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</div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Era of technology</div> <p>The current state of <a href="/wiki/Quantum_computing" title="Quantum computing">quantum computing</a><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> is referred to as the <b>noisy intermediate-scale quantum</b> (<b>NISQ</b>) <b>era</b>,<sup id="cite_ref-:0_2-0" class="reference"><a href="#cite_note-:0-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> characterized by quantum processors containing up to 1,000 <a href="/wiki/Qubit" title="Qubit">qubits</a> which are not advanced enough yet for <a href="/wiki/Fault-tolerant" class="mw-redirect" title="Fault-tolerant">fault-tolerance</a> or large enough to achieve <a href="/wiki/Quantum_advantage" class="mw-redirect" title="Quantum advantage">quantum advantage</a>.<sup id="cite_ref-sciencedaily.com_4-0" class="reference"><a href="#cite_note-sciencedaily.com-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:1_5-0" class="reference"><a href="#cite_note-:1-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> These processors, which are sensitive to their environment (noisy) and prone to <a href="/wiki/Quantum_decoherence" title="Quantum decoherence">quantum decoherence</a>, are not yet capable of continuous <a href="/wiki/Quantum_error_correction" title="Quantum error correction">quantum error correction</a>. This intermediate-scale is defined by the <a href="/wiki/Quantum_volume" title="Quantum volume">quantum volume</a>, which is based on the moderate number of qubits and <a href="/wiki/Quantum_logic_gate" title="Quantum logic gate">gate</a> fidelity. The term NISQ was coined by <a href="/wiki/John_Preskill" title="John Preskill">John Preskill</a> in 2018.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:0_2-1" class="reference"><a href="#cite_note-:0-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>According to <a href="/wiki/Microsoft_Azure_Quantum" title="Microsoft Azure Quantum">Microsoft Azure Quantum</a>'s scheme, NISQ computation is considered level 1, the lowest of the quantum computing implementation levels.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>In October 2023, the 1,000 qubit mark was passed for the first time by Atom Computing's 1,180 qubit quantum processor.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> However, as of 2024, only two quantum processors have over 1,000 qubits, with sub-1,000 quantum processors still remaining the norm.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Algorithms">Algorithms</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Noisy_intermediate-scale_quantum_era&action=edit&section=1" title="Edit section: Algorithms"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>NISQ algorithms</b> are <a href="/wiki/Quantum_algorithm" title="Quantum algorithm">quantum algorithms</a> designed for quantum processors in the NISQ era. Common examples are the <a href="/wiki/Variational_quantum_eigensolver" title="Variational quantum eigensolver">variational quantum eigensolver</a> (VQE) and <a href="/wiki/Quantum_approximate_optimization_algorithm" class="mw-redirect" title="Quantum approximate optimization algorithm">quantum approximate optimization algorithm</a> (QAOA), which use NISQ devices but offload some calculations to classical processors.<sup id="cite_ref-:0_2-2" class="reference"><a href="#cite_note-:0-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> These algorithms have been successful in <a href="/wiki/Quantum_chemistry" title="Quantum chemistry">quantum chemistry</a> and have potential applications in various fields including physics, materials science, data science, cryptography, biology, and finance.<sup id="cite_ref-:0_2-3" class="reference"><a href="#cite_note-:0-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> However, due to noise during circuit execution, they often require error mitigation techniques.