... top 10 quantum algorithms that are revolutionizing hydrogen splitting technology in 2024. Each algorithm leverages advancements in quantum field
A research team in China has developed a quantum search algorithm that extends Grover's quadratic speedup to continuous problems.
The researchers described a new quantum algorithm that works faster than all known classical ones at finding good solutions to a wide class of optimization
This review includes "pure" quantum algorithms as well as quantum heuristics like variational quantum algorithms and, is limited to gate based
[Jump to content](https://en.wikipedia.org/wiki/Quantum_optimization_algorithms#bodyContent). * [(Top)](https://en.wikipedia.org/wiki/Quantum_optimization_algorithms#). * [3.2 QAOA for finding the minimum vertex cover of a graph](https://en.wikipedia.org/wiki/Quantum_optimization_algorithms#QAOA_for_finding_the_minimum_vertex_cover_of_a_graph). * [3.4 Variations of QAOA](https://en.wikipedia.org/wiki/Quantum_optimization_algorithms#Variations_of_QAOA). * [5 See also](https://en.wikipedia.org/wiki/Quantum_optimization_algorithms#See_also). * [6 References](https://en.wikipedia.org/wiki/Quantum_optimization_algorithms#References). * [Article](https://en.wikipedia.org/wiki/Quantum_optimization_algorithms "View the content page [alt-c]"). * [Read](https://en.wikipedia.org/wiki/Quantum_optimization_algorithms). * [Read](https://en.wikipedia.org/wiki/Quantum_optimization_algorithms). In principle the optimal value of C(z){\displaystyle C(z)} can be reached up to arbitrary precision, this is guaranteed by the adiabatic theorem[[10]](https://en.wikipedia.org/wiki/Quantum_optimization_algorithms#cite_note-10)[[11]](https://en.wikipedia.org/wiki/Quantum_optimization_algorithms#cite_note-11) or alternatively by the universality of the QAOA unitaries.[[12]](https://en.wikipedia.org/wiki/Quantum_optimization_algorithms#cite_note-12) However, it is an open question whether this can be done in a feasible way. A study of QAOA and [MaxCut](https://en.wikipedia.org/wiki/Maximum_cut "Maximum cut") algorithm shows that p>11{\displaystyle p>11} is required for scalable advantage.[[16]](https://en.wikipedia.org/wiki/Quantum_optimization_algorithms#cite_note-Lykov_Wurtz_Poole_Saffman_p.-16). Several variations to the basic structure of QAOA have been proposed,[[17]](https://en.wikipedia.org/wiki/Quantum_optimization_algorithms#cite_note-17) which include variations to the ansatz of the basic algorithm. 1. Multi-angle QAOA[[18]](https://en.wikipedia.org/wiki/Quantum_optimization_algorithms#cite_note-18). 2. Expressive QAOA (XQAOA)[[19]](https://en.wikipedia.org/wiki/Quantum_optimization_algorithms#cite_note-19). 3. QAOA+[[20]](https://en.wikipedia.org/wiki/Quantum_optimization_algorithms#cite_note-20). 4. Digitised counteradiabatic QAOA[[21]](https://en.wikipedia.org/wiki/Quantum_optimization_algorithms#cite_note-21). 4. **[^](https://en.wikipedia.org/wiki/Quantum_optimization_algorithms#cite_ref-4 "Jump up")**Ramana, Motakuri V. **[^](https://en.wikipedia.org/wiki/Quantum_optimization_algorithms#cite_ref-12 "Jump up")**Morales, M. * [Edit preview settings](https://en.wikipedia.org/wiki/Quantum_optimization_algorithms#). [](https://en.wikipedia.org/wiki/Quantum_optimization_algorithms?action=edit).
However, it is only through the power of quantum computing that these decoding algorithms can be leveraged to also solve optimization problems. By pairing the quantum interference of DQI with these sophisticated decoding algorithms, a sufficiently large quantum computer could find approximate solutions to these optimization problems — solutions that appear to be beyond the reach of any known classical method. When quantum computing hardware is advanced enough, researchers can use the DQI algorithm to solve classically challenging optimization problems. The promise of DQI is that certain kinds of structure may make the decoding problem much easier, without also making the optimization problem easier to solve using conventional computers. This algebraic structure is reflected in both the original optimization problem (OPI) and the decoding problem that quantum computers can convert it into (Reed-Solomon decoding). In this circumstance, the ability to convert the optimization problem into the decoding problem, using the power of quantum computing, provides advantage.
One algorithm put quantum computing on the map like no other: Shor’s algorithm. This was the first demonstration that a quantum computer can solve a real-world problem dramatically faster than a classical computer, transforming quantum algorithms from theory into a major research area. Current state: Grover’s algorithm has been demonstrated on small quantum computers for trivial searches, confirming the √N speedup in principle. Quantum computers naturally speak the language of quantum chemistry, so algorithms like VQE can in principle simulate complex molecules more efficiently. Quantum machine learning (QML) algorithms aim to accelerate or improve classical ML tasks by exploiting quantum computation. Small-scale demos have run on a few qubits – for instance, using a quantum kernel method to classify toy data sets – hinting at the potential to handle higher-dimensional data in fewer steps than classical algorithms. We’ve surveyed a curated list of quantum algorithms – from near-term workhorses like VQE and QAOA to visionary giants like Shor’s and Grover’s – each unlocking novel capabilities across industries.
Another example is finding a solution in an unsorted data set – this can theoretically be solved by the quantum algorithm known as Grover's algorithm. However,