Introduction:

In quantum computing, quantum supremacy or quantum advantage is the goal of demonstrating that a programmable quantum computer can solve a problem that no classical computer can solve in any feasible amount of time, irrespective of the usefulness of the problem.[1][2][3] The term was coined by John Preskill in 2012,[1][4] but the concept dates to Yuri Manin's 1980[5] and Richard Feynman's 1981[6] proposals of quantum computing.
Conceptually, quantum supremacy involves both the engineering task of building a powerful quantum computer and the computational-complexity-theoretic task of finding a problem that can be solved by that quantum computer and has a superpolynomial speedup over the best known or possible classical algorithm for that task.[7][8]
Examples of proposals to demonstrate quantum supremacy include the boson sampling proposal of Aaronson and Arkhipov,[9] and sampling the output of random quantum circuits.[10][11] The output distributions that are obtained by making measurements in boson sampling or quantum random circuit sampling are flat, but structured in a way so that one cannot classically efficiently sample from a distribution that is close to the distribution generated by the quantum experiment. For this conclusion to be valid, only very mild assumptions in the theory of computational complexity have to be invoked. In this sense, quantum random sampling schemes can have the potential to show quantum supremacy.[12]
A notable property of quantum supremacy is that it can be feasibly achieved by near-term quantum computers,[4] since it does not require a quantum computer to perform any useful task[13] or use high-quality quantum error correction,[14] both of which are long-term goals.[2] Consequently, researchers view quantum supremacy as primarily a scientific goal, with relatively little immediate bearing on the future commercial viability of quantum computing.[2] Due to unpredictable possible improvements in classical computers and algorithms, quantum supremacy may be temporary or unstable, placing possible achievements under significant scrutiny.[15][16] In 1936, Alan Turing published his paper, “On Computable Numbers”,[17] in response to the 1900 Hilbert Problems. Turing's paper described what he called a “universal computing machine”, which later became known as a Turing machine. In 1980, Paul Benioff used Turing's paper to propose the theoretical feasibility of Quantum Computing. His paper, “The Computer as a Physical System: A Microscopic Quantum Mechanical Hamiltonian Model of Computers as Represented by Turing Machines“,[18] was the first to demonstrate that it is possible to show the reversible nature of quantum computing as long as the energy dissipated is arbitrarily small. In 1981, Richard Feynman showed that quantum mechanics could not be efficiently simulated on classical devices.[19] During a lecture, he delivered the famous quote, “Nature isn't classical, dammit, and if you want to make a simulation of nature, you'd better make it quantum mechanical, and by golly it's a wonderful problem, because it doesn't look so easy.”[19] Soon after this, David Deutsch produced a description for a quantum Turing machine and designed an algorithm created to run on a quantum computer.[20]
In 1994, further progress toward quantum supremacy was made when Peter Shor formulated Shor's algorithm, streamlining a method for factoring integers in polynomial time.[21] In 1995, Christopher Monroe and David Wineland published their paper, “Demonstration of a Fundamental Quantum Logic Gate”,[22] marking the first demonstration of a quantum logic gate, specifically the two-bit "controlled-NOT". In 1996, Lov Grover put into motion an interest in fabricating a quantum computer after publishing his algorithm, Grover's Algorithm, in his paper, “A fast quantum mechanical algorithm for database search”.[23] In 1998, Jonathan A. Jones and Michele Mosca published “Implementation of a Quantum Algorithm to Solve Deutsch's Problem on a Nuclear Magnetic Resonance Quantum Computer”,[24] marking the first demonstration of a quantum algorithm.

Quantum supremacy, once a staple of science fiction, is on the cusp of becoming reality. This article explores the current landscape of quantum computing, the pursuit of quantum supremacy, and its potential implications across industries.

Understanding Quantum Computing:

Quantum computing leverages the principles of quantum mechanics, employing quantum bits or qubits that can exist in multiple states simultaneously. Unlike classical bits, which are either 0 or 1, qubits utilize superposition and entanglement to perform computations at an unprecedented scale and speed.

The Quest for Quantum Supremacy:

Google's claim of achieving quantum supremacy in 2019 with its 53-qubit Sycamore processor marked a significant milestone. However, practical applications of quantum supremacy remain elusive due to challenges such as qubit stability and quantum decoherence, hindering the scalability of quantum systems.

