In quantum computing, a quantum algorithm is an algorithm which runs on a realistic model of quantum computation, the most commonly used model being the quantum circuit model of computation. A classical (or non-quantum) algorithm is a finite sequence of instructions, or a step-by-step procedure for solving a problem, where each step or instruction can be performed on a classical computer. Similarly, a quantum algorithm is a step-by-step procedure, where each of the steps can be performed on a quantum computer. Although all classical algorithms can also be performed on a quantum computer, the term quantum algorithm is usually used for those algorithms which seem inherently quantum, or use some essential feature of quantum computation such as quantum superposition or quantum entanglement.
Problems which are undecidable using classical computers remain undecidable using quantum computers. What makes quantum algorithms interesting is that they might be able to solve some problems faster than classical algorithms because the quantum superposition and quantum entanglement that quantum algorithms exploit probably cannot be efficiently simulated on classical computers (see Quantum supremacy).
The best-known algorithms are Shor's algorithm for factoring and Grover's algorithm for searching an unstructured database or an unordered list. Shor's algorithms runs much (almost exponentially) faster than the best-known classical algorithm for factoring, the general number field sieve. Grover's algorithm runs quadratically faster than the best possible classical algorithm for the same task, a linear search.
Quantum algorithms are usually described, in the commonly used circuit model of quantum computation, by a quantum circuit which acts on some input qubits and terminates with a measurement. A quantum circuit consists of simple quantum gates which act on at most a fixed number of qubits. The number of qubits has to be fixed because a changing number of qubits implies non-unitary evolution.
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In quantum computing and specifically the quantum circuit model of computation, a quantum logic gate (or simply quantum gate) is a basic quantum circuit operating on a small number of qubits. They are the building blocks of quantum circuits, like classical logic gates are for conventional digital circuits. Unlike many classical logic gates, quantum logic gates are reversible. It is possible to perform classical computing using only reversible gates.
Shor's algorithm is a quantum algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor. It is one of the few known quantum algorithms with compelling potential applications and strong evidence of superpolynomial speedup compared to best known classical (that is, non-quantum) algorithms. On the other hand, factoring numbers of practical significance requires far more qubits than available in the near future.
In quantum computing, Grover's algorithm, also known as the quantum search algorithm, refers to a quantum algorithm for unstructured search that finds with high probability the unique input to a black box function that produces a particular output value, using just evaluations of the function, where is the size of the function's domain. It was devised by Lov Grover in 1996. The analogous problem in classical computation cannot be solved in fewer than evaluations (because, on average, one has to check half of the domain to get a 50% chance of finding the right input).
Quantum computing has received wide-spread attention lately due the possibility of a near-term breakthrough of quantum supremacy. This course acts as an introduction to the area of quantum computing.
After introducing the foundations of classical and quantum information theory, and quantum measurement, the course will address the theory and practice of digital quantum computing, covering fundament
Today one is able to manipulate matter at the nanoscale were quantum behavior becomes important and possibly information processing will have to take into account laws of quantum physics. We introduce
Covers the concept of quantum computation delegation and the relationship between MIP and RE, addressing common FAQs and discussing helpful materials and interactions with quantum devices.
Explores NISQ algorithms, with a focus on the VQE method and error mitigation techniques.
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We explore applications of quantum computing for radio interferometry and astronomy using recent developments in quantum image processing. We evaluate the suitability of different quantum image representations using a toy quantum computing image reconstruc ...
Elsevier2024
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Entanglement forging based variational algorithms leverage the bipartition of quantum systems for addressing ground-state problems. The primary limitation of these approaches lies in the exponential summation required over the numerous potential basis stat ...
Amer Physical Soc2024
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Quantum support vector machines employ quantum circuits to define the kernel function. It has been shown that this approach offers a provable exponential speedup compared to any known classical algorithm for certain data sets. The training of such models c ...