing/fog/cloud computing, and cloud radio access networks (C-RANs). Finally, we discuss the difficulties associated with the design and implementation of hybrid quantum-classical algorithms. [ABSTRACT FROM AUTHOR]

Quantum communications is a promising technology that will play a fundamental role in the design of future networks. In fact, significant efforts are being undertaken by both the quantum physics and the classical communications communities on developing new architectures, solutions, and practical implementations of quantum communication networks (QCNs). Although these efforts led to various advances in today's technologies, there still exists a non-trivial gap between the research efforts of the two communities on designing and optimizing the performance of QCNs. For instance, most prior works by the classical communications community ignore important quantum physics-based constraints when designing QCNs. For example, many existing works on entanglement distribution do not account for the decoherence of qubits inside quantum memories and, thus, their designs become impractical since they assume an infinite lifetime of quantum states. In this article, we bring forth a novel analysis of the performance of QCNs in a physics-informed manner, by relying on the quantum physics principles that underly the different components of QCNs. The need for the physics-informed approach is then assessed and its fundamental role in designing practical QCNs is analyzed across various open research areas. Moreover, we identify novel physics-informed performance metrics and controls that enable QCNs to leverage the state-of-theart advancements in quantum technologies to enhance their performance. Finally, we analyze multiple pressing challenges and open research directions in QCNs that must be treated using a physics-informed approach to lead practically viable results. Ultimately, this work attempts to bridge the gap between the classical communications and the quantum physics communities in the area of QCNs to foster the development of the future communication networks toward the quantum Internet. [ABSTRACT FROM AUTHOR]

The dawn of quantum computing brings on a revolution in the way combinatorially complex power system problems such as Unit Commitment are solved. The Unit Commitment problem complexity is expected to increase in the future because of the trend toward the increase of penetration of intermittent renewables. Even though quantum computing has proven effective for solving a host of problems, its applications for power systems’ problems have been rather limited. In this paper, a quantum unit commitment is innovatively formulated and the quantum version of the decomposition and coordination alternate direction method of multipliers (ADMM) is established. The above is achieved by devising quantum algorithms and by exploiting the superposition and entanglement of quantum bits (qubits) for solving subproblems, which are then coordinated through ADMM to obtain feasible solutions. The main contributions of this paper include: 1) the innovative development of a quantum model for Unit Commitment; 2) development of decomposition and coordination-supported framework which paves the way for the utilization of limited quantum resources to potentially solve the large-scale discrete optimization problems; 3) devising the novel quantum distributed unit commitment (QDUC) to solve the problem in a larger scale than currently available quantum computers are capable of solving. The QDUC results are compared with those from its classical counterpart, which validate the efficacy of quantum computing. [ABSTRACT FROM AUTHOR]

Recent advances in quantum technologies pave the way for noisy intermediate-scale quantum (NISQ) devices, where the quantum approximation optimization algorithm (QAOA) constitutes a promising candidate for demonstrating tangible quantum advantages based on NISQ devices. In this paper, we consider the maximum likelihood (ML) detection problem of binary symbols transmitted over a multiple-input and multiple-output (MIMO) channel, where finding the optimal solution is exponentially hard using classical computers. Here, we apply the QAOA for the ML detection by encoding the problem of interest into a level- $p$ QAOA circuit having $2p$ variational parameters, which can be optimized by classical optimizers. This level- $p$ QAOA circuit is constructed by applying the prepared Hamiltonian to our problem and the initial Hamiltonian alternately in $p$ consecutive rounds. More explicitly, we first encode the optimal solution of the ML detection problem into the ground state of a problem Hamiltonian. Using the quantum adiabatic evolution technique, we provide both analytical and numerical results for characterizing the evolution of the eigenvalues of the quantum system used for ML detection. Then, for level-1 QAOA circuits, we derive the analytical expressions of the expectation values of the QAOA and discuss the complexity of the QAOA based ML detector. Explicitly, we evaluate the computational complexity of the classical optimizer used and the storage requirement of simulating the QAOA. Finally, we evaluate the bit error rate (BER) of the QAOA based ML detector and compare it both to the classical ML detector and to the classical minimum mean squared error (MMSE) detector, demonstrating that the QAOA based ML detector is capable of approaching the performance of the classical ML detector. [ABSTRACT FROM AUTHOR]

