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Quantum Computing: A Taxonomy, Systematic Review and Future Directions

Sukhpal Singh Gill, Adarsh Kumar, Harvinder Singh, Manmeet Singh, Kamalpreet Kaur, Muhammad Usman, Rajkumar Buyya

arXiv:2010.15559v4cs.ETcs.DC

TL;DR

Quantum computing research faces major hardware challenges, especially qubit decoherence and unreliable operations. This paper systematically reviews the field, proposes a taxonomy, maps studies to research gaps, and surveys software, cryptography, hardware, challenges, and future directions.

  • Problem

    Quantum computing must overcome qubit decoherence, environmental noise, and error accumulation to achieve reliable large-scale computation and practical quantum advantage.

  • Method

    The paper systematically reviews quantum-computing literature, develops a taxonomy, maps related studies to research gaps, and surveys software, cryptography, and hardware.

  • Results

    The review identifies research gaps, discusses current quantum software, post-quantum cryptography, and industrial hardware, and proposes open challenges and future directions.

  • Takeaways & Limitations

    Post-quantum cryptography can improve the computational efficiency and security of many future applications.

  • Takeaways & Limitations

    Quantum technology remains fragile because qubits have short coherence times and quantum operations have relatively large error rates.

Abstract

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Quantum computing is an emerging paradigm with the potential to offer significant computational advantage over conventional classical computing by exploiting quantum-mechanical principles such as entanglement and superposition. It is anticipated that this computational advantage of quantum computing will help to solve many complex and computationally intractable problems in several areas such as drug design, data science, clean energy, finance, industrial chemical development, secure communications, and quantum chemistry. In recent years, tremendous progress in both quantum hardware development and quantum software/algorithm have brought quantum computing much closer to reality. Indeed, the demonstration of quantum supremacy marks a significant milestone in the Noisy Intermediate Scale Quantum (NISQ) era - the next logical step being the quantum advantage whereby quantum computers solve a real-world problem much more efficiently than classical computing. As the quantum devices are expected to steadily scale up in the next few years, quantum decoherence and qubit interconnectivity are two of the major challenges to achieve quantum advantage in the NISQ era. Quantum computing is a highly topical and fast-moving field of research with significant ongoing progress in all facets. This article presents a comprehensive review of quantum computing literature, and taxonomy of quantum computing. Further, the proposed taxonomy is used to map various related studies to identify the research gaps. A detailed overview of quantum software tools and technologies, post-quantum cryptography and quantum computer hardware development to document the current state-of-the-art in the respective areas. We finish the article by highlighting various open challenges and promising future directions for research.

1. INTRODUCTION

Quantum computing uses qubits, superposition, and entanglement to access large computational spaces with potential advantages across complex applications. Despite rapid progress and quantum supremacy, decoherence, scaling, and data-loading challenges continue to limit practical quantum advantage, motivating a comprehensive review of current technologies and future directions.

  • Applications: Quantum computing has potential applications in drug design, data science, clean energy, finance, secure communications, industrial chemistry, and quantum chemistry.The paper describes quantum computing as an emerging paradigm intended to address complex and computationally intractable problems across these areas.
  • Quantum computing foundations: Qubits can occupy ‘0’, ‘1’, or superpositions of both, enabling quantum computers to access exponentially large computational spaces.A qubit can be represented as a|0⟩+ b|1⟩, while multiple qubits can superpose many classical states.
  • Challenges: Decoherence causes qubits to lose coherent properties through environmental interactions, reducing the potential for quantum advantage in NISQ systems.The paper identifies qubit decoherence and interconnectivity as major challenges for achieving quantum advantage while devices scale.
  • Progress toward quantum advantage: Google’s demonstration of quantum supremacy marked a significant milestone, while researchers continue pursuing quantum advantage on useful real-world problems.Quantum advantage is defined in the passage as solving a problem that is intractable on classical computers more efficiently.
  • Article scope: The article reviews quantum computing literature and taxonomy, maps studies to research gaps, and surveys software, cryptography, hardware, open challenges, and future directions.It presents a comprehensive and timely report on progress across hardware, software and algorithms, NISQ error correction, applications, and post-quantum cryptography.

