Physics:Quantum Computing Algorithms in the NISQ Era - Revision history

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	{{Quantum book backlink\|Quantum information and computing}}		{{Quantum book backlink\|Quantum information and computing}}
	{{Quantum article nav\|previous=Physics:Quantum No-cloning theorem\|previous label=No-cloning theorem\|next=Physics:Quantum Noisy Qubits\|next label=Noisy Qubits}}		{{Quantum article nav\|previous=Physics:Quantum No-cloning theorem\|previous label=No-cloning theorem\|next=Physics:Quantum Noisy Qubits\|next label=Noisy Qubits}}

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	{{Short description\|Overview of quantum algorithms suited for current NISQ hardware, including VQE for chemistry, QAOA for optimization, and classics like Grover and Shor}}		{{Short description\|Overview of quantum algorithms suited for current NISQ hardware, including VQE for chemistry, QAOA for optimization, and classics like Grover and Shor}}

	{{Quantum book backlink\|Quantum information and computing}}		{{Quantum book backlink\|Quantum information and computing}}
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	{{Short description\|Overview of quantum algorithms suited for current NISQ hardware, including VQE for chemistry, QAOA for optimization, and classics like Grover and Shor}}~~Book I~~		{{Short description\|Overview of quantum algorithms suited for current NISQ hardware, including VQE for chemistry, QAOA for optimization, and classics like Grover and Shor}}

	{{Quantum book backlink\|Quantum information and computing}}		{{Quantum book backlink\|Quantum information and computing}}

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	~~~~{{Short description\|Overview of quantum algorithms suited for current NISQ hardware, including VQE for chemistry, QAOA for optimization, and classics like Grover and Shor}}		{{Short description\|Overview of quantum algorithms suited for current NISQ hardware, including VQE for chemistry, QAOA for optimization, and classics like Grover and Shor}}Book I

	{{Quantum book backlink\|Quantum information and computing}}		{{Quantum book backlink\|Quantum information and computing}}

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	{{Quantum book backlink\|Quantum information and computing}}		{{Quantum book backlink\|Quantum information and computing}}
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	~~~~{{Short description\|Overview of quantum algorithms suited for current NISQ hardware, including VQE for chemistry, QAOA for optimization, and classics like Grover and Shor}}		{{Short description\|Overview of quantum algorithms suited for current NISQ hardware, including VQE for chemistry, QAOA for optimization, and classics like Grover and Shor}}

	{{Quantum book backlink\|Quantum information and computing}}		{{Quantum book backlink\|Quantum information and computing}}
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	{{Short description\|Overview of quantum algorithms suited for current NISQ hardware, including VQE for chemistry, QAOA for optimization, and classics like Grover and Shor}}		{{Short description\|Overview of quantum algorithms suited for current NISQ hardware, including VQE for chemistry, QAOA for optimization, and classics like Grover and Shor}}