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:1_5-1" class="reference"><a href="#cite_note-:1-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> These methods constitute a way of reducing the effect of noise by running a set of circuits and applying post-processing to the measured data. In contrast to <a href="/wiki/Quantum_error_correction" title="Quantum error correction">quantum error correction</a>, where errors are continuously detected and corrected during the run of the circuit, error mitigation can only use the outcome of the noisy circuits. </p> <div class="mw-heading mw-heading2"><h2 id="Beyond-NISQ_era">Beyond-NISQ era</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Noisy_intermediate-scale_quantum_era&action=edit&section=2" title="Edit section: Beyond-NISQ era"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The creation of a computer with tens of thousands of qubits and enough error correction would eventually end the NISQ era.<sup id="cite_ref-sciencedaily.com_4-1" class="reference"><a href="#cite_note-sciencedaily.com-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> These beyond-NISQ devices would be able to, for example, implement <a href="/wiki/Shor%27s_algorithm" title="Shor's algorithm">Shor's algorithm</a> for very large numbers and break <a href="/wiki/RSA_(cryptosystem)" title="RSA (cryptosystem)">RSA</a> encryption.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p>In April 2024, researchers at Microsoft announced a significant reduction in error rates that required only 4 logical qubits, suggesting that quantum computing at scale could be years away instead of decades.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Noisy_intermediate-scale_quantum_era&action=edit&section=3" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Quantum_complexity_theory" title="Quantum complexity theory">Quantum complexity theory</a></li> <li><a href="/wiki/Quantum_noise" title="Quantum noise">Quantum noise</a></li> <li><a href="/wiki/List_of_companies_involved_in_quantum_computing_or_communication" title="List of companies involved in quantum computing or communication">List of companies involved in quantum computing or communication</a></li> <li><a href="/wiki/List_of_quantum_processors" title="List of quantum processors">List of quantum processors</a></li> <li><a href="/wiki/Timeline_of_quantum_computing_and_communication" title="Timeline of quantum computing and communication">Timeline of quantum computing and communication</a></li> <li><a href="/wiki/Quantum_information" title="Quantum information">Quantum information</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Noisy_intermediate-scale_quantum_era&action=edit&section=4" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output 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(2017-03-31). <a rel="nofollow" class="external text" href="https://link.aps.org/doi/10.1103/PhysRevA.95.032338">"Quantum computation with realistic magic-state factories"</a>. <i>Physical Review A</i>. <b>95</b> (3): 032338. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1605.07197">1605.07197</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2017PhRvA..95c2338O">2017PhRvA..95c2338O</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevA.95.032338">10.1103/PhysRevA.95.032338</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2469-9926">2469-9926</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:55579588">55579588</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+A&rft.atitle=Quantum+computation+with+realistic+magic-state+factories&rft.volume=95&rft.issue=3&rft.pages=032338&rft.date=2017-03-31&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A55579588%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2017PhRvA..95c2338O&rft_id=info%3Aarxiv%2F1605.07197&rft.issn=2469-9926&rft_id=info%3Adoi%2F10.1103%2FPhysRevA.95.032338&rft.aulast=O%27Gorman&rft.aufirst=Joe&rft.au=Campbell%2C+Earl+T.&rft_id=https%3A%2F%2Flink.aps.org%2Fdoi%2F10.1103%2FPhysRevA.95.032338&rfr_id=info%3Asid%2Fen.wikipedia.org%3ANoisy+intermediate-scale+quantum+era" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMaria_Korolov" class="citation web cs1">Maria Korolov. <a rel="nofollow" class="external text" href="https://www.networkworld.com/article/2085751/what-microsofts-error-correction-milestone-means-for-usable-quantum-computing.html">"What Microsoft's error-correction milestone means for usable quantum computing"</a>. <i>Network World</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2024-07-01</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Network+World&rft.atitle=What+Microsoft%E2%80%99s+error-correction+milestone+means+for+usable+quantum+computing&rft.au=Maria+Korolov&rft_id=https%3A%2F%2Fwww.networkworld.com%2Farticle%2F2085751%2Fwhat-microsofts-error-correction-milestone-means-for-usable-quantum-computing.