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class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/e/ec/Quantum_Simulator_Crystal.jpg 1.5x" data-file-width="325" data-file-height="325" /></a><figcaption>In this photograph of a quantum simulator crystal the ions <a href="/wiki/Fluorescence" title="Fluorescence">are fluorescing</a>, indicating the qubits are all in the same state (either "1" or "0"). Under the right experimental conditions, the ion crystal spontaneously forms this nearly perfect triangular <a href="/wiki/Crystal_structure" title="Crystal structure">lattice</a> structure. <i>Credit: Britton/NIST</i></figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Quantum_Simulator_Illustration_(150_dpi).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Quantum_Simulator_Illustration_%28150_dpi%29.jpg/220px-Quantum_Simulator_Illustration_%28150_dpi%29.jpg" decoding="async" width="220" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Quantum_Simulator_Illustration_%28150_dpi%29.jpg/330px-Quantum_Simulator_Illustration_%28150_dpi%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Quantum_Simulator_Illustration_%28150_dpi%29.jpg/440px-Quantum_Simulator_Illustration_%28150_dpi%29.jpg 2x" data-file-width="1200" data-file-height="439" /></a><figcaption>Trapped ion quantum simulator illustration: The heart of the simulator is a two-dimensional crystal of beryllium ions (blue spheres in the graphic); the outermost electron of each ion is a quantum bit (qubit, red arrows). The ions are confined by a large magnetic field in a device called a Penning trap (not shown). Inside the trap the crystal rotates clockwise. <i>Credit: Britton/NIST</i></figcaption></figure> <p><b>Quantum simulators</b> permit the study of a <a href="/wiki/Quantum_system" class="mw-redirect" title="Quantum system">quantum system</a> in a programmable fashion. In this instance, simulators are special purpose devices designed to provide insight about specific <a href="/wiki/Physics" title="Physics">physics</a> problems.<sup id="cite_ref-Johnson2014_1-0" class="reference"><a href="#cite_note-Johnson2014-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-nist-pg_2-0" class="reference"><a href="#cite_note-nist-pg-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Britton_3-0" class="reference"><a href="#cite_note-Britton-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Quantum simulators may be contrasted with generally programmable "digital" <a href="/wiki/Quantum_computing" title="Quantum computing">quantum computers</a>, which would be capable of solving a wider class of quantum problems. </p><p>A <b>universal quantum simulator</b> is a <a href="/wiki/Quantum_computer" class="mw-redirect" title="Quantum computer">quantum computer</a> proposed by <a href="/wiki/Yuri_Manin" title="Yuri Manin">Yuri Manin</a> in 1980<sup id="cite_ref-manin1980vychislimoe_4-0" class="reference"><a href="#cite_note-manin1980vychislimoe-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/Richard_Feynman" title="Richard Feynman">Richard Feynman</a> in 1982.<sup id="cite_ref-f82_5-0" class="reference"><a href="#cite_note-f82-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>A quantum system may be simulated by either a <a href="/wiki/Turing_machine" title="Turing machine">Turing machine</a> or a <a href="/wiki/Quantum_Turing_machine" title="Quantum Turing machine">quantum Turing machine</a>, as a classical <a href="/wiki/Turing_machine" title="Turing machine">Turing machine</a> is able to simulate a <a href="/wiki/Universal_quantum_computer" class="mw-redirect" title="Universal quantum computer">universal quantum computer</a> (and therefore any simpler quantum simulator), meaning they are equivalent from the point of view of <a href="/wiki/Computability_theory" title="Computability theory">computability theory</a>. The simulation of quantum physics by a classical computer has been shown to be inefficient.<sup id="cite_ref-:22_6-0" class="reference"><a href="#cite_note-:22-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> In other words, quantum computers provide no additional <i>power</i> over classical computers in terms of computability, but it is suspected that they can solve certain problems faster than classical computers, meaning they may be in different <a href="/wiki/Complexity_class" title="Complexity class">complexity classes</a>, which is why quantum Turing machines are useful for simulating quantum systems. This is known as <a href="/wiki/Quantum_supremacy" title="Quantum supremacy">quantum supremacy</a>, the idea that there are problems only quantum Turing machines can solve in any <i>feasible</i> amount of time. </p><p>A <a href="/wiki/Quantum_system" class="mw-redirect" title="Quantum system">quantum system</a> of many particles could be simulated by a quantum computer using a number of <a href="/wiki/Qubit" title="Qubit">quantum bits</a> similar to the number of particles in the original system.