	{{Quantum book backlink\|Quantum information and computing}}		{{Quantum book backlink\|Quantum information and computing}}
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	==='''Keywords:'''===		==='''Keywords:'''===
	~~[[Wikipedia:Quantum computing\|~~Quantum Computing]], ~~[[Wikipedia:Artificial intelligence\|~~Artificial intelligence]], ~~[[Wikipedia:Machine Learning\|~~Machine Learning]], ~~[[Wikipedia:Unsupervised learning\|~~Unsupervised learning]], ~~[[Wikipedia:~~Cryptography~~\|Cryptography]]~~, ~~[[Wikipedia:Computer security\|~~Cyber Security]], ~~[[Wikipedia:Qubit\|~~Qubits]], ~~[[Wikipedia:Quantum algorithm\|~~Quantum algorithms]], ~~[[Wikipedia:Threshold theorem\|~~Quantum verification]], ~~[[Wikipedia:Quantum error correction\|~~Quantum error correction]], ~~[[Wikipedia:Applications of quantum mechanics\|~~Quantum applications]], [https://www.preprints.org/search?condition_blocks=%5B%7B%22value%22:%22Variational+Quantum+Algorithms+(VQAs)%22,%22type%22:%22keywords%22,%22operator%22:null%7D%5D&sort_field=relevance&sort_dir=desc&page=1 Variational Quantum Algorithms (VQAs)], [https://www.preprints.org/search?condition_blocks=%5B%7B%22value%22:%22Noisy+Intermediate-Scale+Quantum+(NISQ)%22,%22type%22:%22keywords%22,%22operator%22:null%7D%5D&sort_field=relevance&sort_dir=desc&page=1 Noisy Intermediate-Scale Quantum (NISQ)], [https://www.preprints.org/search?condition_blocks=%5B%7B%22value%22:%22Variational+Quantum+Eigensolver+(VQE)%22,%22type%22:%22keywords%22,%22operator%22:null%7D%5D&sort_field=relevance&sort_dir=desc&page=1 Variational Quantum Eigensolver (VQE)], [https://www.preprints.org/search?condition_blocks=%5B%7B%22value%22:%22Quantum+Approximate+Optimization+Algorithm+(QAOA)%22,%22type%22:%22keywords%22,%22operator%22:null%7D%5D&sort_field=relevance&sort_dir=desc&page=1 Quantum Approximate Optimization Algorithm (QAOA)],[https://www.preprints.org/search?condition_blocks=%5B%7B%22value%22:%22Quantum+Neural+Networks+(QNNs)%22,%22type%22:%22keywords%22,%22operator%22:null%7D%5D&sort_field=relevance&sort_dir=desc&page=1 Quantum Neural Networks (QNNs)], [https://www.preprints.org/search?condition_blocks=%5B%7B%22value%22:%22quantum+advantage%22,%22type%22:%22keywords%22,%22operator%22:null%7D%5D&sort_field=relevance&sort_dir=desc&page=1 Quantum advantage], [https://www.preprints.org/search?condition_blocks=%5B%7B%22value%22:%22barren+plateaus%22,%22type%22:%22keywords%22,%22operator%22:null%7D%5D&sort_field=relevance&sort_dir=desc&page=1 Barren plateaus], [https://www.preprints.org/search?condition_blocks=%5B%7B%22value%22:%22noise+mitigation%22,%22type%22:%22keywords%22,%22operator%22:null%7D%5D&sort_field=relevance&sort_dir=desc&page=1 Noise mitigation], [https://www.preprints.org/search?condition_blocks=%5B%7B%22value%22:%22quantum+optimization%22,%22type%22:%22keywords%22,%22operator%22:null%7D%5D&sort_field=relevance&sort_dir=desc&page=1 Quantum optimization], [https://www.preprints.org/search?condition_blocks=%5B%7B%22value%22:%22quantum+chemistry%22,%22type%22:%22keywords%22,%22operator%22:null%7D%5D&sort_field=relevance&sort_dir=desc&page=1 Quantum chemistry], [https://www.preprints.org/search?condition_blocks=%5B%7B%22value%22:%22quantum+machine+learning%22,%22type%22:%22keywords%22,%22operator%22:null%7D%5D&sort_field=relevance&sort_dir=desc&page=1 Quantum machine learning], [https://www.preprints.org/search?condition_blocks=%5B%7B%22value%22:%22hybrid+quantum-classical+algorithms%22,%22type%22:%22keywords%22,%22operator%22:null%7D%5D&sort_field=relevance&sort_dir=desc&page=1 Hybrid quantum-classical algorithms].		