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ANoisy+intermediate-scale+quantum+era" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Noisy_intermediate-scale_quantum_era&action=edit&section=5" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" 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class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 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title="Quantum information science">Quantum information science</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">General</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/DiVincenzo%27s_criteria" title="DiVincenzo's criteria">DiVincenzo's criteria</a></li> <li><a class="mw-selflink selflink">NISQ era</a></li> <li><a href="/wiki/Quantum_computing" title="Quantum computing">Quantum computing</a> <ul><li><a href="/wiki/Timeline_of_quantum_computing_and_communication" title="Timeline of quantum computing and communication">timeline</a></li></ul></li> <li><a href="/wiki/Quantum_information" title="Quantum information">Quantum information</a></li> <li><a href="/wiki/Quantum_programming" title="Quantum programming">Quantum programming</a></li> <li><a href="/wiki/Quantum_simulator" title="Quantum simulator">Quantum simulation</a></li> <li><a href="/wiki/Qubit" title="Qubit">Qubit</a> <ul><li><a href="/wiki/Physical_and_logical_qubits" title="Physical and logical qubits">physical vs. logical</a></li></ul></li> <li><a href="/wiki/List_of_quantum_processors" title="List of quantum processors">Quantum processors</a> <ul><li><a href="/wiki/Cloud-based_quantum_computing" title="Cloud-based quantum computing">cloud-based</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theorems</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bell%27s_theorem" title="Bell's theorem">Bell's</a></li> <li><a href="/wiki/Eastin%E2%80%93Knill_theorem" title="Eastin–Knill theorem">Eastin–Knill</a></li> <li><a href="/wiki/Gleason%27s_theorem" title="Gleason's theorem">Gleason's</a></li> <li><a href="/wiki/Gottesman%E2%80%93Knill_theorem" title="Gottesman–Knill theorem">Gottesman–Knill</a></li> <li><a href="/wiki/Holevo%27s_theorem" title="Holevo's theorem">Holevo's</a></li> <li><a href="/wiki/No-broadcasting_theorem" title="No-broadcasting theorem">No-broadcasting</a></li> <li><a href="/wiki/No-cloning_theorem" title="No-cloning theorem">No-cloning</a></li> <li><a href="/wiki/No-communication_theorem" title="No-communication theorem">No-communication</a></li> <li><a href="/wiki/No-deleting_theorem" title="No-deleting theorem">No-deleting</a></li> <li><a href="/wiki/No-hiding_theorem" title="No-hiding theorem">No-hiding</a></li> <li><a href="/wiki/No-teleportation_theorem" title="No-teleportation theorem">No-teleportation</a></li> <li><a href="/wiki/PBR_theorem" class="mw-redirect" title="PBR theorem">PBR</a></li> <li><a href="/wiki/Quantum_speed_limit_theorems" class="mw-redirect" title="Quantum speed limit theorems">Quantum speed limit</a></li> <li><a href="/wiki/Threshold_theorem" title="Threshold theorem">Threshold</a></li> <li><a href="/wiki/Solovay%E2%80%93Kitaev_theorem" title="Solovay–Kitaev theorem">Solovay–Kitaev</a></li> <li><a href="/wiki/Schr%C3%B6dinger%E2%80%93HJW_theorem" title="Schrödinger–HJW theorem">Purification</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Quantum<br />communication</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Classical_capacity" title="Classical capacity">Classical capacity</a> <ul><li><a href="/wiki/Entanglement-assisted_classical_capacity" title="Entanglement-assisted classical capacity">entanglement-assisted</a></li> <li><a href="/wiki/Quantum_capacity" title="Quantum capacity">quantum capacity</a></li></ul></li> <li><a href="/wiki/Entanglement_distillation" title="Entanglement distillation">Entanglement distillation</a></li> <li><a href="/wiki/Monogamy_of_entanglement" title="Monogamy of entanglement">Monogamy