<sup id="cite_ref-f82_5-1" class="reference"><a href="#cite_note-f82-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> This has been extended to much larger classes of quantum systems.<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><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><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><p>Quantum simulators have been realized on a number of experimental platforms, including systems of <a href="/wiki/Ultracold_atom" title="Ultracold atom">ultracold quantum gases</a>, polar molecules, trapped ions, photonic systems, quantum dots, and superconducting circuits.<sup id="cite_ref-nat_phys_insight_11-0" class="reference"><a href="#cite_note-nat_phys_insight-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Solving_physics_problems">Solving physics problems</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_simulator&action=edit&section=1" title="Edit section: Solving physics problems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Many important problems in physics, especially <a href="/wiki/Thermodynamics" title="Thermodynamics">low-temperature physics</a> and <a href="/wiki/Many-body_theory" class="mw-redirect" title="Many-body theory">many-body physics</a>, remain poorly understood because the underlying <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a> is vastly complex. Conventional computers, including supercomputers, are inadequate for simulating quantum systems with as few as 30 particles because the dimension of the Hilbert space grows exponentially with particle number.<sup id="cite_ref-Lloyd1996_12-0" class="reference"><a href="#cite_note-Lloyd1996-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> Better computational tools are needed to understand and rationally design materials whose properties are believed to depend on the collective <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum behavior</a> of hundreds of particles.<sup id="cite_ref-nist-pg_2-1" class="reference"><a href="#cite_note-nist-pg-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Britton_3-1" class="reference"><a href="#cite_note-Britton-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Quantum simulators provide an alternative route to understanding the properties of these systems. These simulators create clean realizations of specific systems of interest, which allows precise realizations of their properties. Precise control over and broad tunability of parameters of the system allows the influence of various parameters to be cleanly disentangled. </p><p>Quantum simulators can solve problems which are difficult to simulate on classical computers because they directly exploit quantum properties of real particles. In particular, they exploit a property of quantum mechanics called <a href="/wiki/Quantum_superposition" title="Quantum superposition">superposition</a>, wherein a <a href="/wiki/Quantum_particle" class="mw-redirect" title="Quantum particle">quantum particle</a> is made to be in two distinct states at the same time, for example, aligned and anti-aligned with an external magnetic field. Crucially, simulators also take advantage of a second quantum property called <a href="/wiki/Quantum_entanglement" title="Quantum entanglement">entanglement</a>, allowing the behavior of even physically well separated particles to be correlated.<sup id="cite_ref-nist-pg_2-2" class="reference"><a href="#cite_note-nist-pg-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Britton_3-2" class="reference"><a href="#cite_note-Britton-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-zoler_13-0" class="reference"><a href="#cite_note-zoler-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>Recently quantum simulators have been used to obtain <a href="/wiki/Time_crystal#Experiments" title="Time crystal">time crystals</a><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><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> and <a href="/wiki/Quantum_spin_liquid#Toric_code_type" title="Quantum spin liquid">quantum spin liquids</a>.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Trapped-ion_simulators">Trapped-ion simulators</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_simulator&action=edit&section=2" title="Edit section: Trapped-ion simulators"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Ion_trap" title="Ion trap">Ion trap</a> based system forms an ideal setting for simulating interactions in quantum spin models.<sup id="cite_ref-monroe21a_18-0" class="reference"><a href="#cite_note-monroe21a-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> A <a href="/wiki/Ion_trap" title="Ion trap">trapped-ion</a> simulator, built by a team that included the <a href="/wiki/NIST" class="mw-redirect" title="NIST">NIST</a> can engineer and control interactions among hundreds of <a href="/wiki/Quantum_bit" class="mw-redirect" title="Quantum bit">quantum bits</a> (qubits).