In this work, we propose quantum assisted eigenvalue estimation and target detection algorithms for a large sensor array via Hamiltonian simulation. Quantum algorithms provide complexity advantage of a certain class of problems on a quantum computer with fewer physical resources as compared to their classical counterparts. The proposed algorithms make use of the quantum phase estimation (QPE) as its core computing component. We have introduced an analytical quantum framework to map from classical to quantum in the context of target detection. Target detection involves an appropriate choice of threshold based on the probability of detection or false alarm. We exploited the massive sensor array structure and invoked the random matrix theory to propose an optimal threshold. It also takes into account the quantum measurement noise in the framework. Numerical simulations are performed to ascertain the efficacy of the proposed framework. The results suggest near term applications of the quantum algorithm for large-scale linear systems. [ABSTRACT FROM AUTHOR]

The integration of information and communication technologies has introduced cybersecurity challenges to microgrid (MG) apart from bringing more flexibility, reliability, and resilience. Especially in the upcoming quantum era, the existing cryptographic systems are vulnerable to attacks from quantum computers. Motivated by these challenges, this article proposes a quantum-key-distribution (QKD)-based MG distributed control framework for cybersecurity enhancement. To defend the side-channel attacks and make the framework practical enough for industrial applications, measurement-device-independent QKD (MDI-QKD) is introduced. The following contributions are made in this work. 1) A novel QKD-based quantum-secure control architecture is established to assure the data transmission security in MG distributed control. 2) MDI-QKD with asymmetric protocol is used to form a scalable QKD network for MG control. 3) A method for fast parameter optimization based on deep neural network (DNN) is proposed to adjust the parameters in QKD systems in real-time. Simulations are carried on a 13-bus MG to demonstrate the working principles of the proposed control scheme. The test results also prove the feasibility of the DNN-based parameter optimizer. [ABSTRACT FROM AUTHOR]

Until quantum repeaters become mature, quantum networks remain restricted either to limited areas of directly connected nodes or to nodes connected to a common node. We circumvent this limitation by conceiving quantum networks using secure classical repeaters combined with the quantum secure direct communication (QSDC) principle, which is a compelling form of quantum communication that directly transmits information over a quantum channel. The final component of this promising solution is our classical quantum-resistant algorithm. Explicitly, in these networks, the ciphertext gleaned from a quantum-resistant algorithm is transmitted using QSDC along the nodes, where it is read out by one node and then transmitted to the next node. At the repeaters, the information is protected by our quantum-resistant algorithm, which is secure even in the face of a quantum computer. Hence, our solution offers secure end-to-end communication across the entire network, since it is capable of both eavesdropping detection and prevention in the emerging quantum Internet. It is compatible with operational networks, and will enjoy the compelling services of the popular Internet, including authentication. Hence, it smoothens the transition from the classical Internet to the quantum Internet (Qinternet) by following a gradual evolutionary upgrade. It will act as an alternative network in quantum computing networks in the future. We have presented the first experimental demonstration of a secure classical-repeater-based hybrid quantum network constructed by a serial concatenation of an optical fiber and free-space communication link. In conclusion, secure repeater networks may indeed be constructed using existing technology and continue to support a seamless evolutionary pathway to the future Qinternet of quantum computers. [ABSTRACT FROM AUTHOR]

Contemporary digital infrastructures and systems use and trust Public-Key Cryptography to exchange keys over insecure communication channels. With the development and progress in the research field of quantum computers, well established schemes like RSA and ECC are more and more threatened. The urgent demand to find and standardize new schemes – which are secure in a post-quantum world – was also realized by the National Institute of Standards and Technology which announced a Post-Quantum Cryptography Standardization Project in 2017. Recently, the round three candidates were announced and one of the alternate candidates is the Key Encapsulation Mechanism scheme BIKE. In this article, we investigate different strategies to efficiently implement the BIKE algorithm on Field-Programmable Gate Arrays (FPGAs). To this extend, we improve already existing polynomial multipliers, propose efficient strategies to realize polynomial inversions, and implement the Black-Gray-Flip decoder for the first time. Additionally, our implementation is designed to be scalable and generic with the BIKE specific parameters. All together, the fastest designs achieve latencies of 2.69 ms for the key generation, 0.1 ms for the encapsulation, and 1.89 ms for the decapsulation considering the lowest security level. [ABSTRACT FROM AUTHOR]

