neutral atom quantum computer

Neutral atom quantum computing makes use of several technological advancements in the field laser cooling, magneto-optical trapping and optical tweezers. In one example of the architecture,{{cite journal |last1=Saffman |first1=M |title=Quantum computing with atomic qubits and Rydberg interactions: progress and challenges |journal=Journal of Physics B: Atomic, Molecular and Optical Physics |date=28 October 2016 |volume=49 |issue=20 |pages=202001 |doi=10.1088/0953-4075/49/20/202001 |url=https://iopscience.iop.org/article/10.1088/0953-4075/49/20/202001 |issn=0953-4075|arxiv=1605.05207 |bibcode=2016JPhB...49t2001S }} an array of atoms is loaded into a laser cooled at micro-kelvin temperatures. In each of these atoms, two levels of hyperfine ground subspace are isolated. The qubits are prepared in some initial state using optical pumping. Logic gates are performed using optical or microwave frequency fields and the measurements are done using resonance fluorescence. Most of these architecture are based on rubidium,{{cite journal |last1=Evered |first1=Simon J. |last2=Bluvstein |first2=Dolev |last3=Kalinowski |first3=Marcin |last4=Ebadi |first4=Sepehr |last5=Manovitz |first5=Tom |last6=Zhou |first6=Hengyun |last7=Li |first7=Sophie H. |last8=Geim |first8=Alexandra A. |last9=Wang |first9=Tout T. |last10=Maskara |first10=Nishad |last11=Levine |first11=Harry |last12=Semeghini |first12=Giulia |last13=Greiner |first13=Markus |last14=Vuletić |first14=Vladan |last15=Lukin |first15=Mikhail D. |title=High-fidelity parallel entangling gates on a neutral-atom quantum computer |journal=Nature |date=October 2023 |volume=622 |issue=7982 |pages=268–272 |doi=10.1038/s41586-023-06481-y |pmid=37821591 |pmc=10567572 |language=en |issn=1476-4687|arxiv=2304.05420 |bibcode=2023Natur.622..268E }} caesium,{{cite journal |last1=Graham |first1=T. M. |last2=Song |first2=Y. |last3=Scott |first3=J. |last4=Poole |first4=C. |last5=Phuttitarn |first5=L. |last6=Jooya |first6=K. |last7=Eichler |first7=P. |last8=Jiang |first8=X. |last9=Marra |first9=A. |last10=Grinkemeyer |first10=B. |last11=Kwon |first11=M. |last12=Ebert |first12=M. |last13=Cherek |first13=J. |last14=Lichtman |first14=M. T. |last15=Gillette |first15=M. |last16=Gilbert |first16=J. |last17=Bowman |first17=D. |last18=Ballance |first18=T. |last19=Campbell |first19=C. |last20=Dahl |first20=E. D. |last21=Crawford |first21=O. |last22=Blunt |first22=N. S. |last23=Rogers |first23=B. |last24=Noel |first24=T. |last25=Saffman |first25=M. |title=Multi-qubit entanglement and algorithms on a neutral-atom quantum computer |journal=Nature |date=April 2022 |volume=604 |issue=7906 |pages=457–462 |doi=10.1038/s41586-022-04603-6 |pmid=35444321 |url=https://www.nature.com/articles/s41586-022-04603-6#Sec6 |language=en |issn=1476-4687|arxiv=2112.14589 |bibcode=2022Natur.604..457G }} ytterbium,{{cite journal |last1=Jenkins |first1=Alec |last2=Lis |first2=Joanna W. |last3=Senoo |first3=Aruku |last4=McGrew |first4=William F. |last5=Kaufman |first5=Adam M. |title=Ytterbium Nuclear-Spin Qubits in an Optical Tweezer Array |journal=Physical Review X |date=3 May 2022 |volume=12 |issue=2 |pages=021027 |doi=10.1103/PhysRevX.12.021027 |url=https://journals.aps.org/prx/abstract/10.1103/PhysRevX.12.021027|arxiv=2112.06732 |bibcode=2022PhRvX..12b1027J }}{{cite journal |last1=Ma |first1=S. |last2=Burgers |first2=A. P. |last3=Liu |first3=G. |last4= Wilson |first4=J. |last5=Zhang |first5=B. |last6=Thompson |first6=J. D. |title=Universal Gate Operations on Nuclear Spin Qubits in an Optical Tweezer Array of 171Yb Atoms |journal=Physical Review X |date=3 May 2022 |volume=12 |issue=2 |pages=021028 |doi=10.1103/PhysRevX.12.021028|url=https://journals.aps.org/prx/abstract/10.1103/PhysRevX.12.021028|arxiv=2112.06799 }} and strontium{{cite journal |last1=Madjarov |first1=Ivaylo S. |last2=Covey |first2=Jacob P. |last3=Shaw |first3=Adam L. |last4=Choi |first4=Joonhee |last5=Kale |first5=Anant |last6=Cooper |first6=Alexandre |last7=Pichler |first7=Hannes |last8=Schkolnik |first8=Vladimir |last9=Williams |first9=Jason R. |last10=Endres |first10=Manuel |title=High-fidelity entanglement and detection of alkaline-earth Rydberg atoms |journal=Nature Physics |date=August 2020 |volume=16 |issue=8 |pages=857–861 |doi=10.1038/s41567-020-0903-z |url=https://www.nature.com/articles/s41567-020-0903-z |language=en |issn=1745-2481|arxiv=2001.04455 |bibcode=2020NatPh..16..857M }} atoms.

