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Trapped-ion (TI) quantum bits are a front-runner technology for quantum computing. TI systems with multiple interconnected traps can overcome the hardware connectivity issue inherent in superconducting qubits and can solve practical problems at scale. With a sufficient number of qubits on the horizon, the multi-programming model for Quantum Computers (QC) has been proposed where multiple users share the same QC for their computing. Multi-programming is enticing for quantum cloud providers as it can maximize device utilization, throughput, and profit for clouds. Users can also benefit from the short wait queue. However, shared access to quantum computers can create new security issues. This paper presents one such vulnerability in shared TI systems that require shuttle operations for communication among traps. Repeated shuttle operations increase quantum bit energy and degrade the reliability of computations (fidelity). We show adversarial program design approaches requiring numerous shuttles. We propose a random and systematic methodology for adversary program generation. Our analysis shows shuttle-exploiting attacks can substantially degrade the fidelities of victim programs by $\approx 2 \times $ to $\approx 63 \times $ . Finally, we present several countermeasures such as adopting a hybrid initial mapping policy, padding victim programs with dummy qubits, and capping maximum shuttles.

Quantum Computing is a technology, which promises to overcome the drawbacks of conventional CMOS technology for high density and high performance applications. Its potential to revolutionize today's computing world is attracting more and more researchers towards this field. However, due to the involvement of quantum properties, many beginners find it difficult to follow the field. Therefore, in this research note an effort has been made to introduce the various aspects of quantum computing to researchers, quantum engineers and scientists. The historical background and basic concepts necessary to understand quantum computation and information processing have been introduced in a lucid manner. Various physical implementations and potential application areas of quantum computation have also been discussed in this paper. Recent developments in each realization, in the context of the DiVincenzo criteria, including ion traps based quantum computing, superconducting quantum computing, nuclear magnetic resonance (NMR) quantum computing, spintronics and semiconductor based quantum computing have been discussed.

With the development of lab technology, the low-order correlation function can no longer describe the main effect of decoherence in the quantum many-body system, so it is imperative to study the higher-order correlation function of the system. In this paper, the higher-order correlation function is discussed analytically in the 1D transverse Ising model, and it is searched when the third-order or higher correlation functions play a key role in the decoherence effect. Under the cases of strong coupling and long coherence time, it is indicated that the effect of high-order correlation functions cannot be ignored, and the approximation of the classical Markov process is limited. But the low-order correlation function can describe well in the case of weak coupling and short coherence time. [ABSTRACT FROM AUTHOR]

Quantum key distribution(QKD) is one of the most significant areas in quantum information theory. For nearly four decades, substantial QKD schemes are developed. In early years, the security of QKD protocols is depend on switching different bases, namely based on non-orthogonal state encoding. The most famous example is the BB84 protocol. Later, other techniques were developed for orthogonal state encoding. Examples of such protocols include the GV protocol and order-rearrangement protocols. In this paper, we present two QKD protocols based on orthogonal state encoding. One of them does not need to employ order-rearrangement techniques while the other needs to. We provide analyses for them, demonstrating that they are highly efficient when considering consumptions of both qubits and classical bits. Furthermore, the employment of maximally entangled states could be less than previous ones and so the measurement efficiency could be increased. We also modify the protocols for implementing in noisy channels by applying the testing state method. [ABSTRACT FROM AUTHOR]

The lack of space inversion symmetry endows non-centrosymmetric superconducting materials with various interesting parity-breaking phenomena, including the anomalous Josephson effect. Our paper considers a Josephson junction of two non-centrosymmetric superconductors connected by a uniaxial ferromagnet. We show that this "Chiral Magnetic Josephson junction" (CMJ junction) exhibits a direct analog of the Chiral Magnetic Effect, which has already been observed in Weyl and Dirac semimetals. We suggest that the CMJ can serve as an element of a qubit with a Hamiltonian tunable by the ferromagnet's magnetization. The CMJ junction avoids using an offset magnetic flux in inductively shunted qubits, thus enabling a simpler and more robust architecture. Furthermore, when the uniaxial ferromagnet's easy axis is directed across the junction, the resulting "chiral magnetic qubit" provides robust protection from the noise caused by magnetization fluctuations. [ABSTRACT FROM AUTHOR]