Quantum error mitigation (QEM) is a class of promising techniques capable of reducing the computational error of variational quantum algorithms tailored for current noisy intermediate-scale quantum computers. The recently proposed permutation-based methods are practically attractive, since they do not rely on any a priori information concerning the quantum channels. In this treatise, we propose a general framework termed as permutation filters, which includes the existing permutation-based methods as special cases. In particular, we show that the proposed filter design algorithm always converge to the global optimum, and that the optimal filters can provide substantial improvements over the existing permutation-based methods in the presence of narrowband quantum noise, corresponding to large-depth, high-error-rate quantum circuits. [ABSTRACT FROM AUTHOR]

In a fault tolerant quantum computer, quantum codes are expected to serve the conflicting purposes of protecting quantum information while also allowing that information to be manipulated by fault-tolerant gates. We introduce a new technique for placing limitations on such gates, and apply this technique to a class of quantum codes known as hypergraph product codes contained within the vertical sector. These codes are constructed from input which is a pair of classical linear codes, and generalize the Kitaev surface code which is the hypergraph product of classical repetition codes. We provide a necessary condition on these input codes, under which the resulting hypergraph product code has transversal gates limited to the Clifford group. We conjecture that this condition is satisfied by all $[n,k,d]$ Gallagher codes with $d\ge 3$ and $k\le n/2$. This work is a generalization of an argument due to Bravyi and König, and we also conjecture this is a refinement of the recent notion of disjointness due to Jochym-O’Connor et al. [ABSTRACT FROM AUTHOR]

We discuss quantum computers from the perspective of one of their major building blocks, the hardware controller, explaining how it fits into the computer and the requirements and challenges it poses for engineers and scientists. [ABSTRACT FROM AUTHOR]

Noisy gate-model quantum processing units (QPUs) are currently available from vendors over the cloud, and digital quantum programming approaches exist to run low-depth circuits on physical hardware. These digital representations are ultimately lowered to pulse-level instructions by vendor quantum control systems to affect unitary evolution representative of the submitted digital circuit. Vendors are beginning to open this pulse-level control system to the public via specified interfaces. Robust programming methodologies, software frameworks, and backend simulation technologies for this analog model of quantum computation will prove critical to advancing pulse-level control research and development. Prototypical use cases for this include error mitigation, optimal pulse control, and physics-inspired pulse construction. Here we present an extension to the XACC quantum-classical software framework that enables pulse-level programming for superconducting, gate-model quantum computers, and a novel, general, and extensible pulse-level simulation backend for XACC that scales on classical compute clusters via MPI. Our work enables custom backend Hamiltonian definitions and gate-level compilation to available pulses with a focus on performance and scalability. We end with a demonstration of this capability, and show how to use XACC for pertinent pulse-level programming tasks. [ABSTRACT FROM AUTHOR]

Extensive quantum error correction is necessary in order to perform a useful computation on a noisy quantum computer. Moreover, quantum error correction must be implemented based on imperfect parity check measurements that may return incorrect outcomes or inject additional faults into the qubits. To achieve fault-tolerant error correction, Shor proposed to repeat the sequence of parity check measurements until the same outcome is observed sufficiently many times. Then, one can use this information to perform error correction. A basic implementation of this fault tolerance strategy requires $\Omega (r d^{2})$ parity check measurements for a distance- $d$ code defined by $r$ parity checks. For some specific highly structured quantum codes, Bombin has shown that single-shot fault-tolerant quantum error correction is possible using only $r$ measurements. In this work, we consider a phenomenological noise model for parity check measurements assuming that each bit of a codeword and the measurement outcome suffer from independent bit flips with some error rate $p$. For this model, we demonstrate that fault-tolerant quantum error correction can be achieved using $O(d \log (d))$ measurements for any code with distance $d \geq \Omega (n^\alpha)$ for some constant $\alpha > 0$. Moreover, we prove the existence of a sub-single-shot fault-tolerant quantum error correction scheme using fewer than $r$ measurements. In some cases, the number of parity check measurements required for fault-tolerant quantum error correction is exponentially smaller than the number of parity checks defining the code. The short measurement sequences constructed generally have high weight and our phenomenological noise model is not realistic in this regime. Our error correction strategy could find applications to small codes and LDPC codes if one can manage to keep the weight of the measured parity checks low. [ABSTRACT FROM AUTHOR]