of entanglement</a></li> <li><a href="/wiki/LOCC" title="LOCC">LOCC</a></li> <li><a href="/wiki/Quantum_channel" title="Quantum channel">Quantum channel</a> <ul><li><a href="/wiki/Quantum_network" title="Quantum network">quantum network</a></li></ul></li> <li><a href="/wiki/Quantum_teleportation" title="Quantum teleportation">Quantum teleportation</a> <ul><li><a href="/wiki/Quantum_gate_teleportation" title="Quantum gate teleportation">quantum gate teleportation</a></li></ul></li> <li><a href="/wiki/Superdense_coding" title="Superdense coding">Superdense coding</a></li></ul> </div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Quantum_cryptography" scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Quantum_cryptography" title="Quantum cryptography">Quantum cryptography</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Post-quantum_cryptography" title="Post-quantum cryptography">Post-quantum cryptography</a></li> <li><a href="/wiki/Quantum_coin_flipping" title="Quantum coin flipping">Quantum coin flipping</a></li> <li><a href="/wiki/Quantum_money" title="Quantum money">Quantum money</a></li> <li><a href="/wiki/Quantum_key_distribution" title="Quantum key distribution">Quantum key distribution</a> <ul><li><a href="/wiki/BB84" title="BB84">BB84</a></li> <li><a href="/wiki/SARG04" title="SARG04">SARG04</a></li> <li><a href="/wiki/List_of_quantum_key_distribution_protocols" title="List of quantum key distribution protocols">other protocols</a></li></ul></li> <li><a href="/wiki/Quantum_secret_sharing" title="Quantum secret sharing">Quantum secret sharing</a></li></ul> </div></td></tr></tbody></table><div> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Quantum_algorithm" title="Quantum algorithm">Quantum algorithms</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Amplitude_amplification" title="Amplitude amplification">Amplitude amplification</a></li> <li><a href="/wiki/Bernstein%E2%80%93Vazirani_algorithm" title="Bernstein–Vazirani algorithm">Bernstein–Vazirani</a></li> <li><a href="/wiki/BHT_algorithm" title="BHT algorithm">BHT</a></li> <li><a href="/wiki/Boson_sampling" title="Boson sampling">Boson sampling</a></li> <li><a href="/wiki/Deutsch%E2%80%93Jozsa_algorithm" title="Deutsch–Jozsa algorithm">Deutsch–Jozsa</a></li> <li><a href="/wiki/Grover%27s_algorithm" title="Grover's algorithm">Grover's</a></li> <li><a href="/wiki/HHL_algorithm" title="HHL algorithm">HHL</a></li> <li><a href="/wiki/Hidden_subgroup_problem" title="Hidden subgroup problem">Hidden subgroup</a></li> <li><a href="/wiki/Quantum_annealing" title="Quantum annealing">Quantum annealing</a></li> <li><a href="/wiki/Quantum_counting_algorithm" title="Quantum counting algorithm">Quantum counting</a></li> <li><a href="/wiki/Quantum_Fourier_transform" title="Quantum Fourier transform">Quantum Fourier transform</a></li> <li><a href="/wiki/Quantum_optimization_algorithms" title="Quantum optimization algorithms">Quantum optimization</a></li> <li><a href="/wiki/Quantum_phase_estimation_algorithm" title="Quantum phase estimation algorithm">Quantum phase estimation</a></li> <li><a href="/wiki/Shor%27s_algorithm" title="Shor's algorithm">Shor's</a></li> <li><a href="/wiki/Simon%27s_problem" title="Simon's problem">Simon's</a></li> <li><a href="/wiki/Variational_quantum_eigensolver" title="Variational quantum eigensolver">VQE</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Quantum_complexity_theory" title="Quantum complexity theory">Quantum<br />complexity theory</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/BQP" title="BQP">BQP</a></li> <li><a href="/wiki/Exact_quantum_polynomial_time" title="Exact quantum polynomial time">EQP</a></li> <li><a href="/wiki/QIP_(complexity)" title="QIP (complexity)">QIP</a></li> <li><a href="/wiki/QMA" title="QMA">QMA</a></li> <li><a href="/wiki/PostBQP" title="PostBQP">PostBQP</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Quantum <br /> processor benchmarks</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Quantum_supremacy" title="Quantum supremacy">Quantum supremacy</a></li> <li><a href="/wiki/Quantum_volume" title="Quantum volume">Quantum volume</a></li> <li><a href="/wiki/Randomized_benchmarking" title="Randomized benchmarking">Randomized benchmarking</a> <ul><li><a