Topological quantum error correction (TQEC) is promising for scalable fault-tolerant quantum computation. The required resource of a TQEC circuit can be modeled as its space-time volume of a three-dimensional geometric description. Implementing a quantum algorithm with a reasonable physical qubit number and computation time is challenging for large-scale complex problems. Therefore, it is desirable to minimize the space-time volume for large-scale TQEC circuits. Previous work proposed bridge compression, which can significantly compress a TQEC circuit, but it was performed manually. This article presents the first automated tool that can perform bridge compression on a large-scale TQEC circuit. Our proposed algorithm applies the bridge compression technique to compactify TQEC circuits with modularization. Besides, we offer a time-ordering-aware 2.5-D placement for compacting TQEC circuits and satisfying time-ordered measurement constraints. On the other hand, we suggest friend net-aware routing to effectively reduce the required routing resource under topological deformation. Compared with the state-of-the-art work, experimental results show that our proposed algorithm can averagely reduce space-time volumes by 84%. [ABSTRACT FROM AUTHOR]

Motivated by our recent work published in [23] , we achieve, in this paper, a matrix formulation of the density operator to construct a two-component vector coherent state representation for a supersymmetric harmonic oscillator. We investigate and discuss the main relevant statistical properties. We use the completeness relation to perform the thermodynamic analysis in the diagonal P-representation of the density operator. [ABSTRACT FROM AUTHOR]

We have determined conditions when a pair of coupled waveguides, a common element for integrated room-temperature photonics, can act as a qubit based on a system with a double-well potential. Moreover, we have used slow-varying amplitude approximation (SVA) for the "classical" wave equation to study the propagation of electromagnetic beams in a couple of dielectric waveguides both analytically and numerically. As a part of an extension of the optical-mechanical analogy, we have considered examples of "quantum operations" on the electromagnetic wave state in a pair of waveguides. Furthermore, we have provided examples of "quantum-mechanical" calculations of nonlinear transfer functions for the implementation of the considered element in optical neural networks. [ABSTRACT FROM AUTHOR]

In the last two decades, a lot of research has been done for finding the best physical implementation of a quantum computer. Due to integrablity with classical computation hardware and versatility in creating qubits and quantum gates, silicon quantum dot-based systems are one of the most promising systems. In this paper, we have modelled a universal Clifford set of single qubit quantum gates based on silicon quantum dots framework by using the Lindblad master equation, where electron spin resonance (ESR) has been employed for manipulation of qubit states. State spin probability evolution of each of the gates has been reported in presence of dephasing effect. Moreover, the density matrix approach and quantum process tomography of each of the single qubit gates has been investigated. Furthermore, it has been shown that by increasing the ac magnetic field, we can obtain a high-fidelity NOT gate for a considerably wider range of static magnetic fields. This provides us with greater control by considering both ac magnetic field as well static magnetic field. [ABSTRACT FROM AUTHOR]

It is commonly recognized that Landauer's bound holds in (irreversible) quantum measurement. In this study, we overturned this common sense by extracting a single spin from a spin–spin magnetic interaction experiment to demonstrate that Landauer's bound can be broken quantitatively by a factor of 10 4 ∼ 10 10 via quantum spin tunneling. It is the quantum limit ( ħ / 2 ≈ 10 - 34 J · s ), rather than Landauer's bound, that governs the performance of a spin qubit. An optically-manipulated spin-encoded quantum computer is designed, in which energy bound well below k B T to erase a spin qubit at the expense of a long spin relaxation time is theoretically sensible and experimentally verified. This work may represent the last piece of the puzzle in quantum Landauer erasure in terms of a single spin being the smallest and the closest to the quantum limit. [ABSTRACT FROM AUTHOR]

Remote entanglement distribution plays a crucial role in large-scale quantum networks, and the key enabler for entanglement distribution is quantum routers (or repeaters) that can extend the entanglement transmission distance. However, the performance of quantum routers is far from perfect yet. Amongst the causes, the limited quantum memories in quantum routers largely affect the rate and efficiency of entanglement distribution. To overcome this challenge, this paper presents a new modeling for the maximization of entanglement distribution rate (EDR) on a memory-limited path, which is then transformed into entanglement generation and swapping sub-problems. We propose a greedy algorithm for short-distance entanglement generation so that the quantum memories can be efficiently used. As for the entanglement swapping sub-problem, we model it using an Entanglement Graph (EG), whose solution is yet found to be at least NP-complete. In light of it, we propose a heuristic algorithm by dividing the original EG into several sub-problems, each of which can be solved using dynamic programming (DP) in polynomial time. By conducting simulations, the results show that our proposed scheme can achieve a high EDR, and the developed algorithm has a polynomial-time upper bound and reasonable average runtime complexity. [ABSTRACT FROM AUTHOR]

