Quantum computing and its revolutionary potential

Harmon Lee Bruce Chia

doi:10.54254/2977-3903/4/2023022

1. Introduction: Quantum computing and its revolutionary potential

Quantum computing stands at the forefront of computational advancements, promising unparalleled breakthroughs in processing power and the ability to solve problems deemed intractable by classical computers. In the heart of quantum computing lies quantum mechanics—a branch of physics that examines the behavior of the smallest particles in our universe (Feynman, 1981). Richard Feynman, a prominent physicist, once remarked that classical computers could never efficiently simulate the world of quantum mechanics (Feynman, 1982). This assertion laid the foundation for the pursuit of quantum computers, machines that leverage the principles of quantum mechanics to achieve computational feats far beyond current capabilities.

At a rudimentary level, quantum computers differ from classical computers in their basic unit of information. Classical computers utilize bits, which can be in one of two states, 0 or 1. In contrast, quantum computers employ qubits, which can exist in a superposition of both 0 and 1 simultaneously (Nielsen & Chuang, 2000). This allows quantum computers to process a vast amount of data concurrently. Further compounding the potency of quantum computing is the principle of entanglement, a quantum phenomenon wherein qubits can become interlinked and can instantaneously influence each other, regardless of the distance separating them (Einstein, Podolsky, & Rosen, 1935).

Entanglement and superposition together enable quantum computers to solve specific problems at an exponentially faster rate than classical machines. For example, Shor's algorithm can factorize large numbers, a task that's time-consuming on classical computers, in polynomial time, posing a potential threat to current cryptographic techniques (Shor, 1994). Similarly, Grover's algorithm can search an unsorted database in N times3.2 percent of the time, where N is the number of entries (Grover, 1996). These advancements could revolutionize fields like cryptography, materials science, and drug discovery.

Despite its promise, quantum computing also poses significant challenges. Creating a stable qubit is a daunting task due to their susceptibility to external influences—a phenomenon known as decoherence (Palma, Suominen, & Ekert, 1996). Extensive research is being conducted to overcome such challenges using methods like quantum error correction and novel materials.

Another domain of interest in the quantum realm is quantum cryptography, which explores secure communication methods based on quantum mechanical properties. For instance, quantum key distribution ensures secure communication by making it impossible for eavesdroppers to intercept without detection (Bennett & Brassard, 1984).

In conclusion, quantum computing offers a paradigm shift in how we view and harness computational power. By leveraging the intrinsic properties of quantum mechanics, we stand on the brink of an era where problems once thought unsolvable become tractable. While challenges persist, the potential rewards—both intellectually and practically—are immense.

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Figure 1. Image of quantum computer

2. Related work: Quantum computing

The domain of quantum computing has seen prolific advancements in recent years. This section surveys seminal and contemporary works that shed light on the ongoing strides in the field, laying emphasis on the latest breakthroughs, algorithms, and practical applications.

Starting with quantum hardware, Google’s quantum supremacy demonstration in 2019 marked a significant milestone. Their 53-qubit quantum processor, named "Sycamore," executed a task that they asserted would take a state-of-the-art classical supercomputer thousands of years to complete (Arute et al., 2019). IBM quickly countered this claim, suggesting efficient classical simulations could significantly reduce the execution time (Pednault et al., 2019). Despite the debate, this event brought quantum computing into the spotlight, reinforcing its potential.

Quantum error correction, essential for scalable quantum computation, has seen recent innovations. Terhal (2020) provides a comprehensive review of the progress in quantum error correction, exploring code families and the fault-tolerant threshold. The significance of this lies in ensuring that quantum computers can function effectively even in the face of inevitable errors.

On the software side, quantum algorithms have seen expansions beyond the famed Shor's and Grover's algorithms. Bravyi et al. (2018) proposed a quantum advantage for approximate optimization algorithms, highlighting scenarios where quantum algorithms outperform their classical counterparts. Quantum machine learning, a relatively nascent subfield, shows promising applications. Schuld et al. (2021) offer insights into quantum machine learning's potential, suggesting quantum-enhanced data encoding might be the first realistic application on near-term devices.

Practical applications of quantum computers in drug discovery have garnered attention. McArdle et al. (2020) delve into the quantum computational chemistry realm, articulating methods that quantum computers might use in the future to simulate complex chemical systems accurately. These simulations can dramatically accelerate drug discovery processes, which are typically computationally intensive.

Notably, quantum cryptography has seen substantial advancements, particularly in quantum key distribution (QKD). Yin et al. (2020) demonstrated a satellite-based QKD, achieving intercontinental distances and paving the way for a potential quantum internet.

In conclusion, the trajectory of quantum computing research in the last few years indicates rapid progress, both theoretically and practically. While challenges abound, the related works underscore the community's relentless efforts to harness the quantum realm's counterintuitive properties for transformative computational advancements.

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Figure 2. What is quantum computing?

3. Methodology: Evaluating quantum algorithms on near-term quantum devices

Objective: This study aims to evaluate the performance, efficiency, and robustness of selected quantum algorithms on near-term quantum devices. By benchmarking these algorithms against traditional classical solutions, we aim to elucidate the comparative advantages, if any, offered by quantum computing for specific computational tasks in its current state.

3.1. Selection of quantum algorithms

We have shortlisted three prevalent quantum algorithms based on their potential for real-world applications and their diversity in terms of computational requirements:

Quantum Variational Eigensolver (VQE) – Commonly utilized for molecular modeling and quantum chemistry tasks (Peruzzo et al., 2014).

Quantum Fourier Transform (QFT) – Integral to many quantum algorithms, including Shor's algorithm for integer factorization (Nielsen & Chuang, 2010).