href="/wiki/Cross-entropy_benchmarking" title="Cross-entropy benchmarking">XEB</a></li></ul></li> <li><a href="/wiki/Relaxation_(NMR)" title="Relaxation (NMR)">Relaxation times</a> <ul><li><a href="/wiki/Spin%E2%80%93lattice_relaxation" title="Spin–lattice relaxation"><i>T</i><sub>1</sub></a></li> <li><a href="/wiki/Spin%E2%80%93spin_relaxation" title="Spin–spin relaxation"><i>T</i><sub>2</sub></a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Quantum<br /><a href="/wiki/Model_of_computation" title="Model of computation">computing models</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Adiabatic_quantum_computation" title="Adiabatic quantum computation">Adiabatic quantum computation</a></li> <li><a href="/wiki/Continuous-variable_quantum_information" title="Continuous-variable quantum information">Continuous-variable quantum information</a></li> <li><a href="/wiki/One-way_quantum_computer" title="One-way quantum computer">One-way quantum computer</a> <ul><li><a href="/wiki/Cluster_state" title="Cluster state">cluster state</a></li></ul></li> <li><a href="/wiki/Quantum_circuit" title="Quantum circuit">Quantum circuit</a> <ul><li><a href="/wiki/Quantum_logic_gate" title="Quantum logic gate">quantum logic gate</a></li></ul></li> <li><a href="/wiki/Quantum_machine_learning" title="Quantum machine learning">Quantum machine learning</a> <ul><li><a href="/wiki/Quantum_neural_network" title="Quantum neural network">quantum neural network</a></li></ul></li> <li><a href="/wiki/Quantum_Turing_machine" title="Quantum Turing machine">Quantum Turing machine</a></li> <li><a href="/wiki/Topological_quantum_computer" title="Topological quantum computer">Topological quantum computer</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Quantum_error_correction" title="Quantum error correction">Quantum<br />error correction</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>Codes <ul><li><a href="/wiki/CSS_code" title="CSS code">CSS</a></li> <li><a href="/wiki/Quantum_convolutional_code" title="Quantum convolutional code">quantum convolutional</a></li> <li><a href="/wiki/Stabilizer_code" title="Stabilizer code">stabilizer</a></li> <li><a href="/wiki/Shor_code" class="mw-redirect" title="Shor code">Shor</a></li> <li><a href="/wiki/Bacon%E2%80%93Shor_code" title="Bacon–Shor code">Bacon–Shor</a></li> <li><a href="/wiki/Steane_code" title="Steane code">Steane</a></li> <li><a href="/wiki/Toric_code" title="Toric code">Toric</a></li> <li><a href="/wiki/Gnu_code" title="Gnu code"><i>gnu</i></a></li></ul></li> <li><a href="/wiki/Entanglement-assisted_stabilizer_formalism" title="Entanglement-assisted stabilizer formalism">Entanglement-assisted</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Physical<br />implementations</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Quantum_optics" title="Quantum optics">Quantum optics</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cavity_quantum_electrodynamics" title="Cavity quantum electrodynamics">Cavity QED</a></li> <li><a href="/wiki/Circuit_quantum_electrodynamics" title="Circuit quantum electrodynamics">Circuit QED</a></li> <li><a href="/wiki/Linear_optical_quantum_computing" title="Linear optical quantum computing">Linear optical QC</a></li> <li><a href="/wiki/KLM_protocol" title="KLM protocol">KLM protocol</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Ultracold_atom" title="Ultracold atom">Ultracold atoms</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Neutral_atom_quantum_computer" title="Neutral atom quantum computer">Neutral atom QC</a></li> <li><a href="/wiki/Trapped-ion_quantum_computer" title="Trapped-ion quantum computer">Trapped-ion QC</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Spin_(physics)" title="Spin (physics)">Spin</a>-based</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Kane_quantum_computer" title="Kane quantum computer">Kane QC</a></li> <li><a href="/wiki/Spin_qubit_quantum_computer" title="Spin qubit quantum computer">Spin qubit QC</a></li> <li><a href="/wiki/Nitrogen-vacancy_center" title="Nitrogen-vacancy center">NV center</a></li> <li><a href="/wiki/Nuclear_magnetic_resonance_quantum_computer" title="Nuclear magnetic resonance quantum computer">NMR