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Classical physics cannot explain the operation of these quantum devices, and a scalable quantum computer could perform some calculations exponentially faster than any modern "classical" computer.
In particular, a large-scale quantum computer could break widely used encryption schemes and aid physicists in performing physical simulations; however, the current state of the art is largely experimental and impractical, with several obstacles to useful applications.
The basic unit of information in quantum computing, the qubit (or "quantum bit"), serves the same function as the bit in classical computing. However, unlike a classical bit, which can be in one of two states (a binary), a qubit can exist in a superposition of its two "basis" states, which loosely means it is in both states simultaneously. When measuring a qubit, the result is a probabilistic output of a classical bit. If a quantum computer manipulates the qubit in a particular way, wave interference effects can amplify the desired measurement results. The design of quantum algorithms involves creating procedures that allow a quantum computer to perform calculations efficiently and quickly.
Physically engineering high-quality qubits has proven challenging. If a physical qubit is not sufficiently isolated from its environment, it suffers from quantum decoherence, introducing noise into calculations. National governments have invested heavily in experimental research to develop scalable qubits with longer coherence times and lower error rates. Example implementations include superconductors (which isolate an electrical current by eliminating electrical resistance) and ion traps (which confine a single atomic particle using electromagnetic fields).
In principle, given enough time, a classical computer can solve the same computational problems as a quantum computer. Quantum advantage comes in the form of time complexity rather than computability, and quantum complexity theory shows that some quantum algorithms are exponentially more efficient than the best-known classical algorithms. A large-scale quantum computer could in theory solve computational problems unsolved by a classical computer in any reasonable amount of time. While claims of such quantum supremacy have drawn significant attention to the discipline, near-term practical use cases remain limited.
For many years, the fields of quantum mechanics and computer science formed distinct academic communities. Modern Quantum Theory developed in the 1920s to explain the wave-particle duality observed at atomic scales, and digital computers emerged in the following decades to replace human computers for tedious calculations. Both disciplines had practical applications during World War II; computers played a major role in wartime cryptography, and quantum physics was essential for the nuclear physics used in the Manhattan Project.
As physicists applied quantum mechanical models to computational problems and swapped digital bits for qubits, the field of quantum mechanics and computer science began to converge. In the 1980s, Paul Benioff introduced the Quantum Turing Machine, which uses quantum theory to describe a simplified computer. When digital computers became faster, physicists faced an exponential increase in overhead when simulating quantum dynamics, prompting Yuri Manin and Richard Feynman to independently suggest that hardware based on quantum phenomena might be more efficient for computer simulation. In a 1984 paper, Charles Bennett and Gilles Brassard applied quantum theory to cryptography protocols and demonstrated that quantum key distribution could enhance information security.
Quantum algorithms then emerged for solving oracle problems, such as Deutsch's algorithm in 1985, the Bernstein-Vazirani algorithm in 1993, and Simon's algorithm in 1994. These algorithms did not solve practical problems, but demonstrated mathematically that one could gain more information by querying a black box with a quantum state in superposition, sometimes referred to as quantum parallelism.
Peter Shor built on these results with his 1994 algorithm for breaking the widely used RSA and Diffie–Hellman encryption protocols, which drew significant attention to the field of quantum computing. In 1996, Grover's algorithm established a quantum speedup for the widely applicable unstructured search problem. The same year, Seth Lloyd proved that quantum computers could simulate quantum systems without the exponential overhead present in classical simulations, validating Feynman's 1982 conjecture.
Over the years, experimentalists have constructed small-scale quantum computers using trapped ions and superconductors. In 1998, a two-qubit quantum computer demonstrated the feasibility of the technology, and subsequent experiments have increased the number of qubits and reduced error rates.
In 2019, Google AI and NASA announced that they had achieved quantum supremacy with a 54-qubit machine, performing a computation that is impossible for any classical computer. However, the validity of this claim is still being actively researched.
The threshold theorem shows how increasing the number of qubits can mitigate errors, yet fully fault-tolerant quantum computing remains "a rather distant dream". According to some researchers, noisy intermediate-scale quantum (NISQ) machines may have specialized uses shortly, but noise in quantum gates limits their reliability.
Investment in quantum computing research has increased in the public and private sectors. As one consulting firm summarized;
... investment dollars are pouring in, and quantum-computing start-ups are proliferating. Whilw quantum computing promises to help businesses solve problems that are beyond the reach and speed of conventional high-performance computers, use cases are largely experimental and hypothetical at this early stage.
With a focus on business management's point of view, the potential applications of quantum computing into four major categories are cybersecurity, data analytics, and artificial intelligence, optimization and simulation, and data management and searching.
In December 2023, physicists, for the first time, reported the entanglement of individual molecules, which may have significant applications in quantum computing. Also in December 2023, scientists at Harvard University successfully created "quantum circuits" that correct errors more efficiently than alternative methods, which may potentially remove a major obstacle to practical quantum computers. The Harvard research team was supported by MIT, QuEra Computing, Caltech, and Princeton University and funded by DARPA's Optimization with Noisy Intermediate-Scale Quantum Devices (ONISQ) program. Research efforts are ongoing to jumpstart quantum computing through topological and photonic approaches as well.