2. BUILDING BLOCKS

Quantum computing is grounded in quantum-mechanical principles and relies on interconnected building blocks including processing, gates, control and measurement, error correction, and memory. These components execute reversible operations, store quantum states, manage computation, monitor manipulations, and protect information from noise and decoherence.

  • Foundational principles: Quantum-mechanical principles, including interference, no-cloning, entanglement, and superposition, underpin quantum computing and motivate anticipated speed-ups over traditional techniques.The section presents these concepts as foundational technologies for addressing computationally challenging problems.
  • System components: A large-scale quantum computer comprises a quantum processing unit, quantum gates, control and measurement circuitry, error detection and correction tools, and quantum memories.These are identified as the basic building blocks of quantum computers.
  • Quantum gates: Quantum gates perform unitary, reversible operations using qubits within quantum circuits.Examples include Pauli, phase-shifter, Hadamard, controlled, rotation, swap, and Toffoli gates.
  • Quantum memory: Quantum memories use quantum registers to store multiple superposed quantum states containing computational information such as qubits and qutrits.The section notes that stable quantum systems have been realized using arrays of quantum states.
  • Quantum processing unit: The QPU stores computation as a quantum-mechanical state and communicates with other units through a quantum bus.Its operation differs significantly from that of a conventional CPU because it follows quantum-mechanical principles.
  • Control, measurement, and error correction: Control and measurement circuitry monitors quantum-state manipulations and computations while supporting error detection and correction.Error-correction tools locate and correct gate-operation errors caused by quantum noise and decoherence, using ancilla qubits without disturbing data-qubit information.

3. TAXONOMY

The taxonomy classifies quantum computing technologies by basic, algorithmic, time and gate, and other characteristics. It also describes qubit representation, parallelism, qubit counts, topologies, decoherence time, and measurement time.

  • Taxonomy structure: The taxonomy organizes quantum computing technologies into basic, algorithmic, time and gate, and other characteristics.Figure 5 provides a diagrammatic representation, followed by brief descriptions of each element.
  • Basic Characteristics: Basic characteristics cover qubit implementation, quantum-computing technology classification, and performance metrics.Qubits may be represented in stationary, flying, or mobile ways; stationary representation resembles traditional programming, while mobile representation resembles conventional circuit design.
  • Basic Characteristics: Parallelism supports parallel quantum-gate implementation to prevent or minimize qubit decoherence, while aggregate qubit count informs reliability and scalability.Physical-device arrangements define computer topologies, and architecture optimization is identified as a primary concern.
  • Time and Gate Characteristics: Time and gate characteristics include decoherence time, measurement time, and related timing and control considerations.Decoherence time is the duration a qubit can remain in a specific state, whereas measurement time is the time required for measurement.

4. QUANTUM SOFTWARE TOOLS, TECHNOLOGIES AND PRACTICES

Quantum software development is newer and less established than quantum hardware and simulation, but tools are rapidly proliferating across major platforms. The section surveys available tools and software-engineering practices spanning programming languages, compilation, scheduling, error correction, device control, annealing, and software quality.

  • Quantum Software Tools and Technologies: Quantum software tools are developing rapidly across platforms including Google, IBM, Microsoft, and D-Wave, although many remain at relatively low, assembly-like levels.The comparative analysis covers libraries, toolkits, openness, licensing, interfaces, simulation, real implementation, algorithm support, scheduling, and diagram or matrix support.
  • Software Engineering Practices: Recent studies identify software applications including quantum programming languages, compilers, logical- and physical-level schedulers and optimizers, error-correction firmware, and device-control firmware.These applications collectively address programming, compilation, scheduling, optimization, hardware-error mitigation, and quantum-device operation.
  • Quantum Programming Languages: Quantum programming-language research examines designs, semantics, compilation, commuting, controlled and adjoint operations, and clean and borrowed qubits.These topics are presented as important aspects of the quantum programming-language domain.
  • Compilers, Schedulers, and Optimizers: Quantum compilation studies cover static and dynamic compilation, classical co-processing, automated gate compilation, gate-level instructions, and compilation time, while logical scheduling supports fault-tolerant architectures.Logical processors may receive logical quantum operations alongside control flows and qubit operations; physical optimization targets latency, performance, allocation, and resource sharing.
  • Error Correction and Device Control: Quantum error-correction firmware integrates algorithms with imperfect hardware, while device-control firmware is expected to support advanced control, optimization, and appropriate physical schedules.Error-correction software operates at the lowest stack level to reduce errors from imperfect hardware, complexity, and resource intensity.
  • Quantum Annealing and Software Engineering: Quantum annealing is used to identify global minima and has been applied to stress reduction, pseudo-random functions, and cybersecurity-data analysis, while quantum software engineering addresses development processes and quality attributes.Quantum software engineering includes programming, tools, modeling, implementation, life cycles, processes, and quality attributes.