QC</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Superconducting_quantum_computing" title="Superconducting quantum computing">Superconducting</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Charge_qubit" title="Charge qubit">Charge qubit</a></li> <li><a href="/wiki/Flux_qubit" title="Flux qubit">Flux qubit</a></li> <li><a href="/wiki/Phase_qubit" title="Phase qubit">Phase qubit</a></li> <li><a href="/wiki/Transmon" title="Transmon">Transmon</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Quantum_programming" title="Quantum programming">Quantum<br />programming</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/OpenQASM" title="OpenQASM">OpenQASM</a>–<a href="/wiki/Qiskit" title="Qiskit">Qiskit</a>–<a href="/wiki/IBM_Quantum_Experience" class="mw-redirect" title="IBM Quantum Experience">IBM QX</a></li> <li><a href="/wiki/Quil_(instruction_set_architecture)" title="Quil (instruction set architecture)">Quil</a>–<a href="/wiki/Rigetti_Computing" title="Rigetti Computing">Forest/Rigetti QCS</a></li> <li><a href="/wiki/Cirq" title="Cirq">Cirq</a></li> <li><a href="/wiki/Q_Sharp" title="Q Sharp">Q#</a></li> <li><a href="/wiki/Libquantum" title="Libquantum">libquantum</a></li> <li><a href="/wiki/Quantum_programming" title="Quantum programming">many others...</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Quantum_information_science" title="Category:Quantum information science">Quantum information science</a></li> <li><span class="noviewer" typeof="mw:File"><span title="Template"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Symbol_template_class_pink.svg/16px-Symbol_template_class_pink.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Symbol_template_class_pink.svg/23px-Symbol_template_class_pink.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/83/Symbol_template_class_pink.svg/31px-Symbol_template_class_pink.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Template:Quantum_mechanics_topics" title="Template:Quantum mechanics topics">Quantum mechanics topics</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="History_of_physics_(timeline)" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:History_of_physics" title="Template:History of physics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:History_of_physics" title="Template talk:History of physics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:History_of_physics" title="Special:EditPage/Template:History of physics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="History_of_physics_(timeline)" style="font-size:114%;margin:0 4em"><a href="/wiki/History_of_physics" title="History of physics">History of physics</a> (<a href="/wiki/Timeline_of_fundamental_physics_discoveries" title="Timeline of fundamental physics discoveries">timeline</a>)</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Classical_physics" title="Classical physics">Classical physics</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/History_of_astronomy" title="History of astronomy">Astronomy</a> <ul><li><a href="/wiki/Timeline_of_astronomy" title="Timeline of astronomy">timeline</a></li></ul></li> <li><a href="/wiki/History_of_electromagnetic_theory" title="History of electromagnetic theory">Electromagnetism</a> <ul><li><a href="/wiki/Timeline_of_electromagnetism_and_classical_optics" title="Timeline of electromagnetism and classical optics">timeline</a></li> <li><a href="/wiki/History_of_electrical_engineering" title="History of electrical engineering">Electrical engineering</a></li> <li><a href="/wiki/History_of_Maxwell%27s_equations" title="History of Maxwell's equations">Maxwell's equations</a></li></ul></li> <li><a href="/wiki/History_of_fluid_mechanics" title="History of fluid mechanics">Fluid mechanics</a> <ul><li><a href="/wiki/Timeline_of_fluid_and_continuum_mechanics" title="Timeline of fluid and continuum mechanics">timeline</a></li> <li><a href="/wiki/History_of_aerodynamics" title="History of aerodynamics">Aerodynamics</a></li></ul></li> <li><a href="/wiki/History_of_classical_field_theory" title="History of classical field theory">Field theory</a></li> <li><a href="/wiki/History_of_gravitational_theory" title="History of gravitational theory">Gravitational theory</a> <ul><li><a href="/wiki/Timeline_of_gravitational_physics_and_relativity" title="Timeline