Computer engineers typically describe a modern computer's operation in terms of classical electrodynamics. Within these, "classical" computers, some components (such as semiconductors and random number generators) may rely on quantum behavior, but these components are not isolated from their environment, so any quantum information quickly decohers. While programmers may depend on probability theory when designing a randomized algorithm, quantum mechanical notions like superposition and interference are largely irrelevant to program analysis.
Quantum programs, in contrast, rely on precise control of coherent quantum systems. Physicists describe these systems mathematically using linear algebra, complex numbers model probability amplitudes, vectors model quantum states, and matrices model the operations that can be performed on these states. Programming a quantum computer is then a matter of composing operations in such a way that the resulting program computes a useful result in theory and is implementable in practice.
As physicist, Charlie Bennett describes the relationship between quantum and classical computers;
A classical computer is a quantum computer ... so we shouldn't be asking about "where do quantum speedups come from?" We should say, "well, all computers are quantum ... Where do classical slowdowns come from?"
Just as the bit is the basic concept of classical information theory, the qubit is the fundamental unit of quantum information. The same term qubit is used to refer to an abstract mathematical model and to any physical system that is represented by that model. A classical bit, by definition, exists in either of the two physical systems represented by that model. A classical bit, by definition, exists in either of two physical states, denoted by 0 and 1. A qubit is also described by a state, and two states are often written :0> and :1> serve as the quantum counterparts of the classical states 0 and 1.
However, the quantum states :0> and :1> belong to a vector space, meaning that they can be multiplied by constants and added together, and the result is again a valid quantum state. Such a combination is known as a superposition of :0> and :1>.
In simple terms, a qubit’s state is like a two-dimensional vector. Scientists often use a special notation to write this, like ":ψ⟩" for a state they call "ket psi." Because a qubit has two possible states (0 or 1), any qubit state can be written as a combination of :0⟩ and :1⟩ with coefficients α and β, which are probability amplitudes. These amplitudes are often complex numbers. If one of them is zero, the qubit behaves like a regular bit. But when both are nonzero, the qubit is in a superposition, which is a special quantum state.
When you measure a qubit, it produces a classic 0 or 1. The chance of getting :0⟩ is :α:², and for :1⟩, it’s :β:². These probabilities always add up to 1. For instance, if α and β are both 1/√2, the qubit has an equal chance of being :0⟩ or :1⟩.
Adding qubits expands the system's state space. For two qubits, we get a four-dimensional space with states like :00⟩, :01⟩, :10⟩, and :11⟩. Sometimes, two qubits are "entangled," meaning their states are connected in a way that they can't be described separately. In general, the space of an n-qubit system has 2ⁿ dimensions, making it very complex for classical computers to simulate large quantum systems, as each qubit doubles the amount of data needed.
In quantum computing, we can manipulate the state of a qubit (quantum bit) using "quantum logic gates", similar to how we manipulate bits in classical computers with classical logic gates. One of the basic gates in both classical and quantum computing is the NOT gate, which flips the state of a qubit. For instance, applying a NOT gate to a qubit in state :0⟩ changes it to :1⟩, and vice versa.
When we have multiple qubits, we can apply gates to individual qubits or conditionally apply them based on the state of another qubit. For example, with a two-qubit system, we can use a gate called the Controlled NOT (CNOT) gate. This gate only flips the state of the second qubit if the first qubit is in the state :1⟩. If the first qubit is in the state :0⟩, the second qubit remains unchanged.
In a quantum computer, these gates are connected in a network, allowing us to perform complex operations by combining them in specific ways. Measurements (or observing the qubit states) are typically done at the end of these operations, as measuring too soon can disturb the state of the qubits.
Quantum Parallelism is the heuristic that quantum computers can be thought of as evaluating a function for multiple input values simultaneously. This can be achieved by preparing a quantum system in a superposition of input states and applying a unitary transformation that encodes the function to be evaluated. The resulting state encodes the function's output values for all input values in the superposition, allowing for the computation of multiple outputs simultaneously. This property is key to the speedup of many quantum algorithms.
However, "parallelism" in this sense is insufficient to speed up a computation because the measurement of the end of the computation gives only one value. A quantum algorithm must also incorporate some other conceptual ingredient to be useful.
Quantum computing has significant potential applications in the fields of cryptography and cybersecurity. Quantum cryptography, which relies on the principles of quantum mechanics, offers the possibility of secure communication channels that are resistant to eavesdropping. Quantum Key Distribution (QKD) protocols, such as BB84, enable the secure exchange of cryptographic keys between parties, ensuring the confidentiality and integrity of communication. Moreover, quantum random number generators (QRNGs) can produce high-quality random numbers, which are essential for secure encryption.
However, quantum computing also poses challenges to traditional cryptographic systems. Shor's algorithm, a quantum algorithm for integer factorization, could potentially break widely used public-key cryptography schemes like RSA, which rely on the difficulty of factoring large numbers. Post Quantum Cryptography, which involves the development of cryptographic algorithms that are resistant to attacks by both classical and quantum computers, is an active area of research aimed at addressing this concern.
Ongoing research in quantum cryptography and post-quantum cryptography is crucial for ensuring the security of communication and data in the face of evolving quantum capabilities. Advances in these fields, such as the development of new QKD protocols, the improvement of QRNGs, and the standardization of post-quantum cryptographic algorithms, will play a key role in maintaining the integrity and confidentiality of information in the quantum era.
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