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There is a great deal of focus on how quantum computing as an accelerator differs from other traditional high-performance computing (HPC) resources, including accelerators like GPUs and field-programmable gate arrays. In classical computing, how to design the interfaces that connect the different layers of the software stack, from the applications and high-level programming language description, through compilers and schedulers, and down to the hardware and gate level, has been critical. Likewise, quantum computing's interfaces enable access to quantum technology as a viable accelerator. From the ideation of the quantum application to the manipulation of the quantum chip, each interface has its challenges. In this article, we discuss the structure of this set of quantum interfaces, their many similarities to the traditional HPC compilation stack, and how these interfaces impact the potential of quantum computers as HPC accelerators. [ABSTRACT FROM AUTHOR]

A scalable, non-multiplexed cryogenic 14-nm FinFET quantum bit (qubit) state controller (QSC) for use in the semi-autonomous control of superconducting transmon qubits is reported. The QSC includes an augmented general-purpose digital processor that supports waveform generation and phase rotation operations combined with a low-power current-mode single sideband upconversion ${I}/{Q}$ mixer-based RF arbitrary waveform generator (AWG). Implemented in the 14-nm CMOS FinFET technology, the QSC generates control signals in its target 4.5–5.5-GHz-frequency range, achieving an spurious free dynamic range (SFDR) > 50 dB for a signal bandwidth of 500 MHz. With the controller operating in the 4 K stage of a cryostat and connected to a transmon qubit in the cryostat’s millikelvin stage, measured transmon $T_{1}$ and $T_{2}$ coherence times were 75.7 and 73 $\mu \text{s}$ , respectively, in each case comparable to results achieved using conventional room temperature (RT) controls. In further tests with transmons, a qubit-limited error rate of 7.76 × 10−4 per Clifford gate is achieved, again comparable to the results achieved using RT controls. The QSC’s maximum RF output power is −18 dBm, and power dissipation per qubit under active control is 23 mW. [ABSTRACT FROM AUTHOR]

This article presents a cryo-CMOS quantum controller IC for superconducting qubits. The proposed globally synchronized clock system internally generates different local oscillator (LO) frequencies using multiple phase-locked loops (PLLs) driven by a common reference clock. It provides flexibility in spectral management as well as scalability for expansion to a large-scale quantum controller. The test chip includes two PLLs, four pulse modulator channels, and two receiver channels. Implemented chip in 40-nm CMOS shows full functionalities at 3.5 K. The designed pulse modulator circuits are verified with the specifications for expected fidelity of 99.99%. [ABSTRACT FROM AUTHOR]

Grover’s search algorithm allows a quantum adversary to find a $k$ k -bit secret key of a block cipher by making O($2^{k/2}$ 2 k / 2 ) block cipher queries. Resistance of a block cipher to such an attack is evaluated by quantum resources required to implement Grover’s oracle for the target cipher. The quantum resources are typically estimated by the $\textit {T}$ T -depth of its circuit implementation and the number of qubits used by the circuit (width). Since the AES S-box is the only component which requires $\textit {T}$ T -gates in a quantum implementation of AES, recent research has put its focus on efficient implementation of the AES S-box. However, any efficient implementation with low $\textit {T}$ T -depth will not be practical in the real world without considering qubit consumption of the implementation. In this work, we propose three methods of trade-off between time and space for the quantum implementation of the AES S-box. In particular, one of our methods turns out to use the smallest number of qubits among the existing methods, significantly reducing its $\textit {T}$ T -depth. [ABSTRACT FROM AUTHOR]

Quantum algorithms can be described as quantum circuits and are supposed to be carried out on an ideal quantum device that is far from current ones. The current quantum devices have a significant limitation on the connectivity between quantum bits. In other words, a quantum bit is only allowed to interact with its nearest neighbors (NNs). In reality, quantum bits have to be placed on a grid, where the connectivity between quantum bits is predefined. The predefined connectivity of a grid further determines the possible range of architectures of a quantum device after the placement of quantum bits. In this article, we propose to place quantum bits based on a 2-D hexagonal architecture rather than a 2-D Cartesian architecture. To validate the effectiveness, we leverage a workflow for mapping NN compliant quantum circuits onto targeting grids, where the workflow consists of a global reordering strategy and a local reordering strategy. With the advantages of the hexagonal grid, the overhead of making quantum circuits NN compliant is reduced significantly compared with the Cartesian grid. We also provide a comprehensive set of ablation analyses to gain a better understanding of the contributions of the components within our workflow. According to the experimental results, when changing the grid type from Cartesian to hexagonal, the global reordering strategy is crucial for small quantum circuits. In contrast, the local reordering strategy is more important than the global reordering strategy for large quantum circuits. [ABSTRACT FROM AUTHOR]