Recent Advances and Research Efforts:

Despite the obstacles, the field of quantum computing is advancing rapidly. Major players like IBM, Microsoft, and Intel, alongside startups and research institutions, are heavily investing in quantum computing research. Breakthroughs in qubit stability, error correction, and quantum algorithms are driving progress toward achieving meaningful quantum supremacy.

Applications and Implications:

Quantum computing has the potential to revolutionize numerous industries. Quantum annealers, like those developed by D-Wave Systems, are already being employed to solve optimization problems in logistics, finance, and other fields. Moreover, quantum computing could transform cryptography, drug discovery, materials science, and artificial intelligence, unlocking unprecedented possibilities for innovation and discovery.

Challenges and Future Outlook:

While significant strides have been made, challenges such as scalability and error correction persist. However, ongoing research and collaborative efforts suggest that quantum supremacy is within reach. As advancements continue, quantum computing is poised to bridge the gap between fiction and reality, heralding a new era of computational power and potential.

Conclusion:

Quantum supremacy represents a monumental leap in computing capabilities, offering the promise of solving complex problems beyond the reach of classical computers. While hurdles remain, recent advancements and dedicated research efforts indicate that quantum supremacy is on the horizon. As we approach this milestone, the transformative impact of quantum computing on various industries stands to be profound, paving the way for unparalleled technological advancement and innovation.

References

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4. ^ Turing, Alan (1936). On Computable Numbers, With An Application To The Entscheidungsproblem.
5. ^ Benioff, Paul (1980-05-01). "The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines". Journal of Statistical Physics. 22 (5): 563–591. Bibcode:1980JSP....22..563B. doi:10.1007/BF01011339. ISSN 1572-9613. S2CID 122949592.
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8. ^ Shor, Peter (1996). Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer.
9. ^ Monroe, C.; Meekhof, D. M.; King, B. E.; Itano, W. M.; Wineland, D. J. (1995-12-18). "Demonstration of a Fundamental Quantum Logic Gate". Physical Review Letters. 75 (25): 4714–4717. Bibcode:1995PhRvL..75.4714M. doi:10.1103/PhysRevLett.75.4714. ISSN 0031-9007. PMID 10059979.
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11. ^ Jones, J. A.; Mosca, M. (August 1998). "Implementation of a Quantum Algorithm to Solve Deutsch's Problem on a Nuclear Magnetic Resonance Quantum Computer". The Journal of Chemical Physics. 109 (5): 1648–1653. arXiv:quant-ph/9801027. doi:10.1063/1.476739. ISSN 0021-9606. S2CID 19348964.
12. Hangleiter, Dominik; Eisert, Jens (2023-07-20). "Computational advantage of quantum random sampling". Reviews of Modern Physics. 95 (3): 035001. arXiv:2206.04079. Bibcode:2023RvMP...95c5001H. doi:10.1103/RevModPhys.95.035001. S2CID 249538723.
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14. ^ Aaronson, Scott (2019-10-30). "Opinion | Why Google's Quantum Supremacy Milestone Matters (Published 2019)". The New York Times. ISSN 0362-4331. Retrieved 2020-12-07.
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17. ^ Turing, Alan (1936). On Computable Numbers, With An Application To The Entscheidungsproblem.
18. ^ Benioff, Paul (1980-05-01). "The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines". Journal of Statistical Physics. 22 (5): 563–591. Bibcode:1980JSP....22..563B. doi:10.1007/BF01011339. ISSN 1572-9613. S2CID 122949592.
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21. ^ Shor, Peter (1996). Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer.
22. ^ Monroe, C.; Meekhof, D. M.; King, B. E.; Itano, W. M.; Wineland, D. J. (1995-12-18). "Demonstration of a Fundamental Quantum Logic Gate". Physical Review Letters. 75 (25): 4714–4717. Bibcode:1995PhRvL..75.4714M. doi:10.1103/PhysRevLett.75.4714. ISSN 0031-9007. PMID 10059979.
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24. ^ Jones, J. A.; Mosca, M. (August 1998). "Implementation of a Quantum Algorithm to Solve Deutsch's Problem on a Nuclear Magnetic Resonance Quantum Computer". The Journal of Chemical Physics. 109 (5): 1648–1653. arXiv:quant-ph/9801027. doi:10.1063/1.476739. ISSN 0021-9606. S2CID 19348964.
25.