of gravitational physics and relativity">timeline</a></li></ul></li> <li><a href="/wiki/History_of_materials_science" title="History of materials science">Material science</a> <ul><li><a href="/wiki/Timeline_of_materials_technology" title="Timeline of materials technology">timeline</a></li> <li><a href="/wiki/History_of_metamaterials" title="History of metamaterials">Metamaterials</a></li></ul></li> <li><a href="/wiki/History_of_classical_mechanics" title="History of classical mechanics">Mechanics</a> <ul><li><a href="/wiki/Timeline_of_classical_mechanics" title="Timeline of classical mechanics">timeline</a></li> <li><a href="/wiki/History_of_variational_principles_in_physics" title="History of variational principles in physics">Variational principles</a></li></ul></li> <li><a href="/wiki/History_of_optics" title="History of optics">Optics</a> <ul><li><a href="/wiki/History_of_spectroscopy" title="History of spectroscopy">Spectroscopy</a></li></ul></li> <li><a href="/wiki/History_of_thermodynamics" title="History of thermodynamics">Thermodynamics</a> <ul><li><a href="/wiki/Timeline_of_thermodynamics" title="Timeline of thermodynamics">timeline</a></li> <li><a href="/wiki/History_of_energy" title="History of energy">Energy</a></li> <li><a href="/wiki/History_of_entropy" title="History of entropy">Entropy</a></li> <li><a href="/wiki/History_of_perpetual_motion_machines" title="History of perpetual motion machines">Perpetual motion</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Modern_physics" title="Modern physics">Modern physics</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>Computational physics <ul><li><a href="/wiki/Timeline_of_computational_physics" title="Timeline of computational physics">timeline</a></li></ul></li> <li>Condensed matter <ul><li><a href="/wiki/Timeline_of_condensed_matter_physics" title="Timeline of condensed matter physics">timeline</a></li> <li><a href="/wiki/History_of_superconductivity" title="History of superconductivity">Superconductivity</a></li></ul></li> <li>Cosmology <ul><li><a href="/wiki/Timeline_of_cosmological_theories" title="Timeline of cosmological theories">timeline</a></li> <li><a href="/wiki/History_of_the_Big_Bang_theory" title="History of the Big Bang theory">Big Bang theory</a></li></ul></li> <li><a href="/wiki/History_of_general_relativity" title="History of general relativity">General relativity</a> <ul><li><a href="/wiki/Tests_of_general_relativity" title="Tests of general relativity">tests</a></li></ul></li> <li><a href="/wiki/History_of_geophysics" title="History of geophysics">Geophysics</a></li> <li>Nuclear physics <ul><li><a href="/wiki/Discovery_of_nuclear_fission" title="Discovery of nuclear fission">Fission</a></li> <li><a href="/wiki/History_of_nuclear_fusion" title="History of nuclear fusion">Fusion</a></li> <li><a href="/wiki/History_of_nuclear_power" title="History of nuclear power">Power</a></li> <li><a href="/wiki/History_of_nuclear_weapons" title="History of nuclear weapons">Weapons</a></li></ul></li> <li><a href="/wiki/History_of_quantum_mechanics" title="History of quantum mechanics">Quantum mechanics</a> <ul><li><a href="/wiki/Timeline_of_quantum_mechanics" title="Timeline of quantum mechanics">timeline</a></li> <li><a href="/wiki/History_of_atomic_theory" title="History of atomic theory">Atoms</a></li> <li><a href="/wiki/History_of_molecular_theory" title="History of molecular theory">Molecules</a></li> <li><a href="/wiki/History_of_quantum_field_theory" title="History of quantum field theory">Quantum field theory</a></li></ul></li> <li><a href="/wiki/History_of_subatomic_physics" title="History of subatomic physics">Subatomic physics</a> <ul><li><a href="/wiki/Timeline_of_atomic_and_subatomic_physics" title="Timeline of atomic and subatomic physics">timeline</a></li></ul></li> <li><a href="/wiki/History_of_special_relativity" title="History of special relativity">Special relativity</a> <ul><li><a href="/wiki/Timeline_of_special_relativity_and_the_speed_of_light" title="Timeline of special relativity and the speed of light">timeline</a></li> <li><a href="/wiki/History_of_Lorentz_transformations" title="History of Lorentz transformations">Lorentz transformations</a></li> <li><a