We are developing a new instrument, the RF Josephson arbitrary waveform synthesizer (RF-JAWS), for communications metrology and quantum information applications. An important aspect of the RF-JAWS design is the accurate and traceable characterization of its superconducting devices. In this article, we present a procedure for characterizing microwave superconducting devices in a cryogenic RF probe station via a vector network analyzer (VNA) calibrated with a custom cryogenic calibration kit colocated with the superconducting device under test (DUT) in the cryogenic environment. By de-embedding lossy and dispersive RF interconnects linking the superconducting DUT to the measurement apparatus at room temperature, we characterize the DUT exactly at the cryogenic on-wafer reference plane. More importantly, we operate our VNA with an external modulated source and our procedure features metrology-grade multiline thru-reflect-line calibration and absolute power and phase corrections, as opposed to the more common relative scattering-parameter correction. In addition, we apply an X-parameter model to account for impedance mismatch in cryogenic Josephson microwave sources. Our techniques are also suitable for cryogenic characterization of microwave superconducting devices for solid-state quantum computers and could help to optimize the quantum-classical interfaces in these systems. [ABSTRACT FROM AUTHOR]

We present and analyze a quantum algorithm to estimate credit risk more efficiently than Monte Carlo simulations can do on classical computers. More precisely, we estimate the economic capital requirement, i.e. the difference between the Value at Risk and the expected value of a given loss distribution. The economic capital requirement is an important risk metric because it summarizes the amount of capital required to remain solvent at a given confidence level. We implement this problem for a realistic loss distribution and analyze its scaling to a realistic problem size. In particular, we provide estimates of the total number of required qubits, the expected circuit depth, and how this translates into an expected runtime under reasonable assumptions on future fault-tolerant quantum hardware. [ABSTRACT FROM AUTHOR]

Loading data in a quantum device is required in several quantum computing applications. Without an efficient loading procedure, the cost to initialize the algorithms can dominate the overall computational cost. A circuit-based quantum random access memory named FF-QRAM can load $M$ M $n$ n -bit patterns with computational cost $O(CMn)$ O (C M n) to load continuous data where $C$ C depends on the data distribution. In this article, we propose a strategy to load continuous data without post-selection with computational cost $O(Mn$ O (M n ). The proposed method is based on the probabilistic quantum memory, a strategy to load binary data in quantum devices, and the FF-QRAM using standard quantum gates, and is suitable for noisy intermediate-scale quantum computers. [ABSTRACT FROM AUTHOR]

Quantum computing systems are developing rapidly as powerful solvers for a variety of real-world calculations. Traditionally, many of these same applications are solved using conventional high-performance computing (HPC) systems, which have progressed sharply through decades of hardware and software improvements. Here, we present a perspective on the motivations and challenges of pairing quantum computing systems with modern HPC infrastructure. We outline considerations and requirements for the use cases, macroarchitecture, microarchitecture, and programming models needed to integrate near-term quantum computers with HPC system, and we conclude with the expectation that such efforts are well within reach of current technology. [ABSTRACT FROM AUTHOR]

Quantum computers are domain-specific accelerators that can solve commercially important problems that are beyond the capability of conventional computers. Quantum computing is at an inflection point where small systems with a few dozen qubits have been demonstrated and the number of qubits is expected to increase to several hundred over the coming years. However, the qubit quality is likely to remain quite low making it difficult to execute programs reliably. Furthermore, scaling the designs to a large number of qubits would require specialized hardware that operates at cryogenic conditions. This article describes the compiler and hardware support for enabling reliable and scalable quantum computers. [ABSTRACT FROM AUTHOR]

Despite its tremendous potential, it is still unclear how quantum computing will scale to satisfy the requirements of its most powerful applications. Among other issues, there are hard limits to the number of qubits that can be integrated into a single chip. Multicore architectures are a firm candidate for unlocking the scalability of quantum processors. Nonetheless, the vulnerability and complexity of quantum communications make this a challenging approach. A comprehensive design should imply consolidating the communications stack in the quantum computer architecture. In this article, we explain how this vision, by entangling communications and computation in the core of the design, may help to solve the open challenges. We also summarize the first results of our application of structured design methodologies backing this vision. With our work, we hope to contribute with design guidelines that may help unleash the potential of quantum computing. [ABSTRACT FROM AUTHOR]

