Quantum simulator

Many important problems in physics, especially low-temperature physics and many-body physics, remain poorly understood because the underlying quantum mechanics 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.{{Cite journal

| title = Universal quantum simulators

| year = 1996

| author = Lloyd, S.

| journal = Science

| pages = 1073–8

| volume = 273

| issue = 5278

| doi = 10.1126/science.273.5278.1073

| pmid = 8688088

|bibcode = 1996Sci...273.1073L | s2cid = 43496899

}} Better computational tools are needed to understand and rationally design materials whose properties are believed to depend on the collective quantum behavior of hundreds of particles. 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.

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 superposition, wherein a quantum particle 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 entanglement, allowing the behavior of even physically well separated particles to be correlated.{{cite journal

|doi=10.1038/nphys2275

|url=http://211.144.68.84:9998/91keshi/Public/File/34/8-4/pdf/nphys2275.pdf

|bibcode=2012NatPh...8..264C

|title=Goals and opportunities in quantum simulation

|year=2012

|last1=Cirac

|first1=J. Ignacio

|last2=Zoller

|first2=Peter

|journal=Nature Physics

|volume=8

|issue=4

|pages=264–266

|s2cid=109930964

}}{{Dead link|date=February 2020 |bot=InternetArchiveBot |fix-attempted=yes }}

Recently quantum simulators have been used to obtain time crystals{{Cite journal |last1=Kyprianidis |first1=A. |last2=Machado |first2=F. |last3=Morong |first3=W. |last4=Becker |first4=P. |last5=Collins |first5=K. S. |last6=Else |first6=D. V. |last7=Feng |first7=L. |last8=Hess |first8=P. W. |last9=Nayak |first9=C. |last10=Pagano |first10=G. |last11=Yao |first11=N. Y. |date=2021-06-11 |title=Observation of a prethermal discrete time crystal |url=https://www.science.org/doi/10.1126/science.abg8102 |journal=Science |language=en |volume=372 |issue=6547 |pages=1192–1196 |arxiv=2102.01695 |bibcode=2021Sci...372.1192K |doi=10.1126/science.abg8102 |issn=0036-8075 |pmid=34112691 |s2cid=231786633}}{{Cite web |last1=S |first1=Robert |last2=ers |last3=Berkeley |first3=U. C. |date=2021-11-10 |title=Creating Time Crystals Using New Quantum Computing Architectures |url=https://scitechdaily.com/creating-time-crystals-using-new-quantum-computing-architectures/ |access-date=2021-12-27 |website=SciTechDaily |language=en-US}} and quantum spin liquids.{{Cite journal |last1=Semeghini |first1=G. |last2=Levine |first2=H. |last3=Keesling |first3=A. |last4=Ebadi |first4=S. |last5=Wang |first5=T. T. |last6=Bluvstein |first6=D. |last7=Verresen |first7=R. |last8=Pichler |first8=H. |last9=Kalinowski |first9=M. |last10=Samajdar |first10=R. |last11=Omran |first11=A. |date=2021-12-03 |title=Probing topological spin liquids on a programmable quantum simulator |url=https://www.science.org/doi/10.1126/science.abi8794 |journal=Science |volume=374 |issue=6572 |pages=1242–1247 |arxiv=2104.04119 |bibcode=2021Sci...374.1242S |doi=10.1126/science.abi8794 |pmid=34855494 |s2cid=233204440}}{{Cite web |last=Wood |first=Charlie |date=2021-12-02 |title=Quantum Simulators Create a Totally New Phase of Matter |url=https://www.quantamagazine.org/quantum-simulators-create-a-totally-new-phase-of-matter-20211202/ |access-date=2022-03-11 |website=Quanta Magazine |language=en}}

Ion trap based system forms an ideal setting for simulating interactions in quantum spin models.{{cite journal |doi=10.1103/RevModPhys.93.025001|issn=0034-6861 |title=Programmable quantum simulations of spin systems with trapped ions |year=2021 |last1=Monroe |first1=C | last2=et |first2=al |journal=Rev. Mod. Phys. |volume=93 |issue=4 |pages= 025001 |arxiv=1912.07845 |bibcode=2021RvMP...93b5001M |s2cid=209386771 }} A trapped-ion simulator, built by a team that included the NIST can engineer and control interactions among hundreds of quantum bits (qubits).{{cite journal |last1=Britton |first1=Joseph W. |last2=Sawyer |first2=Brian C. |last3=Keith |first3=Adam C. |last4=Wang |first4=C.-C. Joseph |last5=Freericks |first5=James K. |last6=Uys |first6=Hermann |last7=Biercuk |first7=Michael J. |last8=Bollinger |first8=John J. |title=Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins |journal=Nature |date=25 April 2012 |volume=484 |issue=7395 |pages=489–492 |doi=10.1038/nature10981 |pmid=22538611 |arxiv=1204.5789 |bibcode = 2012Natur.484..489B |s2cid=4370334 }} 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.