Quantum Computing, Artificial intelligence, Machine Learning, Unsupervised learning, Cryptography, Cyber Security, Qubits, Quantum algorithms, Quantum verification, Quantum error correction, Quantum applications, [https://www.preprints.org/search?condition_blocks=%5B%7B%22value%22:%22Variational+Quantum+Algorithms+(VQAs)%22,%22type%22:%22keywords%22,%22operator%22:null%7D%5D&sort_field=relevance&sort_dir=desc&page=1 Variational Quantum Algorithms (VQAs)], [https://www.preprints.org/search?condition_blocks=%5B%7B%22value%22:%22Noisy+Intermediate-Scale+Quantum+(NISQ)%22,%22type%22:%22keywords%22,%22operator%22:null%7D%5D&sort_field=relevance&sort_dir=desc&page=1 Noisy Intermediate-Scale Quantum (NISQ)], [https://www.preprints.org/search?condition_blocks=%5B%7B%22value%22:%22Variational+Quantum+Eigensolver+(VQE)%22,%22type%22:%22keywords%22,%22operator%22:null%7D%5D&sort_field=relevance&sort_dir=desc&page=1 Variational Quantum Eigensolver (VQE)], [https://www.preprints.org/search?condition_blocks=%5B%7B%22value%22:%22Quantum+Approximate+Optimization+Algorithm+(QAOA)%22,%22type%22:%22keywords%22,%22operator%22:null%7D%5D&sort_field=relevance&sort_dir=desc&page=1 Quantum Approximate Optimization Algorithm (QAOA)],[https://www.preprints.org/search?condition_blocks=%5B%7B%22value%22:%22Quantum+Neural+Networks+(QNNs)%22,%22type%22:%22keywords%22,%22operator%22:null%7D%5D&sort_field=relevance&sort_dir=desc&page=1 Quantum Neural Networks (QNNs)], [https://www.preprints.org/search?condition_blocks=%5B%7B%22value%22:%22quantum+advantage%22,%22type%22:%22keywords%22,%22operator%22:null%7D%5D&sort_field=relevance&sort_dir=desc&page=1 Quantum advantage], [https://www.preprints.org/search?condition_blocks=%5B%7B%22value%22:%22barren+plateaus%22,%22type%22:%22keywords%22,%22operator%22:null%7D%5D&sort_field=relevance&sort_dir=desc&page=1 Barren plateaus], [https://www.preprints.org/search?condition_blocks=%5B%7B%22value%22:%22noise+mitigation%22,%22type%22:%22keywords%22,%22operator%22:null%7D%5D&sort_field=relevance&sort_dir=desc&page=1 Noise mitigation], [https://www.preprints.org/search?condition_blocks=%5B%7B%22value%22:%22quantum+optimization%22,%22type%22:%22keywords%22,%22operator%22:null%7D%5D&sort_field=relevance&sort_dir=desc&page=1 Quantum optimization], [https://www.preprints.org/search?condition_blocks=%5B%7B%22value%22:%22quantum+chemistry%22,%22type%22:%22keywords%22,%22operator%22:null%7D%5D&sort_field=relevance&sort_dir=desc&page=1 Quantum chemistry], [https://www.preprints.org/search?condition_blocks=%5B%7B%22value%22:%22quantum+machine+learning%22,%22type%22:%22keywords%22,%22operator%22:null%7D%5D&sort_field=relevance&sort_dir=desc&page=1 Quantum machine learning], [https://www.preprints.org/search?condition_blocks=%5B%7B%22value%22:%22hybrid+quantum-classical+algorithms%22,%22type%22:%22keywords%22,%22operator%22:null%7D%5D&sort_field=relevance&sort_dir=desc&page=1 Hybrid quantum-classical algorithms].

