At our current technological pace, it's become increasingly hard to make more compact classical computers. Proceeding with this as one of the motivations for developing quantum computers, recent years have seen a surge in interest and therefore investment in the field with aims to surpass the capabilities of its classical counterpart. The term quantum supremacy, although it gets thrown around quite often, is a very intricate concept. Assessing all its parts to establish a robust definition and foundational ground rules is crucial as we go further. Theoretically discussed wonders that can be achieved by quantum computer sounds promising-from the rapid acceleration in the development of artificial intelligence and cryptography to quantum chemistry and modelling chemical reactions. But how far do we need to go for it to become a reality? Are we there yet? All these questions arise as there have been claims of quantum supremacy which are contentious at the least. A major reason for worry is the intractability of quantum computers that makes sceptics wonder if it's a pursuit equivalent to chasing the wind. Quantum computers will not make classical computers obsolete is another view point which does hold water as quantum computers seem to be useful only in solving specific problems. Even though the endeavour for quantum supremacy is still ongoing, companies have also gravitated towards Quantum advantage. This paper lays out an idiosyncratic view of what we can achieve and what we already have.
At our current technological pace, it's become increasingly hard to make more compact classical computers. Proceeding with this as one of the motivations for developing quantum computers, recent years have seen a surge in interest and therefore investment in the field with aims to surpass the capabilities of its classical counterpart. The term quantum supremacy, although it gets thrown around quite often, is a very intricate concept. Assessing all its parts to establish a robust definition and foundational ground rules is crucial as we go further. Theoretically discussed wonders that can be achieved by quantum computer sounds promising-from the rapid acceleration in the development of artificial intelligence and cryptography to quantum chemistry and modelling chemical reactions. But how far do we need to go for it to become a reality? Are we there yet? All these questions arise as there have been claims of quantum supremacy which are contentious at the least. A major reason for worry is the intractability of quantum computers that makes sceptics wonder if it's a pursuit equivalent to chasing the wind. Quantum computers will not make classical computers obsolete is another view point which does hold water as quantum computers seem to be useful only in solving specific problems. Even though the endeavour for quantum supremacy is still ongoing, companies have also gravitated towards Quantum advantage. This paper lays out an idiosyncratic view of what we can achieve and what we already have.
Quantum computing represents a paradigm shift in computation, leveraging the principles of quantum mechanics to solve problems deemed intractable for classical computers. This paper traces the evolution of quantum computing from theoretical foundations to recent technological milestones. It highlights key developments such as quantum algorithms, error correction, and qubit technologies. The paper also examines quantum supremacy, current quantum hardware implementations, and the potential disruption in cryptography, materials science, and artificial intelligence. Despite significant challenges in stability, scalability, and noise, quantum computing is on a trajectory to redefine computational boundaries. Future research directions and policy implications are also discussed.
Quantum computation was envisioned by Feynman as a valuable means of solving quantum problems [1]. The question is, how do we prove the superiority of quantum computing over classical devices? A common misconception in describing the power of a quantum computer over a classical computer is that quantum bits can be prepared in a superposition of an exponential number of states, which cannot be achieved with classical bits. This statement is certainly true, but it does not tell us, specifically, what problems quantum computers can efficiently solve while classical computers fail to do so. In fact, based exactly on the technique of Feynman's path integral, the output (i.e. transition amplitude) of any quantum circuit can be calculated classically with a polynomial amount of memory (although the temporal cost would be exponential). Therefore any quantum computation can be simulated classically; the key question is about the efficiency. Much effort has been made trying to pin down the power of quantum computers based on the machinery of the computational complexity theory. In particular, the class of computational (decision) problems that can be solved efficiently by a quantum computer is called BQP (bounded-error quantum polynomial time); the counterpart for classical computers is called P (polynomial time). Of course, BQP cannot be less than P; in principle quantum computers can simulate classical computers efficiently. The point is that the foundation of quantum computation cannot be established without a proof showing that BQP is strictly larger than P (i.e. BQP ≠ P). In this sense, this question is as interesting as the famous challenge of proving P ≠ NP (non-deterministic polynomial time). A well known instance of an NP problem is the factoring problem; Shor's quantum algorithm is capable of solving the factoring problem in polynomial