5. QUANTUM AND POST-QUANTUM CRYPTOGRAPHY

Quantum cryptography applies quantum mechanics at the physical network layer, whereas post-quantum cryptography uses mathematical techniques based on hard arithmetic problems. The section reviews QKD security, emerging quantum communication applications, and challenges spanning security, hardware, performance, cost, and quantum-related design.

  • Foundations: Quantum cryptography applies quantum mechanics to cryptography at the physical network layer, while post-quantum cryptography uses mathematical techniques based on hard arithmetic problems.Post-quantum cryptosystems also consider challenges from quantum adversaries and features such as no-cloning.
  • Quantum Key Distribution: Quantum cryptography is considered secure with unlimited quantum key length, and QKD is based on the one-time pad.The one-time pad is identified as an example of an unlimited-key-length cryptosystem.
  • Quantum Key Distribution: Quantum drones and quantum satellites are being explored to share keys and establish multimedia communications.These approaches are presented as examples of ways to support secure QKD.
  • Challenges: Quantum cryptography must address efficient encryption and decryption, reduced traffic, high bandwidth, and secure quantum-network operations.The cited requirements include time-efficient mechanisms for each quantum network entity and reduced encryption, decryption, or signature traffic.
  • Challenges: Quantum cryptography challenges are categorized into security attacks and challenges, hardware challenges, performance and cost-related challenges, and quantum-related design challenges.The categories cover attack feasibility, experimentation and performance issues, and design concerns in quantum systems.

5.1 QUANTUM KEY DISTRIBUTION (QKD)

QKD protects information security through quantum-mechanical principles, including the no-cloning theorem, which prevents perfect copying of quantum states. The review covers discrete- and continuous-variable approaches and protocols including COW, DPS, six-state, and decoy-state QKD.

  • QKD foundations: QKD protects information security against attacks that exploit computational limitations in traditional cryptography-based key distribution, supported by the no-cloning theorem.The theorem states that a perfect copy of a quantum system or its states cannot be made.
  • QKD approaches: QKD can use discrete or continuous variables, with non-Gaussian CV-QKD extended through discrete modulation to increase secret key rates and support long-range repeaters.The approach supports discrete-modulation CV-QKD over CV quantum repeaters and long-range systems.
  • COW QKD: COW-QKD encodes logical bits in sequences of weak coherent pulses, while practical mechanisms aim to increase bit rates and reduce interference visibility.Unconditional security proofs remain challenging for protocols using asymmetric coherent signals rather than qubits.
  • DPS QKD: DPS-QKD sends a highly attenuated phase-shifted coherent pulse with a one-bit receiver delay, and recent work emphasizes side-channel attacks.The protocol is described as simple and efficient, with several studied variations.
  • Six-state and decoy-state QKD: 21.6% tolerance level is observed for four-dimensional qubits using one-way classical communication with passive basis selection in decoy, achieving security equivalent to six-state QKD.The six-state protocol tolerates noisier channels and detects higher error rates during eavesdropping, while decoy-state QKD constrains single-photon gains and error rates.

5.2 POST-QUANTUM CRYPTOGRAPHY

Post-quantum cryptography develops primitives and protocols intended to resist quantum attacks that threaten classical schemes based on factorization and discrete logarithms. The section surveys lattice-, code-, multivariate-, isogeny-, and hybrid-based approaches, emphasizing their hardness assumptions, security properties, and implementation challenges.