href="/wiki/Tests_of_special_relativity" title="Tests of special relativity">tests</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Recent developments</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>Quantum information <ul><li><a href="/wiki/Timeline_of_quantum_computing_and_communication" title="Timeline of quantum computing and communication">timeline</a></li></ul></li> <li><a href="/wiki/History_of_loop_quantum_gravity" title="History of loop quantum gravity">Loop quantum gravity</a></li> <li><a href="/wiki/History_of_nanotechnology" title="History of nanotechnology">Nanotechnology</a></li> <li><a href="/wiki/History_of_string_theory" title="History of string theory">String theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">On specific discoveries</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Discovery_of_cosmic_microwave_background_radiation" title="Discovery of cosmic microwave background radiation">Cosmic microwave background</a></li> <li><a href="/wiki/Discovery_of_graphene" title="Discovery of graphene">Graphene</a></li> <li><a href="/wiki/First_observation_of_gravitational_waves" title="First observation of gravitational waves">Gravitational waves</a></li> <li>Subatomic particles <ul><li><a href="/wiki/Timeline_of_particle_discoveries" title="Timeline of particle discoveries">timeline</a></li> <li><a href="/wiki/Search_for_the_Higgs_boson" title="Search for the Higgs boson">Higgs boson</a></li> <li><a href="/wiki/Discovery_of_the_neutron" title="Discovery of the neutron">Neutron</a></li></ul></li> <li><a href="/wiki/R%C3%B8mer%27s_determination_of_the_speed_of_light" title="Rømer's determination of the speed of light">Speed of light</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">By periods</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Copernican_Revolution" title="Copernican Revolution">Copernican Revolution</a></li> <li><a href="/wiki/Golden_age_of_physics" title="Golden age of physics">Golden age of physics</a></li> <li><a href="/wiki/Golden_age_of_cosmology" title="Golden age of cosmology">Golden age of cosmology</a></li> <li><a href="/wiki/Physics_in_the_medieval_Islamic_world" title="Physics in the medieval Islamic world">Medieval Islamic world</a> <ul><li><a href="/wiki/Astronomy_in_the_medieval_Islamic_world" title="Astronomy in the medieval Islamic world">Astronomy</a></li></ul></li> <li><a class="mw-selflink selflink">Noisy intermediate-scale quantum era</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">By groups</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Harvard_Computers" title="Harvard Computers">Harvard Computers</a></li> <li><a href="/wiki/The_Martians_(scientists)" title="The Martians (scientists)">The Martians</a></li> <li><a href="/wiki/Oxford_Calculators" title="Oxford Calculators">Oxford Calculators</a></li> <li><a href="/wiki/Via_Panisperna_boys" title="Via Panisperna boys">Via Panisperna boys</a></li> <li><a href="/wiki/Women_in_physics" title="Women in physics">Women in physics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Scientific disputes</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bohr%E2%80%93Einstein_debates" title="Bohr–Einstein debates">Bohr–Einstein</a></li> <li><a href="/wiki/Chandrasekhar%E2%80%93Eddington_dispute" title="Chandrasekhar–Eddington dispute">Chandrasekhar–Eddington</a></li> <li><a href="/wiki/Galileo_affair" title="Galileo affair">Galileo affair</a></li> <li><a href="/wiki/Leibniz%E2%80%93Newton_calculus_controversy" title="Leibniz–Newton calculus controversy">Leibniz–Newton</a></li> <li><a href="/wiki/Mechanical_equivalent_of_heat" title="Mechanical equivalent of heat">Joule–von Mayer</a></li> <li><a href="/wiki/Great_Debate_(astronomy)" title="Great Debate (astronomy)">Shapley–Curtis</a></li> <li>Relativity priority <ul><li><a href="/wiki/Relativity_priority_dispute" title="Relativity priority dispute">Special relativity</a></li> <li><a href="/wiki/General_relativity_priority_dispute" title="General relativity priority dispute">General relativity</a></li></ul></li> <li><a href="/wiki/Transfermium_Wars" title="Transfermium Wars">Transfermium Wars</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" 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