<sup id="cite_ref-britton12a_19-0" class="reference"><a href="#cite_note-britton12a-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> Previous endeavors were unable to go beyond 30 quantum bits. The capability of this simulator is 10 times more than previous devices. It has passed a series of important benchmarking tests that indicate a capability to solve problems in material science that are impossible to model on conventional computers. </p><p>The trapped-ion simulator consists of a tiny, single-plane crystal of hundreds of <a href="/wiki/Beryllium" title="Beryllium">beryllium ions</a>, less than 1 millimeter in diameter, hovering inside a device called a <a href="/wiki/Penning_trap" title="Penning trap">Penning trap</a>. The outermost <a href="/wiki/Electron" title="Electron">electron</a> of each ion acts as a tiny <a href="/w/index.php?title=Quantum_magnet&action=edit&redlink=1" class="new" title="Quantum magnet (page does not exist)">quantum magnet</a> and is used as a qubit, the quantum equivalent of a “1” or a “0” in a conventional computer. In the benchmarking experiment, physicists used laser beams to cool the ions to near absolute zero. Carefully timed microwave and <a href="/wiki/Laser_pulse" class="mw-redirect" title="Laser pulse">laser pulses</a> then caused the qubits to interact, mimicking the quantum behavior of materials otherwise very difficult to study in the laboratory. Although the two systems may outwardly appear dissimilar, their behavior is engineered to be mathematically identical. In this way, simulators allow researchers to vary parameters that could not be changed in natural solids, such as atomic <a href="/wiki/Lattice_spacing" class="mw-redirect" title="Lattice spacing">lattice spacing</a> and geometry. </p><p>Friedenauer et al., adiabatically manipulated 2 spins, showing their separation into ferromagnetic and antiferromagnetic states.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> Kim et al., extended the trapped ion quantum simulator to 3 spins, with global antiferromagnetic Ising interactions featuring frustration and showing the link between frustration and entanglement<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> and Islam et al., used adiabatic quantum simulation to demonstrate the sharpening of a <a href="/wiki/Phase_transition" title="Phase transition">phase transition</a> between paramagnetic and ferromagnetic ordering as the number of spins increased from 2 to 9.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> Barreiro et al. created a digital quantum simulator of interacting spins with up to 5 trapped ions by coupling to an open reservoir<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> and Lanyon <i>et al.</i> demonstrated digital quantum simulation with up to 6 ions.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> Islam, et al., demonstrated adiabatic quantum simulation of the transverse Ising model with variable (long) range interactions with up to 18 trapped ion spins, showing control of the level of spin frustration by adjusting the antiferromagnetic interaction range.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> Britton, et al. from NIST has experimentally benchmarked Ising interactions in a system of hundreds of qubits for studies of quantum magnetism.<sup id="cite_ref-britton12a_19-1" class="reference"><a href="#cite_note-britton12a-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> Pagano, et al., reported a new cryogenic ion trapping system designed for long time storage of large ion chains demonstrating coherent one and two-qubit operations for chains of up to 44 ions.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> Joshi, et al., probed the quantum dynamics of 51 individually controlled ions, realizing a long-range interacting spin chain.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Ultracold_atom_simulators">Ultracold atom simulators</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_simulator&action=edit&section=3" title="Edit section: Ultracold atom simulators"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Many <a href="/wiki/Ultracold_atom" title="Ultracold atom">ultracold atom</a> experiments are examples of quantum simulators. These include experiments studying <a href="/wiki/Bose-Hubbard_model" class="mw-redirect" title="Bose-Hubbard model">bosons</a> or <a href="/wiki/Fermi-Hubbard_model" class="mw-redirect" title="Fermi-Hubbard model">fermions</a> in <a href="/wiki/Optical_lattice" title="Optical lattice">optical lattices</a>, the unitary Fermi gas, <a href="/wiki/Rydberg_atom" title="Rydberg atom">Rydberg atom</a> arrays in <a href="/wiki/Optical_tweezers" title="Optical tweezers">optical tweezers</a>. A common thread for these experiments is the capability of realizing generic Hamiltonians, such as the <a href="/wiki/Hubbard_model" title="Hubbard model">Hubbard</a> or <a href="/wiki/Ising_model" title="Ising model">transverse-field Ising</a> Hamiltonian. Major aims of these experiments include identifying low-temperature phases or tracking out-of-equilibrium dynamics for various models, problems which are theoretically and numerically intractable.