Noisy intermediate scale quantum (NISQ) computers are becoming a reality thanks to the recent advances made by researchers who physically build such systems. In order to execute corresponding quantum algorithms (usually provided in terms of quantum circuits), certain physical constraints in the architectures need to be satisfied. More precisely, physical constraints restrict the possible interactions between qubits which frequently result in cases where qubits which are supposed to interact in a quantum circuit are not allowed to interact on the physical device. Thus far, this is addressed by dedicated methods that map the logical quantum circuit to a physical realization and satisfy the constraints by inserting further operations. This leads to additional costs which harm the fidelity of the circuit and, hence, urgently need to be avoided. Unfortunately, current state-of-the-art approaches for this mapping process take the existing architectures as invariant and only try to reduce the number of additionally needed operations. In contrast, (slight) changes in the, respectively, given architectures (which still keep the underlying physical constraints satisfied) might be possible and may allow for even better (i.e., less costly) mappings. But this potential has not been investigated yet. In this work, we explore this potential. More precisely, we introduce several schemes for generating alternative coupling graphs (and, by this, quantum computing architectures) that still might be able to satisfy physical constraints but, at the same time, allow for a more efficient realization of the desired quantum functionality. Evaluations confirm the potential of those alternative coupling graphs and demonstrate that they can reduce the mapping overhead by up to 60% in the best case and up to almost 40% on average. [ABSTRACT FROM AUTHOR]

Layout synthesis, an important step in quantum computing, processes quantum circuits to satisfy device layout constraints. In this paper, we construct QUEKO benchmarks for this problem, which have known optimal depths and gate counts. We use QUEKO to evaluate the optimality of current layout synthesis tools, including Cirq from Google, Qiskit from IBM, ⟨t|ket〉 from Cambridge Quantum Computing, and a recent academic work. To our surprise, despite over a decade of research and development by academia and industry on compilation and synthesis for quantum circuits, we are still able to demonstrate large optimality gaps: 1.5-12x on average on a smaller device and 5-45x on average on a larger device. This suggests substantial room for improvement of the efficiency of quantum computer by better layout synthesis tools. Finally, we also prove the NP-completeness of the layout synthesis problem for quantum computing. We have made the QUEKO benchmarks open-source. [ABSTRACT FROM AUTHOR]

Quantum computers offer huge potential performance, and biological computers can revolutionize pharmaceuticals. However, simple "engineering" descriptions and standardized approaches are needed. We provide "layperson" descriptions of quantum and biological computer architectures, comparisons with digital computers, and discussions of industry-standard models. [ABSTRACT FROM AUTHOR]

Development of practical quantum computers would require 1000's of qubits and equally large number of read-out, bias and drive lines. New materials that combine low passive loss and good RF properties are needed. Here we report performance of signal interconnects comprised of high-temperature YBCO films that are exfoliated from a metal substrate and transferred to a E-Kapton tape. The technology offers low-loss transition between 60 K to sub-mK environments and interfacing with off-shelf flexible silicon electronics. We demonstrate <1 dB/m attenuation at 6 GHz at 77 K. The microstrip assemblies demonstrated no degradation upon multiple cycling to liquid Nitrogen and conduction cooling down to 18 K. We discuss the design of a practical high-density signal cable with passive loss well below 1 μW per line. The YBCO-on-Kapton technology offers a practical pathway to large error-corrected quantum computing systems. [ABSTRACT FROM AUTHOR]

This article summarizes the current status of classical communication networks and identifies some critical open research challenges that can only be solved by leveraging quantum technologies. Until now, the main goal of quantum communication networks has been security. However, quantum networks can do more than just exchange secure keys or serve the needs of quantum computers. In fact, the scientific community is still investigating the possible use cases/benefits that quantum communication networks can bring. Thus, this article aims to point out and clearly describe how quantum communication networks can enhance in-network distributed computing and reduce the overall end-to-end latency, beyond the intrinsic limits of classical technologies. Furthermore, we also explain how entanglement can reduce the communication complexity (overhead) that future classical virtualized networks will experience. [ABSTRACT FROM AUTHOR]

Code-based cryptography based on binary Goppa codes is a promising solution for thwarting attacks based on quantum computers. The McEliece cryptosystem is a code-based public-key cryptosystem which is believed to be resistant against quantum attacks. In fact, it is successfully advanced to the second round of the post-quantum cryptography standardization competition early 2019. Due to its very large key size, different variants of binary Goppa codes have been proposed. Nevertheless, research has shown that such codes can be thwarted through the injection of faults, causing erroneous outputs. In this work, we present countermeasures for the implementation of different composite field arithmetic units used in the McEliece cryptosystem. The proposed architectures use overhead-aware and tailored signatures. We apply these error detection signatures to the McEliece cryptosystem and perform field-programmable gate array (FPGA) implementations to show the feasibility of adopting the proposed schemes. We benchmark the overhead and performance degradation of the proposed approaches and show their suitability for constrained embedded systems. [ABSTRACT FROM AUTHOR]