	=== Quantum Computing Algorithms ===		=== Quantum Computing Algorithms ===
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	=See also=		=See also=
	{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}		{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}
	* ~~[[Wikipedia:Quantum Computing\|~~Quantum computing]]		* Quantum computing

	==Sources==		==Sources==
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	* [https://blog.google/innovation-and-ai/technology/research/quantum-echoes-willow-verifiable-quantum-advantage/] Quantum Echoes algorithm is a big step toward real-world applications for quantum computing. Google Blog, Oct 2025.		* [https://blog.google/innovation-and-ai/technology/research/quantum-echoes-willow-verifiable-quantum-advantage/] Quantum Echoes algorithm is a big step toward real-world applications for quantum computing. Google Blog, Oct 2025.

	='''~~[[:Physics:Quantum Computing Algorithms in the NISQ Era/Quiz\|~~ The Learning Quiz]]'''=		=''' The Learning Quiz'''=
	==References==		==References==
	<div style="column-count:3; break-inside:avoid; column-gap:2em;">		<div style="column-count:3; break-inside:avoid; column-gap:2em;">

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	{{Short description\|Overview of quantum algorithms suited for current NISQ hardware, including VQE for chemistry, QAOA for optimization, and classics like Grover and Shor}}		{{Short description\|Overview of quantum algorithms suited for current NISQ hardware, including VQE for chemistry, QAOA for optimization, and classics like Grover and Shor}}

	{{Quantum book backlink\|Quantum information and computing}}		{{Quantum book backlink\|Quantum information and computing}}
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	The advent of quantum computers heralds a new ground-breaking era within the realm of data integrity and cybersecurity. With improving scalable computing power, quantum computers can effortlessly break the security of traditional cryptosystems, relying on factorization and discrete logarithms, both of which are considered hard problems for classical computers. By contrast, quantum computers have efficient processing capabilities to solve these hard problems within polynomial time <ref name="41Z1">A. Singh, K. Dev, H. Siljak, H. D. Joshi, and M. Magarini, "Quantum Internet—Applications, Functionalities, Enabling Technologies, Challenges, and Research Directions," ''IEEE Communications Surveys & Tutorials'', vol. 23, no. 4, pp. 2218–2247, 2021. [https://doi.org/10.1109/COMST.2021.3109944 DOI: 10.1109/COMST.2021.3109944]</ref>. For example, an adversary equipped with a quantum computer may break the RSA(Rivest-Shamir-Adleman) security in polynomial time by exploiting Shor’s algorithm for factoring large numbers. It is clear that such a possibility, despite not yet practical, poses potential threats to the integrity of communication networks <ref name="41Z2">P. W.Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,” SIAM review, vol. 41, no. 2, pp. 303–332, 1999.</ref> that need to be analyzed and mitigated. In fact the potential threat represented by the Shor’s algorithm has led to new developments in classical cryptographic approaches, with the work on post-quantum cryptography and on a completely new paradigm to grant security named quantum cryptography <ref name="41Z3">S. Pirandola, L. Andersen, U., L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. L. Pereira, M. Razavi, J. Shamsul Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and W. P., “Advances in quantum cryptography,” Advances in Optics and Photonics, vol. 12, no. 4, pp. 1012–1236, 2020.</ref>, or more precisely Quantum-Key Distribution (QKD). The novelty of QKD is that, instead of adding layers of security based on conventional (i.e. computationally hard to solve) algorithms, it uses fundamental properties of quantum particles to protect information from unauthorized parties. QKD protocols, are themselves composite algorithms where transmission of quantum signals, encryption/decryption, signatures, authentication, and hashing are all combined <ref name="41Z4">S. Pirandola and S. L. Braunstein, “Physics: Unite to build a quantum internet,” Nature, vol. 532, no. 7598, pp. 169–171, 2016.</ref> to achieve (theoretically) unconditional security.		The advent of quantum computers heralds a new ground-breaking era within the realm of data integrity and cybersecurity. With improving scalable computing power, quantum computers can effortlessly break the security of traditional cryptosystems, relying on factorization and discrete logarithms, both of which are considered hard problems for classical computers. By contrast, quantum computers have efficient processing capabilities to solve these hard problems within polynomial time <ref name="41Z1">A. Singh, K. Dev, H. Siljak, H. D. Joshi, and M. Magarini, "Quantum Internet—Applications, Functionalities, Enabling Technologies, Challenges, and Research Directions," ''IEEE Communications Surveys & Tutorials'', vol. 23, no. 4, pp. 2218–2247, 2021. [https://doi.org/10.1109/COMST.2021.3109944 DOI: 10.1109/COMST.2021.3109944]</ref>. For example, an adversary equipped with a quantum computer may break the RSA(Rivest-Shamir-Adleman) security in polynomial time by exploiting Shor’s algorithm for factoring large numbers. It is clear that such a possibility, despite not yet practical, poses potential threats to the integrity of communication networks <ref name="41Z2">P. W.Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,” SIAM review, vol. 41, no. 2, pp. 303–332, 1999.</ref> that need to be analyzed and mitigated. In fact the potential threat represented by the Shor’s algorithm has led to new developments in classical cryptographic approaches, with the work on post-quantum cryptography and on a completely new paradigm to grant security named quantum cryptography <ref name="41Z3">S. Pirandola, L. Andersen, U., L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. L. Pereira, M. Razavi, J. Shamsul Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and W. P., “Advances in quantum cryptography,” Advances in Optics and Photonics, vol. 12, no. 4, pp. 1012–1236, 2020.</ref>, or more precisely Quantum-Key Distribution (QKD). The novelty of QKD is that, instead of adding layers of security based on conventional (i.e. computationally hard to solve) algorithms, it uses fundamental properties of quantum particles to protect information from unauthorized parties. QKD protocols, are themselves composite algorithms where transmission of quantum signals, encryption/decryption, signatures, authentication, and hashing are all combined <ref name="41Z4">S. Pirandola and S. L. Braunstein, “Physics: Unite to build a quantum internet,” Nature, vol. 532, no. 7598, pp. 169–171, 2016.</ref> to achieve (theoretically) unconditional security.
	<div style="display: flex; justify-content: space-around;">		<div style="display: flex; justify-content: space-around;">
	[[File:~~Shor's algorithm quantum circuit~~.png\|200px]] [[File:~~BB84-network setup~~.~~svg~~\|200px]] [[File:~~B92 protocol quantum key distribution~~.~~svg~~\|200px\| B92 Protocol Quantum Key Distribution (Translated: Light source - Источник света)]]		[[File:Quantum_book1_computing_algorithms_in_the_nisq_era_yellow.png\|200px]] [[File:Quantum_book1_computing_algorithms_in_the_nisq_era_yellow.png\|200px]] [[File:Quantum_book1_computing_algorithms_in_the_nisq_era_yellow.png\|200px\| B92 Protocol Quantum Key Distribution (Translated: Light source - Источник света)]]
	</div>		</div>
	(Illustrative visuals from Wikimedia Commons related to Shor's algorithm and Quantum Key Distribution protocols.)		(Illustrative visuals from Wikimedia Commons related to Shor's algorithm and Quantum Key Distribution protocols.)
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	[[File:Quantum circuit.jpg\|200px]]		[[File:Quantum circuit.jpg\|200px]]
	[[File:Qcircuit RZtheta.svg\|200px]]		[[File:Qcircuit RZtheta.svg\|200px]]
	[[File:~~Phase estimation~~.png\|200px]]		[[File:Quantum_book1_computing_algorithms_in_the_nisq_era_yellow.png\|200px]]
	</div>		</div>