  • Foundations: Post-quantum cryptography comprises primitives and protocols designed to remain secure against quantum-computer attacks.Existing cryptographic systems rely on integer factorization, discrete logarithms, and elliptic-curve discrete logarithms, which quantum computers could theoretically solve.
  • Lattice-based cryptography: Lattice-based cryptography derives security from computationally hard lattice problems, but worst-case solution recovery and standardization remain concerns.Worst-case-to-average-case reductions and structured ideal lattices are discussed as security-enhancing approaches requiring further assessment.
  • Code-based cryptography: Code-based cryptography relies on hard syndrome decoding, offering fast McEliece encryption and decryption but requiring large keys and resisting fault- and disclosure-based attacks.Its security analysis also considers Grover or quantum-walk complexity and the hardness of distinguishing a code from a pseudorandom code.
  • Multivariate cryptography: Multivariate cryptosystems base efficiency on the difficulty of solving quadratic equations over a field and include mature signature, encryption, and public-key variants.Examples include Rainbow, TTS, TRMS, GeMSS, LUOV, MQDSS, Oil and Vinegar, HFE, and related schemes.
  • Isogeny and hybrid cryptography: Isogeny-based schemes rely on the difficulty of computing supersingular endomorphism rings, while hybrid schemes integrate post-quantum mechanisms into key exchange and authentication.Isogeny protocols include signature/encryption, key exchange, and hash functions; hybrid deployment depends on communication standards and infrastructure availability.

6. SCALABLE QUANTUM COMPUTER HARDWARE

Scalable quantum-computer hardware is being pursued through analog and digital architectures, but decoherence and noise remain central barriers to reliable, error-free computation. Trapped-ion and superconducting systems currently support cloud-accessible machines, while other material systems, including silicon, require further development for scalability.

  • Analog and digital architectures are the two main approaches to physically implementing quantum computers.
  • Decoherence and noise cause computational errors, suppress quantum advantage, and make quantum error correction essential for industrial systems.Even error rates below 1% can accumulate detrimentally across the circuit depths needed for real-world problems.
  • Large-scale efforts involving academic and government-affiliated laboratories, corporations, and startups are developing qubits, gates, control circuitry, cooling systems, and user interfaces for industrial quantum computers.
  • Five major candidate material systems are evaluated using performance metrics, with trapped-ion and superconducting qubits underpinning current cloud-accessible quantum machines.The other three systems remain under intense research and require significant further development before becoming available for quantum computing.
  • Silicon-based quantum computers are predicted to support scalability with error-correction schemes, and recent advances in silicon spin-qubit design reinforce their candidacy.

7. FUTURE DIRECTIONS · 7.1 ENGINEERING/DESIGN CHALLENGES · 7.2 RELIABLE QUANTUM COMPUTING

The paper identifies future research areas across three maturity horizons and highlights fragility, fault tolerance, fabrication, testing, and error correction as central challenges for reliable quantum computing. It also points to AI- and ML-based dynamic error detection and correction as a potential reliability improvement with added system complexity.

  • 7. FUTURE DIRECTIONS: Research priorities are organized across three maturity levels: 5 years, 5 to 10 years, and more than ten years.These areas are presented as a quantum-computing hype cycle.
  • 7. FUTURE DIRECTIONS: Post-quantum cryptography is identified as being at the peak of the quantum-computing hype cycle.The passage also notes substantial research on simulations for complex quantum experiments.
  • 7.1 ENGINEERING/DESIGN CHALLENGES: Quantum technology is fragile because superconducting qubits have short coherence times and quantum operations have relatively large error rates.Superconducting qubits can forget their information in nanoseconds, while material faults and environmental instabilities can also cause errors.
  • 7.2 RELIABLE QUANTUM COMPUTING: Practical fault-tolerant quantum computation remains difficult because implementing quantum error correction is still an open problem.Quantum states require operation at very low temperatures, and fabrication must be highly accurate.
  • 7.2 RELIABLE QUANTUM COMPUTING: Qubits are difficult to test after fabrication because tolerances are tight, and incorrectly placed qubits must be avoided to reduce errors.The passage emphasizes fabrication and post-fabrication testing constraints.
  • 7.2 RELIABLE QUANTUM COMPUTING: Recursive error correction is needed to attain adequate fault tolerance and enable sustainable quantum computation.The passage presents recursive correction as necessary for sufficient fault tolerance.
  • 7.2 RELIABLE QUANTUM COMPUTING: AI- and ML-based techniques may dynamically detect and correct errors, improving reliability while increasing system complexity.The passage describes this trade-off as a future direction for delivering valuable and reliable service.