Nowadays, the classical Internet is mainly envisioned as the underlying communication infrastructure of the Quantum Internet, aimed at providing services such as signaling and coordination messages. However, the interplay between the classical and the quantum Internet is complex and its understanding is pivotal for an effective design of the Quantum Internet protocol stack. The aim of the article is to shed light on this interplay, by highlighting the fact that such an interplay is indeed bidirectional rather than unidirectional. The Quantum Internet exhibits the potential of supporting and even enhancing classical Internet functionalities. [ABSTRACT FROM AUTHOR]

Quantum entanglement brings high-speed and inherently privacy-preserving transmission for information communication in quantum networks. The qubit scarcity is an important issue that cannot be ignored in quantum networks due to the limited storage capacity of quantum devices, the short lifespan of qubits, and so on. In this article, we first formulate the qubit competition problem as the Cooperative-Qubit-Allocation-Problem (CQAP) by taking into account both the waiting time and the fidelity of end-to-end entanglement with the given transmission link set. We then model the CQAP as a Markov Decision Process (MDP) and adopt a Reinforcement Learning (RL) algorithm to self-adaptively and cooperatively allocate qubits among quantum repeaters. Further, we introduce an Active Learning (AL) algorithm to improve the efficiency of the RL algorithm by reducing its trial-error times. Simulation results demonstrate that our proposed algorithm outperforms the benchmark algorithms, with 23.5 ms reduction on the average waiting time and 19.2 improvement on the average path maturity degree, respectively. [ABSTRACT FROM AUTHOR]

In the coming years, quantum networks will allow quantum applications to thrive thanks to the new opportunities offered by end-to-end entanglement of qubits on remote hosts via quantum repeaters. On a geographical scale, this will lead to the dawn of the quantum internet. While a fullblown deployment is yet to come, the research community is already working on a variety of individual enabling technologies and solutions. In this article, with the guidance of extensive simulations, we take a broader view and investigate the problems of quality of service (QoS) and provisioning in the context of quantum networks, which are very different from their counterparts in classical data networks due to some of their fundamental properties. Our work leads the way toward a new class of studies that will allow the research community to better understand the challenges of quantum networks and their potential commercial exploitation. [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 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]

The quantum computer has been claimed to show more quantum advantage than the classical computer in solving some specific problems. Many companies and research institutes try to develop quantum computers with different physical implementations. Currently, most people only focus on the number of qubits in a quantum computer and consider it as a standard to evaluate the performance of the quantum computer intuitively. However, it is quite misleading in most times, especially for investors or governments. This is because the quantum computer works in a quite different way than classical computers. Thus, quantum benchmarking is of great importance. Currently, many quantum benchmarks are proposed from different aspects. In this paper, we review the existing performance benchmarking protocols, models, and metrics. We classify the benchmarking techniques into three categories: physical benchmarking, aggregative benchmarking, and application-level benchmarking. We also discuss the future trend for quantum computer's benchmarking and propose setting up the QTOP100. [ABSTRACT FROM AUTHOR]

The states of the qubit, the basic unit of quantum information, are 2 × 2 positive semi-definite Hermitian matrices with trace 1. We contribute to the program to axiomatize quantum mechanics by characterizing these states in terms of an entropic uncertainty principle formulated on an eight-point phase space. We do this by employing Rényi entropy (a generalization of Shannon entropy) suitably defined for the signed phase-space probability distributions that arise in representing quantum states. [ABSTRACT FROM AUTHOR]

Quantum systems with a finite number of states at all times have been a primary element of many physical models in nuclear and elementary particle physics, as well as in condensed matter physics. Today, however, due to a practical demand in the area of developing quantum technologies, a whole set of novel tasks for improving our understanding of the structure of finite-dimensional quantum systems has appeared. In the present article we will concentrate on one aspect of such studies related to the problem of explicit parameterization of state space of an NN-level quantum system. More precisely, we will discuss the problem of a practical description of the unitary SU(N){SU(N)}-invariant counterpart of the NN-level state space BN{\mathcal{B}_N}, i.e., the unitary orbit space BN/SU(N){B_N/SU(N)}. It will be demonstrated that the combination of well-known methods of the polynomial invariant theory and convex geometry provides useful parameterization for the elements of BN/SU(N){B_N/SU(N)}. To illustrate the general situation, a detailed description ofBN/SU(N){B_N/SU(N)} for low-level systems: qubit (N=2{N= 2}), qutrit (N=3{N=3}), quatrit (N=4{N= 4}) - will be given.