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	[[File:Quantum circuit that exhibits Parity Measurement.png\|200px]]		[[File:Quantum circuit that exhibits Parity Measurement.png\|200px]]
	[[File:~~QuantumPhaseEstimationCircuit~~.png\|200px]]		[[File:Quantum_book1_computing_algorithms_in_the_nisq_era_yellow.png\|200px]]
	[[File:Z1z2z3z4z5 parity measurement circuit.png\|200px]]		[[File:Z1z2z3z4z5 parity measurement circuit.png\|200px]]
	</div>		</div>

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	{{Short description\|Overview of quantum algorithms suited for current NISQ hardware, including VQE for chemistry, QAOA for optimization, and classics like Grover and Shor}}		{{Short description\|Overview of quantum algorithms suited for current NISQ hardware, including VQE for chemistry, QAOA for optimization, and classics like Grover and Shor}}

	{{Quantum book backlink\|Quantum information and computing}}		{{Quantum book backlink\|Quantum information and computing}}
	{{Quantum article nav\|previous=Physics:Quantum No-cloning theorem\|previous label=No-cloning theorem\|next=Physics:Quantum Noisy Qubits\|next label=Noisy Qubits}}		{{Quantum article nav\|previous=Physics:Quantum No-cloning theorem\|previous label=No-cloning theorem\|next=Physics:Quantum Noisy Qubits\|next label=Noisy Qubits}}