The trapped-ion simulator consists of a tiny, single-plane crystal of hundreds of beryllium ions, less than 1 millimeter in diameter, hovering inside a device called a Penning trap. The outermost electron of each ion acts as a tiny quantum magnet 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 laser pulses 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 lattice spacing and geometry.

Friedenauer et al., adiabatically manipulated 2 spins, showing their separation into ferromagnetic and antiferromagnetic states.{{cite journal |last1=Friedenauer |first1=A. |last2=Schmitz |first2=H. |last3=Glueckert |first3=J. T. |last4=Porras |first4=D. |last5=Schaetz |first5=T. |title=Simulating a quantum magnet with trapped ions |journal=Nature Physics |date=27 July 2008 |volume=4 |issue=10 |pages=757–761 |doi=10.1038/nphys1032 |bibcode=2008NatPh...4..757F|doi-access=free }}

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{{cite journal |last1=Kim |first1=K. |last2=Chang |first2=M.-S. |last3=Korenblit |first3=S. |last4=Islam |first4=R. |last5=Edwards |first5=E. E.|author5-link= Emily E. Edwards |last6=Freericks |first6=J. K. |last7=Lin |first7=G.-D. |last8=Duan |first8=L.-M. |last9=Monroe |first9=C. |title=Quantum simulation of frustrated Ising spins with trapped ions |journal=Nature |date=June 2010 |volume=465 |issue=7298 |pages=590–593 |doi=10.1038/nature09071 |bibcode=2010Natur.465..590K |pmid=20520708 |s2cid=2479652 }}

and Islam et al., used adiabatic quantum simulation to demonstrate the sharpening of a phase transition between paramagnetic and ferromagnetic ordering as the number of spins increased from 2 to 9.{{cite journal |last1=Islam |first1=R. |last2=Edwards |first2=E.E. |author2-link= Emily E. Edwards |last3=Kim |first3=K. |last4=Korenblit |first4=S. |last5=Noh |first5=C. |last6=Carmichael |first6=H. |last7=Lin |first7=G.-D. |last8=Duan |first8=L.-M. |last9=Joseph Wang |first9=C.-C. |last10=Freericks |first10=J.K. |last11=Monroe |first11=C. |title=Onset of a quantum phase transition with a trapped ion quantum simulator |journal=Nature Communications |date=5 July 2011 |volume=2 |issue=1 |pages=377 |doi=10.1038/ncomms1374 |pmid=21730958 |arxiv=1103.2400 |bibcode=2011NatCo...2..377I |s2cid=33407 }}

Barreiro et al. created a digital quantum simulator of interacting spins with up to 5 trapped ions by coupling to an open reservoir{{cite journal |last1=Barreiro |first1=Julio T. |last2=Müller |first2=Markus |last3=Schindler |first3=Philipp |last4=Nigg |first4=Daniel |last5=Monz |first5=Thomas |last6=Chwalla |first6=Michael |last7=Hennrich |first7=Markus |last8=Roos |first8=Christian F. |last9=Zoller |first9=Peter |last10=Blatt |first10=Rainer |title=An open-system quantum simulator with trapped ions |journal=Nature |date=23 February 2011 |volume=470 |issue=7335 |pages=486–491 |doi=10.1038/nature09801 |pmid=21350481 |arxiv=1104.1146 |bibcode=2011Natur.470..486B |s2cid=4359894 }} and

Lanyon et al. demonstrated digital quantum simulation with up to 6 ions.{{cite journal |last1=Lanyon |first1=B. P. |last2=Hempel |first2=C. |last3=Nigg |first3=D. |last4=Muller |first4=M. |last5=Gerritsma |first5=R. |last6=Zahringer |first6=F. |last7=Schindler |first7=P. |last8=Barreiro |first8=J. T. |last9=Rambach |first9=M. |last10=Kirchmair |first10=G. |last11=Hennrich |first11=M. |last12=Zoller |first12=P. |last13=Blatt |first13=R. |last14=Roos |first14=C. F. |title=Universal Digital Quantum Simulation with Trapped Ions |journal=Science |date=1 September 2011 |volume=334 |issue=6052 |pages=57–61 |doi=10.1126/science.1208001 |arxiv=1109.1512 |bibcode=2011Sci...334...57L |pmid=21885735 |s2cid=206535076 }}