time, which is not achievable with the best classical algorithm discovered so far. However, we still cannot rigorously exclude the possibility of the existence of an efficient classical algorithm for factoring. Although again without a proof, it is commonly believed that quantum computers are unable to solve some of the NP problems. In fact, the proof of this statement (if true) provides a possible path to prove P ≠ NP. A potentially less demanding question would be, when do we expect a quantum computer to be able to perform some well defined tasks (not necessarily related to any practical problem) that cannot be simulated with any currently available classical device, within a reasonable time? Once achieved, the status is called ‘quantum supremacy' [2]. One may ask, what about Grover's search algorithm, which provides a quadratic speedup over the classical search? Can we say that we can already achieve quantum supremacy with Grover's algorithm? The problem is that, instead of taking the large-N limit, quantum supremacy requires us to determine the actual number of qubits and gates that can no longer be simulated by classical computers within a reasonable time. To elaborate further, we remark that there can be two notions of classical simulation, namely ‘strong simulation' versus ‘weak simulation'. Strong simulation refers to the cases of calculating the transition probabilities, or expectation values of observables, to a high accuracy in polynomial time. Weak simulation requires the probability distributions to be accurately reproduced, which involves ‘sampling' the different outcomes of the quantum devices. Some quantum circuits that cannot be strongly simulated with an efficient classical means may have efficient classical methods for weak simulation [3]. However, we should be careful about the accuracy requirement in the simulation tasks. For example, for many decision problems, it may be sufficient to determine the transition amplitudes to within an additive error, instead of multiplicative error. In other words, the classical simulability of quantum computational problems depends on the accuracy requirement. Currently, there are three popular approaches for achieving quantum supremacy (see Fig. 1), namely (i) boson sampling [4], (ii) sampling IQP (instantaneous quantum polynomial) circuits [5], and (iii) sampling chaotic quantum circuits [6]. In all of these approaches, distributions of different bit strings or photon numbers are sampled from the quantum devices. Furthermore, they all involve the assumption that classical computers are unable to efficiently determine the transition amplitudes, and/or reproduce (or approximate) the distributions of quantum devices performing these tasks, in the sense of both strong and weak simulations. Three different approaches for achieving quantum supremacy: (a) boson sampling; (b) IQP circuits; (c) chaotic quantum circuits. In boson sampling, single photons are injected into different modes of a linear optical network. The task is to determine the photon distributions at the output ports. The key feature of boson sampling is that the transition amplitudes are related to the permanents of complex matrices, which are in general very difficult to calculate exactly, or approximate to within an multiplicative error; these problems belong to the #P-hard complexity class. Moreover, efficient weak simulation of boson sampling is believed to be impossible, unless the polynomial hierarchy collapses to its third level. However, a recent numerical study suggests that, in order to achieve quantum supremacy with boson sampling, one needs to simultaneously generate at least 50 or more single photons, which is still highly technologically challenging. An interesting question is whether linear optics, in the setting of boson sampling, can be applied to solve decision problems. In this case, the transition amplitudes may need to be determined to an additive error. However, we found that a large class of decision problems associated with boson sampling can be simulated by a classical computer [7], settling an open problem [8] by Aaronson and Hance. IQP circuits represent a simplified quantum-circuit model. The initial state starts from the all-zero state, |000…0〉, followed by applying Hadamard gates to each qubit. Then, diagonal gates are applied to the qubits, followed by applying Hadamard gates to each qubit again. The argument of showing the complexity in simulating IQP circuits is similar to that of boson sampling. In fact, the complexity of boson sampling was inspired by the complexity results of IQP circuits. However, when subject to noise, IQP circuits may become classically simulable [9]. Lastly, chaotic quantum circuits refer to the class of quantum circuits where two-qubit gates are applied regularly, while single-qubit gates are applied randomly from a gate set. The output distributions of these circuits approach the so-called Porter–Thomas distribution, which is a characteristic feature of quantum chaos. Recently, there have been several numerical investigations aiming to explore the ultimate limit of classical computing in simulating low-depth quantum circuits. For the ideal cases, one needs to consider both the qubit number and circuit depth for benchmarking quantum supremacy. However, in the presence of noise, these chaotic circuits may also become classically simulable for high-depth circuits [10]. Finally, other than these three approaches, one should expect that quantum supremacy can be achieved for many practical applications, e.g. simulation of quantum chemistry or quantum machine learning. When will it happen? Only time will tell!