Existing microgrid communication relies on classical public key systems, which are vulnerable to attacks from quantum computers. This paper uses quantum key distribution (QKD) to solve these quantum-era microgrid challenges. Specifically, this paper makes the following novel contributions: 1) it devises a novel QKD simulator capable of simulating QKD protocols; 2) it offers a QKD-based microgrid communication architecture for microgrids; 3) it shows how to build a quantum-secure microgrid testbed in an RTDS environment; 4) it develops a key pool sharing (KPS) strategy to improve the cyberattack resilience of the QKD-based microgrid; and 5) it analyzes the impacts of critical QKD parameters with the testbed. Test results provide insightful resources for building a quantum-secure microgrid. [ABSTRACT FROM AUTHOR]

This article is written in recognition of W. Bledsoe, who with Browning, introduced the N-tuple subspace classifier in 1959. This 1959 article was the first article to introduce subspace classifiers and the sum rule to combine the outputs of the classifiers. A mathematical notation is given to easily express in a precise and unambiguous way everything going on in the N-tuple subspace classifier. Extensions of the N-tuple method are discussed using a generalized product expression and we relate the generalization to graphical models. We discuss the sum rule, the product rule, and the plurality voting rule for combining the scores of the subspace classifiers. We selected a representative sample of papers that the 1959 N-tuple subspace classifier inspired. Some of the papers introduced specialized improvements. Many of the papers showed the value of the N-tuple subspace classifier in all kinds of applications and compared the results of one or more varieties of the N-tuple subspace classifier with other state-of-the-art classifiers. Their experiments showed that the N-tuple subspace classifier was competitive with the state-of-the-art classifiers and often had a higher accuracy. Finally, we highlight some papers that describe experiments of the N-tuple subspace classifier executing in a quantum computer. [ABSTRACT FROM AUTHOR]

Quantum algorithm design usually assumes access to a perfect quantum computer with ideal properties like full connectivity, noise-freedom, and arbitrarily long coherence time. In noisy intermediate-scale quantum (NISQ) devices, however, the number of qubits is highly limited and quantum operation error and qubit coherence are not negligible. Besides, the connectivity of physical qubits in a quantum processing unit (QPU) is also strictly constrained. Thereby, additional operations like SWAP gates have to be inserted to satisfy this constraint while preserving the functionality of the original circuit. This process is known as quantum circuit transformation. Adding additional gates will increase both the size and depth of a quantum circuit and, therefore, cause further decay of the performance of a quantum circuit. Thus, it is crucial to minimize the number of added gates. In this article, we propose an efficient method to solve this problem. We first choose by using simulated annealing an initial mapping which fits well with the input circuit and then, with the help of a heuristic cost function, stepwise apply the best-selected SWAP gates until all quantum gates in the circuit can be executed. Our algorithm runs in time polynomial in all parameters, including the size and the qubit number of the input circuit, and the qubit number in the QPU. Its space complexity is quadratic to the number of edges in the QPU. The experimental results on extensive realistic circuits confirm that the proposed method is efficient and the number of added gates of our algorithm is, on average, only 57% of that of state-of-the-art algorithms on IBM Q20 (Tokyo), the most recent IBM quantum device. [ABSTRACT FROM AUTHOR]

Quantum computers are available via the Internet for students and small-scale research. What if similar access could be extended to quantum hardware? [ABSTRACT FROM AUTHOR]

Recently dynamic social networks witnessed a massive surge in popularity, especially in the area of anomaly detection. Although the text-based methods have achieved impressive detection performances, their applications are limited to the social text provided by users. This research focuses on graph-based methods and proposes a universal method for generalized social networks. Different from the existing graph-based methods that summarize a number of structural features, the proposed nodes' evolution diversity inspired method (NEDM) detects anomalies in dynamic social networks from the perspective of diverse evolution mechanisms. More specifically, NEDM applies link prediction algorithms at the micro-level to fit evolution mechanisms followed by the behaviors of nodes, and designs indices to evaluate their fitting degrees in edge removal and generation processes. In addition, the behavior of a node is represented as a quantum superposition state where such behavior follows different evolution mechanisms with uncertain probabilities. We propose a quantum mechanism based particle swarm optimization algorithm (QMPSO) in NEDM. QMPSO determines the optimal observation states of the behaviors of different nodes, and maximally reflects the evolutional fluctuations in the evolution processes of social networks. As a result, NEDM can quantify the evolutional fluctuations in different periods, and detect anomalies in dynamic social networks. Comparing with art-of-the-state methods and real social data in extensive experiments on disparate real-world social networks, we verify the outstanding performance of NEDM in terms of both accuracy and universality. [ABSTRACT FROM AUTHOR]