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> Other experiments have realized condensed matter models in regimes which are difficult or impossible to realize with conventional materials, such as the <a href="/wiki/Quantum_spin_Hall_effect" title="Quantum spin Hall effect">Haldane model</a> and the <a href="/wiki/Quantum_Hall_effect" title="Quantum Hall effect">Harper-Hofstadter model</a>.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Superconducting_qubits">Superconducting qubits</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_simulator&action=edit&section=4" title="Edit section: Superconducting qubits"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Quantum simulators using superconducting qubits fall into two main categories. First, so called <a href="/wiki/Quantum_annealing" title="Quantum annealing">quantum annealers</a> determine ground states of certain Hamiltonians after an adiabatic ramp. This approach is sometimes called <a href="/wiki/Adiabatic_quantum_computing" class="mw-redirect" title="Adiabatic quantum computing">adiabatic quantum computing</a>. Second, many systems emulate specific Hamiltonians and study their ground state properties, <a href="/wiki/Quantum_phase_transition" title="Quantum phase transition">quantum phase transitions</a>, or time dynamics.<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> Several important recent results include the realization of a <a href="/wiki/Mott_insulator" title="Mott insulator">Mott insulator</a> in a driven-dissipative <a href="/wiki/Bose-Hubbard_model" class="mw-redirect" title="Bose-Hubbard model">Bose-Hubbard system</a> and studies of phase transitions in lattices of superconducting resonators coupled to qubits.<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<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=Quantum_simulator&action=edit&section=5" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Hamiltonian_simulation" title="Hamiltonian simulation">Hamiltonian simulation</a></li> <li><a href="/wiki/Quantum_Turing_machine" title="Quantum Turing machine">Quantum Turing machine</a></li> <li><a href="/wiki/Quantum_computing" title="Quantum computing">Quantum computing</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=Quantum_simulator&action=edit&section=6" 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 .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-Johnson2014-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-Johnson2014_1-0">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFJohnsonClarkJaksch2014" class="citation journal cs1">Johnson, Tomi H.; Clark, Stephen R.; Jaksch, Dieter (2014). "What is a quantum simulator?". <i>EPJ Quantum Technology</i>. <b>1</b> (10). <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/1405.2831">1405.2831</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1140%2Fepjqt10">10.1140/epjqt10</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:120250321">120250321</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=EPJ+Quantum+Technology&rft.atitle=What+is+a+quantum+simulator%3F&rft.volume=1&rft.issue=10&rft.date=2014&rft_id=info%3Aarxiv%2F1405.2831&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A120250321%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1140%2Fepjqt10&rft.aulast=Johnson&rft.aufirst=Tomi+H.&rft.au=Clark%2C+Stephen+R.&rft.au=Jaksch%2C+Dieter&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuantum+simulator" class="Z3988"></span></span> </li> <li id="cite_note-nist-pg-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-nist-pg_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-nist-pg_2-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-nist-pg_2-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"> <span class="noviewer" typeof="mw:File"><span><img alt="Public Domain" src="//upload.wikimedia.org/wikipedia/en/thumb/6/62/PD-icon.svg/12px-PD-icon.svg.png" decoding="async" width="12" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/6/62/PD-icon.svg/18px-PD-icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/6/62/PD-icon.svg/24px-PD-icon.svg.png 2x" data-file-width="196" data-file-height="196" /></span></span> This article incorporates <a href="/wiki/Copyright_status_of_works_by_the_federal_government_of_the_United_States" title="Copyright status of works by the federal government of the United States">public domain material</a> from <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMichael_E._Newman" class="citation cs1">Michael E. Newman. <a rel="nofollow" class="external text" href="https://www.nist.gov/public_affairs/tech-beat/tb20120502.cfm/"><i>NIST Physicists Benchmark Quantum Simulator with Hundreds of Qubits</i></a>. <a href="/wiki/National_Institute_of_Standards_and_Technology" title="National Institute of Standards and Technology">National Institute of Standards and Technology</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2013-02-22</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=NIST+Physicists+Benchmark+Quantum+Simulator+with+Hundreds+of+Qubits&rft.pub=National+Institute+of+Standards+and+Technology&rft.au=Michael+E.