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.{{cite journal |last1=Islam |first1=R. |last2=Senko |first2=C. |last3=Campbell |first3=W. C. |last4=Korenblit |first4=S. |last5=Smith |first5=J. |last6=Lee |first6=A. |last7=Edwards |first7=E. E. |author7-link= Emily E. Edwards |last8=Wang |first8=C.- C. J. |last9=Freericks |first9=J. K. |last10=Monroe |first10=C. |title=Emergence and Frustration of Magnetism with Variable-Range Interactions in a Quantum Simulator |journal=Science |date=2 May 2013 |volume=340 |issue=6132 |pages=583–587 |doi=10.1126/science.1232296 |pmid=23641112 |arxiv=1210.0142 |bibcode = 2013Sci...340..583I |s2cid=14692151 }}

Britton, et al. from NIST has experimentally benchmarked Ising interactions in a system of hundreds of qubits for studies of quantum magnetism.

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.{{cite journal |last1=Pagano |first1=G |last2=Hess |first2=P W |last3=Kaplan |first3=H B |last4=Tan |first4=W L |last5=Richerme |first5=P |last6=Becker |first6=P |last7=Kyprianidis |first7=A |last8=Zhang |first8=J |last9=Birckelbaw |first9=E |last10=Hernandez |first10=M R |last11=Wu |first11=Y |last12=Monroe |first12=C |title=Cryogenic trapped-ion system for large scale quantum simulation |journal=Quantum Science and Technology |date=9 October 2018 |volume=4 |issue=1 |pages=014004 |doi=10.1088/2058-9565/aae0fe |arxiv=1802.03118 |s2cid=54518534 }} Joshi, et al., probed the quantum dynamics of 51 individually controlled ions, realizing a long-range interacting spin chain.{{cite journal |last1=Joshi |first1=M.K. |last2=Kranzl |first2=F. |last3=Schuckert |first3=A. |last4=Lovas |first4=I. |last5=Maier |first5=C. |last6=Blatt |first6=R. |last7=Knap |first7=M. |last8=Roos |first8=C.F. |title=Observing emergent hydrodynamics in a long-range quantum magnet |journal=Science |date=13 May 2022 |volume=6594 |issue=376 |pages=720–724 |doi=10.1126/science.abk2400 |pmid=35549407 |arxiv=2107.00033 |bibcode=2022Sci...376..720J |s2cid=235694285 |url=https://www.science.org/doi/10.1126/science.abk2400 |access-date=13 May 2022}}