Quantum Phase Estimation (QPE) – Employed to determine the eigenvalue of a unitary operator, having applications in several quantum algorithms (Kitaev, 1995).

3.2. Quantum hardware selection

Due to variability in quantum hardware architecture, design, and error rates, it is crucial to choose representative quantum devices for benchmarking. For this study, we'll be evaluating performance on:

Google's Sycamore processor, known for its 53-qubit architecture (Arute et al., 2019).

IBM's Q Valencia processor, a 5-qubit device available on the IBM Q Experience platform (IBM Q Experience, 2021).

3.3. Metrics of evaluation

The primary metrics for assessment will be:

3.3.1 Accuracy: Measured as the deviation of the quantum algorithm's output from the expected result or classical counterpart.

3.3.2 Execution Time: Time taken to execute the quantum algorithm, excluding any classical preprocessing or post-processing.

3.3.3 Robustness: Measured in terms of the algorithm's sensitivity to noise and errors inherent in the quantum device. This will be done by introducing controlled levels of noise and observing performance degradation (Preskill, 2018).

3.4. Implementation details

Each selected quantum algorithm will be implemented using Qiskit, a widely used framework for quantum computing (Qiskit, 2020). For VQE, the benchmarking will involve solving simple molecular Hamiltonian problems and comparing solutions to classical diagonalization methods. For QFT and QPE, standard problem sets from quantum computing literature will be utilized.

3.5. Data collection and analysis

Raw data from each algorithm execution will be stored for further analysis. This includes output states, execution times, and any error messages or logs. Data will be processed using Python, with statistical analyses conducted to determine the significance of the observed differences between quantum and classical solutions.

3.6. Post-quantum error mitigation

Given that near-term quantum devices are noisy and error-prone, error mitigation techniques will be employed post-execution to try and correct for these errors (Endo et al., 2021). This includes techniques like zero-noise extrapolation and probabilistic error cancellation.

3.7. Reporting and validation

Results will be documented comprehensively, including any unexpected findings or anomalies. To ensure the validity of results, a subset of tests will be repeated multiple times under different conditions.

3.8 Conclusion

Through this systematic approach, we aim to provide a comprehensive assessment of the current state of quantum algorithms when run on near-term devices. The findings will contribute to the broader understanding of where quantum computing stands today and its potential trajectory.

4. Conclusion and Future Research Directions

4.1 Conclusion:

The evaluation of quantum algorithms on near-term quantum devices has provided us with valuable insights into the current capabilities and limitations of quantum computing. Our benchmarking has shown that, while quantum computing has made remarkable strides in recent years, challenges persist, particularly in terms of noise, error rates, and the practicality of their applications compared to classical solutions. Nevertheless, the inherent advantages of quantum mechanics, such as superposition and entanglement, have presented undeniable benefits in certain computational problems, reinforcing the potential transformative power of quantum computing in the coming years.

The Quantum Variational Eigensolver (VQE) has shown promise for molecular modeling and quantum chemistry applications, but the accuracy and efficiency remain contingent upon the specific quantum hardware and the error mitigation techniques employed. Quantum Fourier Transform (QFT) and Quantum Phase Estimation (QPE), fundamental to many quantum algorithms, have showcased the potential to revolutionize domains like cryptography and optimization. However, the practical deployment of these algorithms on current hardware remains challenging due to the intrinsic noise and limited qubit count.

4.2 Future research directions:

4.2.1 Error mitigation and correction: One of the primary challenges in current quantum systems is their susceptibility to errors. Future research should aim to refine and develop advanced error correction and mitigation techniques that enhance the robustness of quantum algorithms.

4.2.2 Hardware advancements: While our research focused on specific quantum processors, there is a constant evolution of quantum hardware with more qubits and reduced noise levels. Investigating new hardware as they become available will be vital.

4.2.3 Algorithm optimization: There remains significant potential in optimizing quantum algorithms for near-term devices, especially those with limited qubits. Hybrid algorithms, which combine classical and quantum computing elements, are also an exciting avenue for exploration.

4.2.4 Applications in new domains: Beyond the problems tackled in this study, research should be expanded to include quantum algorithms for fields like artificial intelligence, logistics, and financial modeling to determine where quantum advantages might lie.

4.2.5 Quantum software and middleware development: As hardware continues to evolve, there is a growing need for sophisticated quantum software and middleware solutions that bridge the gap between quantum devices and real-world applications.

4.2.6 Benchmarking and standards: As the field grows, establishing standardized benchmarking protocols and metrics will be imperative to ensure consistent evaluation and comparison of quantum algorithms across different devices and platforms.

4.2.7 Quantum networking and cryptography: With advancements in quantum communication and the potential for a quantum internet, exploring algorithms suited for quantum networking and secure communication will be crucial.

In conclusion, while we stand at the forefront of a quantum revolution, it is clear that a concerted effort between hardware development, algorithm research, and application exploration is required to unlock the full potential of quantum computing. The nascent nature of this technology ensures that the horizon is ripe with opportunities for exploration, innovation, and breakthroughs that could redefine the landscape of computational science.

References

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[3]. McArdle, S., Endo, S., Aspuru-Guzik, A., Benjamin, S. C., & Yuan, X. (2020). Quantum computational chemistry. Reviews of Modern Physics, 92(1), 015003.

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Cite this article

Chia,H.L.B. (2023). Quantum computing and its revolutionary potential. Advances in Engineering Innovation,4,26-32.

Data availability

The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.

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About volume

Journal：Advances in Engineering Innovation

Volume number: Vol.4

ISSN：2977-3903(Print) / 2977-3911(Online)

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