7.3 QUANTUM-ASSISTED MACHINE LEARNING

Quantum-assisted machine learning applies quantum technology to improve the scalability and efficiency of machine-learning algorithms for large datasets. Tensor-network perspectives support workflow exploration and resource management, potentially reducing noise effects on quantum-hardware performance.

  • Machine-learning researchers routinely use principal component analysis, vector quantization, Gaussian models, regression, and classification.
  • Quantum technology can improve the scalability and efficiency of machine-learning algorithms for large datasets using devices with 100–1000 qubits.
  • Tensor-network perspectives can be used to explore quantum-assisted machine-learning workflows and develop innovative models for quantum-computer resource management.
  • Effective resource management can reduce the impact of noise fluctuations on quantum-hardware performance.

7.4 ENERGY MANAGEMENT · 7.5 QUANTUM INTERNET · 7.6 ROBOTICS

The paper identifies energy efficiency as a potential advantage of quantum computing, while presenting quantum Internet and robotics as promising applications constrained by distinctive technical challenges. Quantum computing may support distributed computation, intensive robotic tasks, graph-based reasoning, and robotic kinematics.

  • 7.4 ENERGY MANAGEMENT: Quantum computers are expected to execute particular tasks more energy-efficiently than supercomputers and cloud data centres.Lower energy use could reduce computational cost and carbon emissions.
  • 7.5 QUANTUM INTERNET: Quantum Internet could enable distributed quantum computing through new communications and substantially improved computing capabilities.Its network design must address teleportation, entanglement, quantum measurement, and no-cloning.
  • 7.5 QUANTUM INTERNET: Quantum Internet network design is constrained by teleportation, entanglement, quantum measurement, and no-cloning.These constraints arise because quantum Internet uses quantum-mechanical laws.
  • 7.6 ROBOTICS: Quantum computing can augment robots performing intensive tasks such as drug discovery, logistics, cryptography, and finance.Quantum-powered robots may also access cloud-based quantum computing services.
  • 7.6 ROBOTICS: Quantum computing can enhance robotic senses for manufacturing, including identification of several features.The supplied passage indicates this application but truncates the specific features being identified.
  • 7.6 ROBOTICS: Quantum random walks can reduce the complexity of graph-search problems as data volume increases.Artificial-intelligence-based robotics use graph search to deduce new information, but complexity grows with increasing data.
  • 7.6 ROBOTICS: Quantum neural networks may address robotic kinematics by enhancing machine activity and recognizing joint friction and inertia.The passage frames kinematics as a problem involving the mechanical movement of robotics.

7.7 SIMULATIONS FOR COMPLEX QUANTUM EXPERIMENTS · 7.8 POST-QUANTUM CRYPTOGRAPHY

Quantum simulators may enable small-scale studies of complex chemistry, physics, and biology problems that are difficult for classical systems. Post-quantum cryptography aims to protect communications and implanted medical devices against attacks enabled by large quantum computers.

  • 7.7 SIMULATIONS FOR COMPLEX QUANTUM EXPERIMENTS: 50-100 qubit quantum simulators could become available in coming years for simulating complex chemistry, physics, and biology problems.These small-scale devices are presented as tools for realizing natural systems and addressing problems difficult to solve classically.
  • 7.7 SIMULATIONS FOR COMPLEX QUANTUM EXPERIMENTS: Quantum simulators can realize natural systems while solving complex problems that are difficult to solve on classical systems.The passage connects simulation capabilities with studying complex scientific systems.
  • 7.7 SIMULATIONS FOR COMPLEX QUANTUM EXPERIMENTS: Understanding quantum technology requires collaboration among researchers from an extensive range of fields and expertise in classical computing.The passage emphasizes combining broad research expertise with fundamental classical-computing knowledge.
  • 7.8 POST-QUANTUM CRYPTOGRAPHY: Cryptography must improve security for implanted medical devices, care systems, and online communication.The passage identifies these applications as requiring stronger cryptographic protection.
  • 7.8 POST-QUANTUM CRYPTOGRAPHY: Widely used cryptosystems are expected to be damaged once large quantum computers come into existence.This motivates the development of cryptographic systems designed for the quantum-computing threat model.
  • 7.8 POST-QUANTUM CRYPTOGRAPHY: Post-quantum cryptography denotes cryptographic algorithms, generally public-key algorithms, designed to remain secure against attackers using large quantum computers.Its security assumption explicitly includes a quantum-computer attacker.