Quantum computers are becoming a reality today due to the rapid progress made by researchers in the last years. In the process of building quantum computers, IBM has developed several versions—starting from 5-qubit architectures like IBM QX2 and IBM QX4 to larger 16- or 20-qubit architectures. These architectures support arbitrary rotations of a single qubit and a controlled negation (CNOT) involving two qubits. The two qubit operations come with added coupling-map restrictions that only allow specific physical qubits to be the control and target qubits of the operation. In order to execute a quantum circuit on the IBM QX architecture, CNOT gates must satisfy the so-called coupling constraints of the architecture. Previous works addressed this issue with the objective of reducing the number of gates and the circuit depth. However, in this article, we show that further improvements are possible. To this end, we present a general approach for further improving the number of gate operations and depth of the mapped circuit. The proposed approach encompasses the selection of physical qubits, determining initial and local permutations efficiently to obtain the final circuit mapped to the given IBM QX architecture. Through experiments, improvements are observed over existing methods in terms of the number of gates and circuit depth. [ABSTRACT FROM AUTHOR]

The latest research indicates that quantum computers will be realized in the near future. In theory, the computation speed of a quantum computer is much faster than current computers, which will pose a serious threat to current cryptosystems. Post-quantum cryptography (PQC) is a class of cryptography based on underlying mathematical problems that are considered infeasible to crack even with access to a quantum computer. The supersingular isogeny Diffie–Hellman (SIDH) key exchange protocol is a new post-quantum cryptosystem, which offers advantages in reduced secret key length and attack resistance. SIDH is the basis of the supersingular isogeny key encapsulation (SIKE) protocol, which is in the second round of the U.S. National Institute of Standards and Technology (NIST) PQC standardization process. In this article, we propose a new modular multiplication algorithm and a new interleaved hardware architecture for SIDH. Performance results for the proposed modular multiplier using four parameter sets for the prime, p that correspond to the SIKE Round 2 parameter sets show significant advantages in speed. [ABSTRACT FROM AUTHOR]

Superconducting quantum computers (SQCs) can solve some specific problems which are deeply believed to be intractable for classical computers. One of the key components of SQCs is a high-precision synchronous control system which consists of arbitrary waveform generators (AWGs) and an array of digitizers. Here, we propose a scalable, self-adaptive, synchronous triggering system which allows the synchronization of dozens of qubits with jitters of around 3 ps. The system achieves better phase noise performance than the commercial instruments we tested. Using this scheme, we have successfully implemented the synchronous control and measurement of all the qubits on a 23-qubit quantum processor. [ABSTRACT FROM AUTHOR]

We advocate for a fundamentally different way to perform quantum computation by using three-level qutrits instead of qubits. In particular, we substantially reduce the resource requirements of quantum computations by exploiting a third state for temporary variables (ancilla) in quantum circuits. Past work with qutrits has demonstrated only constant factor improvements, owing to the log2(3) binary-to-ternary compression factor. We present a novel technique using qutrits to achieve a logarithmic runtime decomposition of the Generalized Toffoli gate using no ancilla---an exponential improvement over the best qubit-only equivalent. Our approach features a 70x improvement in total two-qudit gate count over the qubit-only decomposition. This results in improvements for important algorithms for arithmetic and QRAM. Simulation results under realistic noise models indicate over 90% mean reliability (fidelity) for our circuit, versus under 30% for the qubit-only baseline. These results suggest that qutrits offer a promising path toward extending the frontier of quantum computers. [ABSTRACT FROM AUTHOR]

Current quantum computers have very different qubit implementations, instruction sets, qubit connectivity, and noise characteristics. Using real-system evaluations on seven quantum systems from three leading vendors, our work explores fundamental design questions concerning hardware choices, architecture, and compilation. [ABSTRACT FROM AUTHOR]