Many ultracold atom experiments are examples of quantum simulators. These include experiments studying bosons or fermions in optical lattices, the unitary Fermi gas, Rydberg atom arrays in optical tweezers. A common thread for these experiments is the capability of realizing generic Hamiltonians, such as the Hubbard or transverse-field Ising 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.{{cite journal |last1=Bloch |first1=Immanuel |last2=Dalibard |first2=Jean |last3=Nascimbene |first3=Sylvain |title=Quantum simulations with ultracold quantum gases |journal=Nature Physics |date=2012 |volume=8 |issue=4 |pages=267–276 |doi=10.1038/nphys2259 |bibcode=2012NatPh...8..267B |s2cid=17023076 }}{{cite journal |last1=Gross |first1=Christian |last2=Bloch |first2=Immanuel |title=Quantum simulations with ultracold atoms in optical lattices |journal=Nature |date=September 8, 2017 |volume=357 |issue=6355 |pages=995–1001 |doi=10.1126/science.aal3837 |pmid=28883070 |bibcode=2017Sci...357..995G |doi-access=free }} Other experiments have realized condensed matter models in regimes which are difficult or impossible to realize with conventional materials, such as the Haldane model and the Harper-Hofstadter model.{{cite journal |last1=Jotzu |first1=Gregor |last2=Messer |first2=Michael |last3=Desbuquois |first3=Rémi |last4=Lebrat |first4=Martin |last5=Uehlinger |first5=Thomas |last6=Greif |first6=Daniel |last7=Esslinger |first7=Tilman |title=Experimental realization of the topological Haldane model with ultracold fermions |journal=Nature |date=13 November 2014 |volume=515 |issue=7526 |pages=237–240 |doi=10.1038/nature13915 |pmid=25391960 |arxiv=1406.7874 |bibcode=2014Natur.515..237J |s2cid=204898338 }}{{cite journal |last1=Simon |first1=Jonathan |title=Magnetic fields without magnetic fields |journal=Nature |date=13 November 2014 |volume=515 |issue=7526 |pages=202–203 |doi=10.1038/515202a|pmid=25391956 |doi-access=free }}{{cite journal |last1=Zhang |first1=Dan-Wei |last2=Zhu |first2=Yan-Qing |last3=Zhao |first3=Y. X. |last4=Yan |first4=Hui |last5=Zhu |first5=Shi-Liang |title=Topological quantum matter with cold atoms |journal=Advances in Physics |date=29 March 2019 |volume=67 |issue=4 |pages=253–402 |doi=10.1080/00018732.2019.1594094|arxiv=1810.09228 |s2cid=91184189 }}{{Cite journal|last1=Alberti|first1=Andrea|last2=Robens|first2=Carsten|last3=Alt|first3=Wolfgang|last4=Brakhane|first4=Stefan|last5=Karski|first5=Michał|last6=Reimann|first6=René|last7=Widera|first7=Artur|last8=Meschede|first8=Dieter|date=2016-05-06|title=Super-resolution microscopy of single atoms in optical lattices|journal=New Journal of Physics|language=en|volume=18|issue=5|pages=053010|doi=10.1088/1367-2630/18/5/053010|arxiv=1512.07329 |bibcode=2016NJPh...18e3010A |issn=1367-2630|doi-access=free}}{{Citation|last1=Robens|first1=Carsten|title=Quantum Walks with Neutral Atoms: Quantum Interference Effects of One and Two Particles|date=2016-09-18|url=https://www.worldscientific.com/doi/abs/10.1142/9789813200616_0001|work=Laser Spectroscopy|pages=1–15|publisher=WORLD SCIENTIFIC|doi=10.1142/9789813200616_0001|isbn=978-981-320-060-9|access-date=2020-05-25|last2=Brakhane|first2=Stefan|last3=Meschede|first3=Dieter|last4=Alberti|first4=A.|arxiv=1511.03569|s2cid=118452312}}

Quantum simulators using superconducting qubits fall into two main categories. First, so called quantum annealers determine ground states of certain Hamiltonians after an adiabatic ramp. This approach is sometimes called adiabatic quantum computing. Second, many systems emulate specific Hamiltonians and study their ground state properties, quantum phase transitions, or time dynamics.{{cite journal |last1=Paraoanu |first1=G. S. |title=Recent Progress in Quantum Simulation Using Superconducting Circuits |journal=Journal of Low Temperature Physics |date=4 April 2014 |volume=175 |issue=5–6 |pages=633–654 |doi=10.1007/s10909-014-1175-8 |arxiv=1402.1388 |bibcode=2014JLTP..175..633P |s2cid=119276238 }} Several important recent results include the realization of a Mott insulator in a driven-dissipative Bose-Hubbard system and studies of phase transitions in lattices of superconducting resonators coupled to qubits.{{cite journal |last1=Ma |first1=Ruichao |last2=Saxberg |first2=Brendan |last3=Owens |first3=Clai |last4=Leung |first4=Nelson |last5=Lu |first5=Yao |last6=Simon |first6=Jonathan |last7=Schuster |first7=David I. |title=A dissipatively stabilized Mott insulator of photons |journal=Nature |date=6 February 2019 |volume=566 |issue=7742 |pages=51–57 |doi=10.1038/s41586-019-0897-9|pmid=30728523 |arxiv=1807.11342 |bibcode=2019Natur.566...51M |s2cid=59606678 }}{{cite journal |last1=Fitzpatrick |first1=Mattias |last2=Sundaresan |first2=Neereja M. |last3=Li |first3=Andy C. Y. |last4=Koch |first4=Jens |last5=Houck |first5=Andrew A. |title=Observation of a Dissipative Phase Transition in a One-Dimensional Circuit QED Lattice |journal=Physical Review X |date=10 February 2017 |volume=7 |issue=1 |pages=011016 |doi=10.1103/PhysRevX.7.011016| arxiv=1607.06895|bibcode=2017PhRvX...7a1016F |s2cid=3550701 }}

• Hamiltonian simulation
• Quantum Turing machine
• Quantum computing

{{reflist|30em}}

• [https://web.archive.org/web/20081123183419/http://www.ceid.upatras.gr/tech_news/papers/quantum_theory.pdf Deutsch's 1985 paper]

{{Quantum information}}

{{emerging technologies|quantum=yes|other=yes}}

Category:Quantum computing