In this work, superposition of spin coherent states composed of two qubits is formed and by calculating the geometric measure of mixing of the system introduced in this work, the degree of mixedness of the studied state is investigated. In the following, the changes in the entanglement of the introduced state are studied by using the negativity measure. Finally, by drawing the appropriate plots, according to the influential parameters in this system, we examine the maximum and the minimum of the changes in the mixedness and entanglement and also their relationship to the mixed system consisting of two-qubit spin coherent states. It was observed that for maximizing α, when the changes of parameters indicate the purity of the state, the entanglement of the system reaches its maximum value for two-qubit systems. Also, for all values of coherence parameter, the entanglement decreases when mixedness of the system increases.

Psychology suffers from the absence of mathematically-formalized primitives. As a result, conceptual and quantitative studies lack an ontological basis that would situate them in the company of natural sciences. The article addresses this problem by describing a minimal psychic structure, expressed in the algebra of quantum theory. The structure is demarcated into categories of emotion and color, renowned as elementary psychological phenomena. This is achieved by means of quantum-theoretic qubit state space, isomorphic to emotion and color experiences both in meaning and math. In particular, colors are mapped to the qubit states through geometric affinity between the HSL-RGB color solids and the Bloch sphere, widely used in physics. The resulting correspondence aligns with the recent model of subjective experience, producing a unified spherical map of emotions and colors. This structure is identified as a semantic atom of natural thinking-a unit of affectively-colored personal meaning, involved in elementary acts of a binary decision. The model contributes to finding a unified ontology of both inert and living Nature, bridging previously disconnected fields of research. In particular, it enables theory-based coordination of emotion, decision, and cybernetic sciences, needed to achieve new levels of practical impact. [ABSTRACT FROM AUTHOR]

We study bifurcation behavior of a high-quality (high-Q) Josephson oscillator coupled to a superconducting qubit. It is shown that the probability of capture into the state of dynamic equilibrium is sensitive to qubit states. On this basis we present a new measurement method for the superposition state of a qubit due to its influence on transition probabilities between oscillator levels located in the energy region near the classical separatrix. The quantum-mechanical behavior of a bifurcation oscillator is also studied, which makes it possible to understand the mechanism of "entanglement" of oscillator and qubit states during the measurement process. The optimal parameters of the driving current and the state of the oscillator are found for performing one-qubit gates with the required precision, when the influence on the qubit from measurement back-action is minimal. A measurement protocol for state populations of the qubit entangled with the oscillator is presented. [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]

The cross fusion of quantum mechanics and information science forms quantum information science. Quantum logic gates and quantum entanglement are very important building blocks in quantum information processing. In this paper, we propose one-step schemes for realizing quantum swap gates and generating two-mode entangled coherent states via circuit QED. In our scheme, due to the adiabatic elimination of the excited state of the qutrit under the condition of large detuning, the decoherence of the spontaneous emission of the qutrit can be ignored. The fidelity of the quantum swap gate remains at a very high level. In addition, we also explore the nonclassical properties of two-mode entangled coherent states prepared in our scheme by addressing the second-order correlation function and intermodal squeezing. In particular, two classes of entangled coherent states demonstrate distinct entanglement and nonclassical behavior. [ABSTRACT FROM AUTHOR]

We define a formal framework for equivalence checking of sequential quantum circuits. The model we adopt is a quantum state machine, which is a natural quantum generalization of Mealy machines. A major difficulty in checking quantum circuits (but not present in checking classical circuits) is that the state spaces of quantum circuits are continuums. This difficulty is resolved by our main theorem showing that equivalence checking of two quantum Mealy machines can be done with input sequences that are taken from some chosen basis (which are finite) and have a length quadratic in the dimensions of the state Hilbert spaces of the machines. Based on this theoretical result, we develop an (and to the best of our knowledge, the first) algorithm for checking equivalence of sequential quantum circuits with running time $\mathcal {O}(2^{3m+5l}(2^{3m}{\,+\,}2^{3l}))$ , where $m$ and $l$ denote the numbers of input and internal qubits, respectively. The complexity of our algorithm is comparable with that of the known algorithms for checking classical sequential circuits in the sense that both are exponential in the number of (qu)bits. Several case studies and experiments are presented. [ABSTRACT FROM AUTHOR]