Along with the resistance against quantum computers, isogeny-based cryptography offers attractive cryptosystems due to small key sizes and compatibility with the current elliptic curve primitives. While the state-of-the-art implementation uses Montgomery curves, which facilitates efficient elliptic curve arithmetic and isogeny computations, other forms of elliptic curves can be used to produce an efficient result. In this paper, we present the new hybrid method for isogeny-based cryptosystem using Edwards curves. Unlike the previous hybrid methods, we exploit Edwards curves for recovering the curve coefficients and Montgomery curves for other operations. To this end, we first carefully examine and compare the computational cost of Montgomery and Edwards isogenies. Then, we fine-tune and tailor Edwards isogenies in order to blend with Montgomery isogenies efficiently. Additionally, we present the implementation results of Supersingular Isogeny Diffie–Hellman (SIDH) key exchange using the proposed method. We demonstrate that our method outperforms the previously proposed hybrid method, and is as fast as Montgomery-only implementation. Our results show that proper use of Edwards curves for isogeny-based cryptosystem can be quite practical. [ABSTRACT FROM AUTHOR]

Recent progress in quantum physics shows that quantum computers may be a reality in the not too distant future. Post-quantum cryptography (PQC) refers to cryptographic schemes that are based on hard problems which are believed to be resistant to attacks from quantum computers. The supersingular isogeny Diffie-Hellman (SIDH) key exchange protocol shows promising security properties among various post-quantum cryptosystems that have been proposed. In this paper, we propose two efficient modular multiplication algorithms with special primes that can be used in SIDH key exchange protocol. Hardware architectures for the two proposed algorithms are also proposed. The hardware implementations are provided and compared with the original modular multiplication algorithm. The results show that the proposed finite field multiplier is over 6.79 times faster than the original multiplier in hardware. Moreover, the SIDH hardware/software codesign implementation using the proposed FFM2 hardware is over 31 percent faster than the best SIDH software implementation. [ABSTRACT FROM AUTHOR]

In the past years, quantum computers more and more have evolved from an academic idea to an upcoming reality. IBM’s project IBM ${Q}$ can be seen as evidence of this progress. Launched in March 2017 with the goal to provide access to quantum computers for a broad audience, this allowed users to conduct quantum experiments on a 5-qubit and, since June 2017, also on a 16-qubit quantum computer (called IBM QX2 and IBM QX3, respectively). Revised versions of these 5- and 16-qubit quantum computers (named IBM QX4 and IBM QX5, respectively) are available since September 2017. In order to use these, the desired quantum functionality (e.g., provided in terms of a quantum circuit) has to be properly mapped so that the underlying physical constraints are satisfied—a complex task. This demands solutions to automatically and efficiently conduct this mapping process. In this paper, we propose a methodology which addresses this problem, i.e., maps the given quantum functionality to a realization which satisfies all constraints given by the architecture and, at the same time, keeps the overhead in terms of additionally required quantum gates minimal. The proposed methodology is generic, can easily be configured for similar future architectures, and is fully integrated into IBM’s SDK. Experimental evaluations show that the proposed approach clearly outperforms IBM’s own mapping solution. In fact, for many quantum circuits, the proposed approach determines a mapping to the IBM architecture within minutes, while IBM’s solution suffers from long runtimes and runs into a timeout of 1 h in several cases. As an additional benefit, the proposed approach yields mapped circuits with smaller costs (i.e., fewer additional gates are required). All implementations of the proposed methodology are publicly available at http://iic.jku.at/eda/research/ibm_qx_mapping. [ABSTRACT FROM AUTHOR]

Being important parts of the superconducting quantum computer, the high-speed arbitrary waveform generator (AWG), ultraprecision dc source, and high-speed digitizer are used to manipulate the qubit. The complexity of an experimental setup increases rapidly as the number of qubits grows. Cumbersome instrument management, distortion of signals, and inefficiency of data transmission are gradually highlighted and become the bottlenecks in scaling up the number of qubits. In addition, fault-tolerant quantum computing has real-time feedback requirements of qubit states. To deal with these challenges, we propose an instrument management software design in this paper. The software maps the resources of separate instruments to a unified virtual instrument, achieving the scalability of the instruments. The processing and correction of signals are deployed on a server, which automatically corrects the distortion of the signals. By designing a multi-threaded mechanism for the AWG and a custom-defined data-link protocol for the digitizer, the efficiency of the software meets the requirements of experiments. Cooperating with the AWG and digitizer, the software provides the real-time feedback capability using an instruction compiler. Thus, the software meets the requirements of superconducting quantum computing, as demonstrated through its application to a 12-bit quantum experiment. [ABSTRACT FROM AUTHOR]