7.9 NUMERICAL WEATHER PREDICTION · 7.10 QUANTUM CLOUD COMPUTING AND CRYPTOGRAPHY

Numerical weather prediction has advanced through improved classical hardware and software but remains constrained by bit-based computation and the need for further upgrades. Quantum cloud computing could support real-life applications by providing remote access to powerful quantum-computer nodes through quantum links, including experimentally demonstrated blind quantum computing efforts.

  • 7.9 NUMERICAL WEATHER PREDICTION: Classical computing advances have substantially improved weather-forecasting capabilities since the 1950s.These developments were propelled by hardware and software improvements.
  • 7.9 NUMERICAL WEATHER PREDICTION: Supercomputers are assembled from classical computers to perform the colossal calculations required for weather forecasting.They generate forecasts for the atmosphere, ocean, land, and other Earth-system components.
  • 7.9 NUMERICAL WEATHER PREDICTION: State-of-the-art weather predictions still require substantial upgrades for societal applications.The passage presents this need despite improvements over time.
  • 7.10 QUANTUM CLOUD COMPUTING AND CRYPTOGRAPHY: Unconditionally secure quantum cloud computing could become important for real-life applications if powerful quantum computers become widely available.Its feasibility is framed as contingent on future availability of powerful quantum computers.
  • 7.10 QUANTUM CLOUD COMPUTING AND CRYPTOGRAPHY: A few powerful quantum-computer nodes in a cloud could simplify clients’ computational work.Clients would communicate with quantum clouds through a quantum link to transfer jobs and associated qubits.
  • 7.10 QUANTUM CLOUD COMPUTING AND CRYPTOGRAPHY: Research has experimentally demonstrated blind quantum computing as part of efforts toward quantum cloud computing.The passage introduces blind quantum computing as an experimental direction after describing quantum-link communication.

8. SUMMARY AND CONCLUSIONS · Appendix A: List of Abbreviations

The paper reviews quantum computing literature, proposes a taxonomy to identify research gaps, and discusses quantum software, post-quantum cryptography, and industrial quantum computers. It concludes that quantum computing remains constrained by scalability, control overhead, error correction, and uncertainty about replacing classical supercomputers.

  • 8. SUMMARY AND CONCLUSIONS: The study systematically reviews quantum computing literature and maps a proposed taxonomy to related studies to identify research gaps.It also discusses quantum software tools and technologies, post-quantum cryptography, and industrial quantum computers.
  • 8. SUMMARY AND CONCLUSIONS: Entanglement and superposition are identified as quantum-mechanical phenomena expected to support solutions to computational problems.
  • 8. SUMMARY AND CONCLUSIONS: Post-quantum cryptography is presented as improving computational efficiency and security for futuristic applications.The discussion addresses securing classical cryptographic primitives and protocols against quantum computers.
  • 8. SUMMARY AND CONCLUSIONS: Present-day industrial quantum computers cannot yet replace classical supercomputers because practically realizable qubit numbers remain difficult to scale.The timing of such replacement remains an open question despite expectations of an exciting next decade.
  • 8. SUMMARY AND CONCLUSIONS: Efficient quantum-algorithm execution requires many physical qubits and close, continuous classical-platform-to-quantum-chip connectivity, creating substantial control overhead.
  • 8. SUMMARY AND CONCLUSIONS: Fault-tolerant and reliable quantum computation remains challenging because quantum error correction is still an open problem.The fragile nature of quantum states also requires operating bits at very low temperatures.
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