Over the last three decades computers have become exceptionally compact and faster. Now that we have reached the fifth generation of computers which include concepts of artificial intelligence, what’s next? There is a lot of fuss about quantum computers being a strong contender for the next generation of computing. Recently we heard stories about small scale quantum computers being built by technology giants like IBM and Google and also an instance of quantum supremacy.
One of the key features of quantum computing is its core concept, leveraging the principles of quantum mechanics, which we have avoided with our classic computers. Quantum computers are the first ones to deviate from the basic concept of bits. To understand this difference in the fundamental concepts, we start with basic building blocks in conventional computers, bits and draw contrasts with those in quantum computers. Further explore how rudimentary operations are performed in both machines by comparing addition operations of 2 and 3 bits. Followed by a brief detail on current research on quantum computers and claims on their supremacy over current machines. Then we elaborate on the world of new possibilities and unsolvable problems quantum computers have the ability to tackle.
This paper aims at giving a gist of quantum computing to beginners, starting with fundamentals to current research by identifying stark contrasts with conventional machines. It also explores the need of new computation powers and why we have reached almost the tail end of processing power of classical computers.
"Quantum supremacy" is such a level of performance of a quantum computer that it provides solutions to problems requiring practically unattainable power from conventional supercomputers. As of today, quantum supremacy is achieved only on some model tasks by several quantum computers, but the development of quantum computing is going on all over the world. The development of quantum computing includes not only the creation of quantum computers, but also the creation of infrastructure for access to computing power, the development of software, and the capability to use quantum computers together with conventional supercomputers. The countries in which these laboratories have been formed have become leaders in the field of quantum computing. Quantum computer laboratories focus on the development, modeling, integration, and adaptation of practical applications for the new quantum computer. The presentation of the first quantum computer is an important milestone. This is not a one-off initiative, but part of a broad strategy for promoting breakthrough technologies in various fields. All these efforts are part of an international strategic plan for the development of quantum computing aimed at maintaining the technological leadership of developers, preserving the competitiveness of high-tech industry, and ensuring the sustainable economic growth of smart technologies.
This article discusses the concept of quantum supremacy and the challenges associated with achieving it. It explains the fundamental principles of quantum computing, such as superposition and entanglement, and how they can be harnessed to perform calculations at a speed that is impossible with classical computers. The article explores the challenges associated with achieving quantum supremacy, such as noise and error correction, scaling, and hardware and software development. The article also discusses the implications of achieving quantum supremacy in various fields, such as cryptography, machine learning, fundamental physics, materials discovery, biological systems, climate modeling, and optimization. It highlights the potential for quantum computers to revolutionize many areas of science and technology and to solve some of the most complex and pressing problems facing our world today. Overall, this article provides a comprehensive overview of the concept of quantum supremacy, the challenges associated with achieving it, and the potential implications for various fields. It is a valuable resource for anyone interested in quantum computing and its potential to transform the world around us.
Quantum computing, leveraging the principles of superposition and entanglement, has emerged as a revolutionary technology with the potential to outperform classical computers in specific tasks. This paper explores the concept of quantum supremacy, marked by Google's Sycamore processor, and its implications for classical computing. It discusses the foundations of quantum computing, including qubits, superposition, and key quantum algorithms like Shor's and Grover's, highlighting their advantages over classical systems. This study addresses the milestones in achieving quantum supremacy, including experimental benchmarks and performance comparisons. The challenges in scaling quantum systems, mitigating decoherence, and addressing criticisms of quantum supremacy claims are examined. Additionally, the paper outlines emerging applications in cryptography, optimization, and artificial intelligence and emphasizes the importance of hybrid quantum-classical systems in bridging current technological gaps. The future of quantum computing lies in advancing fault-tolerant systems and fostering interdisciplinary collaborations to realize its transformative potential across industries.