+Newman&rft_id=https%3A%2F%2Fwww.nist.gov%2Fpublic_affairs%2Ftech-beat%2Ftb20120502.cfm%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuantum+simulator" class="Z3988"></span></span> </li> <li id="cite_note-Britton-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-Britton_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Britton_3-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Britton_3-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBrittonSawyerKeithWang2012" class="citation journal cs1">Britton, Joseph W.; Sawyer, Brian C.; Keith, Adam C.; Wang, C.-C. 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"A dissipatively stabilized Mott insulator of photons". <i>Nature</i>. <b>566</b> (7742): 51–57. <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/1807.11342">1807.11342</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/2019Natur.566...51M">2019Natur.566...51M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fs41586-019-0897-9">10.1038/s41586-019-0897-9</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/30728523">30728523</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:59606678">59606678</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=A+dissipatively+stabilized+Mott+insulator+of+photons&rft.volume=566&rft.issue=7742&rft.pages=51-57&rft.date=2019-02-06&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A59606678%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2019Natur.566...51M&rft_id=info%3Aarxiv%2F1807.11342&rft_id=info%3Apmid%2F30728523&rft_id=info%3Adoi%2F10.1038%2Fs41586-019-0897-9&rft.aulast=Ma&rft.aufirst=Ruichao&rft.au=Saxberg%2C+Brendan&rft.au=Owens%2C+Clai&rft.au=Leung%2C+Nelson&rft.au=Lu%2C+Yao&rft.au=Simon%2C+Jonathan&rft.au=Schuster%2C+David+I.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuantum+simulator" class="Z3988"></span></span> </li> <li id="cite_note-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-37">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFitzpatrickSundaresanLiKoch2017" class="citation journal cs1">Fitzpatrick, Mattias; Sundaresan, Neereja M.; Li, Andy C. Y.; Koch, Jens; Houck, Andrew A. (10 February 2017). "Observation of a Dissipative Phase Transition in a One-Dimensional Circuit QED Lattice". <i>Physical Review X</i>. <b>7</b> (1): 011016. <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/1607.06895">1607.06895</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/2017PhRvX...7a1016F">2017PhRvX...7a1016F</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%2FPhysRevX.7.011016">10.1103/PhysRevX.7.011016</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:3550701">3550701</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+X&rft.atitle=Observation+of+a+Dissipative+Phase+Transition+in+a+One-Dimensional+Circuit+QED+Lattice&rft.volume=7&rft.issue=1&rft.pages=011016&rft.date=2017-02-10&rft_id=info%3Aarxiv%2F1607.06895&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A3550701%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1103%2FPhysRevX.7.011016&rft_id=info%3Abibcode%2F2017PhRvX...7a1016F&rft.aulast=Fitzpatrick&rft.aufirst=Mattias&rft.au=Sundaresan%2C+Neereja+M.&rft.au=Li%2C+Andy+C.+Y.&rft.au=Koch%2C+Jens&rft.au=Houck%2C+Andrew+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuantum+simulator" class="Z3988"></span></span> </li> </ol></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=Quantum_simulator&action=edit&section=7" 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" href="https://web.archive.org/web/20081123183419/http://www.ceid.upatras.gr/tech_news/papers/quantum_theory.pdf">Deutsch's 1985 paper</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol 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.navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Quantum_information_science" 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"><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 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Quantum_information" title="Template:Quantum information"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Quantum_information" title="Template talk:Quantum information"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Quantum_information" title="Special:EditPage/Template:Quantum information"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Quantum_information_science" style="font-size:114%;margin:0 4em"><a href="/wiki/Quantum_information_science" 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 href="/wiki/Noisy_intermediate-scale_quantum_era" title="Noisy intermediate-scale quantum era">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 class="mw-selflink selflink">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="Emerging_technologies" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2" style="text-align: center;"><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:Emerging_technologies" title="Template:Emerging technologies"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Emerging_technologies" title="Template talk:Emerging technologies"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Emerging_technologies" title="Special:EditPage/Template:Emerging technologies"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Emerging_technologies" style="font-size:114%;margin:0 4em"><a href="/wiki/Emerging_technologies" title="Emerging technologies">Emerging technologies</a></div></th></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%">Fields</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%;text-align: center;"><a href="/wiki/Quantum_technology" class="mw-redirect" title="Quantum technology">Quantum</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/Quantum_algorithm" title="Quantum algorithm">algorithms</a></li> <li><a href="/wiki/Quantum_amplifier" title="Quantum amplifier">amplifier</a></li> <li><a href="/wiki/Quantum_bus" title="Quantum bus">bus</a></li> <li><a href="/wiki/Quantum_cellular_automaton" title="Quantum cellular automaton">cellular automata</a></li> <li><a href="/wiki/Quantum_channel" title="Quantum channel">channel</a></li> <li><a href="/wiki/Quantum_circuit" title="Quantum circuit">circuit</a></li> <li><a href="/wiki/Quantum_complexity_theory" title="Quantum complexity theory">complexity theory</a></li> <li><a href="/wiki/Quantum_computing" title="Quantum computing">computing</a></li> <li><a href="/wiki/Quantum_cryptography" title="Quantum cryptography">cryptography</a> <ul><li><a href="/wiki/Post-quantum_cryptography" title="Post-quantum cryptography">post-quantum</a></li></ul></li> <li><a href="/wiki/Quantum_dynamics" title="Quantum dynamics">dynamics</a></li> <li><a href="/wiki/Quantum_electronics" class="mw-redirect" title="Quantum electronics">electronics</a></li> <li><a href="/wiki/Quantum_error_correction" title="Quantum error correction">error correction</a></li> <li><a href="/wiki/Quantum_finite_automaton" title="Quantum finite automaton">finite automata</a></li> <li><a href="/wiki/Quantum_image_processing" title="Quantum image processing">image processing</a></li> <li><a href="/wiki/Quantum_imaging" title="Quantum imaging">imaging</a></li> <li><a href="/wiki/Quantum_information" title="Quantum information">information</a></li> <li><a href="/wiki/Quantum_key_distribution" title="Quantum key distribution">key distribution</a></li> <li><a href="/wiki/Quantum_logic" title="Quantum logic">logic</a></li> <li><a href="/wiki/Quantum_logic_clock" title="Quantum logic clock">logic clock</a></li> <li><a href="/wiki/Quantum_logic_gate" title="Quantum logic gate">logic gate</a></li> <li><a href="/wiki/Quantum_machine" title="Quantum machine">machine</a></li> <li><a href="/wiki/Quantum_machine_learning" title="Quantum machine learning">machine learning</a></li> <li><a href="/wiki/Quantum_metamaterial" title="Quantum metamaterial">metamaterial</a></li> <li><a href="/wiki/Quantum_network" title="Quantum network">network</a></li> <li><a href="/wiki/Quantum_neural_network" title="Quantum neural network">neural network</a></li> <li><a href="/wiki/Quantum_optics" title="Quantum optics">optics</a></li> <li><a href="/wiki/Quantum_programming" title="Quantum programming">programming</a></li> <li><a href="/wiki/Quantum_sensor" title="Quantum sensor">sensing</a></li> <li><a class="mw-selflink selflink">simulator</a></li> <li><a href="/wiki/Quantum_teleportation" title="Quantum teleportation">teleportation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: center;">Other</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/Acoustic_levitation" title="Acoustic levitation">Acoustic levitation</a></li> <li><a href="/wiki/Anti-gravity" title="Anti-gravity">Anti-gravity</a></li> <li><a href="/wiki/Cloak_of_invisibility" title="Cloak of invisibility">Cloak of invisibility</a></li> <li><a href="/wiki/Digital_scent_technology" title="Digital scent technology">Digital scent technology</a></li> <li><a href="/wiki/Force_field_(technology)" title="Force field (technology)">Force field</a> <ul><li><a href="/wiki/Plasma_window" title="Plasma window">Plasma window</a></li></ul></li> <li><a href="/wiki/Immersion_(virtual_reality)" title="Immersion (virtual reality)">Immersive virtual reality</a></li> <li><a href="/wiki/Magnetic_refrigeration" title="Magnetic refrigeration">Magnetic refrigeration</a></li> <li><a href="/wiki/Phased-array_optics" title="Phased-array optics">Phased-array optics</a></li> <li><a href="/wiki/Thermoacoustic_heat_engine" title="Thermoacoustic heat engine">Thermoacoustic heat engine</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-abovebelow" colspan="2" style="text-align: center;"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="List-Class article"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/d/db/Symbol_list_class.svg/16px-Symbol_list_class.svg.png" decoding="async" width="16" height="16" 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