Global single qubit gates on all the atoms can be done either by applying a microwave field for qubits encoded in the Hyperfine manifold such as Rb and Cs or by applying an RF magnetic field for qubits encoded in the nuclear spin such as Yb and Sr. Focused laser beams can be used to do single-site one qubit rotation using a lambda-type three level Raman scheme (see figure). In this scheme, the rotation between the qubit states is mediated by an intermediate excited state. Single qubit gate fidelities have been shown to be as high as .999 in state-of-the-art experiments.{{cite journal |last1=Graham |first1=T. M. |last2=Song |first2=Y. |last3=Scott |first3=J. |last4=Poole |first4=C. |last5=Phuttitarn |first5=L. |last6=Jooya |first6=K. |last7=Eichler |first7=P. |last8=Jiang |first8=X. |last9=Marra |first9=A. |last10=Grinkemeyer |first10=B. |last11=Kwon |first11=M. |last12=Ebert |first12=M. |last13=Cherek |first13=J. |last14=Lichtman |first14=M. T. |last15=Gillette |first15=M. |last16=Gilbert |first16=J. |last17=Bowman |first17=D. |last18=Ballance |first18=T. |last19=Campbell |first19=C. |last20=Dahl |first20=E. D. |last21=Crawford |first21=O. |last22=Blunt |first22=N. S. |last23=Rogers |first23=B. |last24=Noel |first24=T. |last25=Saffman |first25=M. |title=Multi-qubit entanglement and algorithms on a neutral-atom quantum computer |journal=Nature |date=April 2022 |volume=604 |issue=7906 |pages=457–462 |doi=10.1038/s41586-022-04603-6 |pmid=35444321 |url=https://www.nature.com/articles/s41586-022-04603-6 |language=en |issn=1476-4687|arxiv=2112.14589 |bibcode=2022Natur.604..457G }}{{cite journal |last1=Xia |first1=T. |last2=Lichtman |first2=M. |last3=Maller |first3=K. |last4=Carr |first4=A. W. |last5=Piotrowicz |first5=M. J. |last6=Isenhower |first6=L. |last7=Saffman |first7=M. |title=Randomized Benchmarking of Single-Qubit Gates in a 2D Array of Neutral-Atom Qubits |journal=Physical Review Letters |date=12 March 2015 |volume=114 |issue=10 |pages=100503 |doi=10.1103/PhysRevLett.114.100503 |pmid=25815916 |url=https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.100503|arxiv=1501.02041 |bibcode=2015PhRvL.114j0503X }}

To do universal quantum computation, we need at least one two-qubit entangling gate.{{cite book |last1=Nielsen |first1=Michael A. |last2=Chuang |first2=Isaac L. |title=Quantum Computation and Quantum Information: 10th Anniversary Edition |date=9 December 2010 |doi=10.1017/CBO9780511976667 |isbn=978-1-107-00217-3 |url=https://www.cambridge.org/highereducation/books/quantum-computation-and-quantum-information/01E10196D0A682A6AEFFEA52D53BE9AE#overview |language=en}} Early proposals for gates included gates that depended on inter-atomic forces. These forces are weak and the gates were predicted to be slow. The first fast gate{{cn|reason=priority claims need secondary references|date=October 2024}} based on Rydberg states was proposed for charged atoms {{cite journal |last1=Beige |first1=A |last2=Huelga |first2=SF|last3=Knight |first3=PL|last4=Plenio |first4=MB|last5=Thompson |first5=RC |title=Coherent manipulation of two dipole-dipole interacting ions |journal=Journal of Modern Optics |date=2000 |volume=47 |issue=2/3 |pages=401–414 |doi=10.1080/09500340008244051 |url=https://doi.org/10.1080/09500340008244051|arxiv=quant-ph/9903059|hdl=10044/1/258 }} making use of the principle of Rydberg Blockade. The principle was later transferred and developed further for neutral atoms. Since then, most gates that have been proposed use this principle.{{cn|reason=overview statements need secondary references|date=October 2024}}

Atoms that have been excited to very large principal quantum number $n$ are known as Rydberg atoms. These highly excited atoms have several desirable properties including high decay life-time and amplified couplings with electromagnetic fields.{{cite journal |last1=Saffman |first1=M. |last2=Walker |first2=T. G. |last3=Mølmer |first3=K. |title=Quantum information with Rydberg atoms |journal=Reviews of Modern Physics |date=18 August 2010 |volume=82 |issue=3 |pages=2313–2363 |doi=10.1103/RevModPhys.82.2313 |url=https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.82.2313|arxiv=0909.4777 |bibcode=2010RvMP...82.2313S }}

The basic principle for Rydberg mediated gates is called the Rydberg blockade.{{cite journal |last1=Walker |first1=Thad G. |last2=Saffman |first2=Mark |title=Chapter 2 - Entanglement of Two Atoms Using Rydberg Blockade |journal=Advances in Atomic, Molecular, and Optical Physics |date=1 July 2012 |volume=61 |pages=81–115 |url=https://www.sciencedirect.com/science/article/abs/pii/B9780123964823000028 |publisher=Academic Press|doi=10.1016/B978-0-12-396482-3.00002-8 |isbn=978-0-12-396482-3 |arxiv=1202.5328 }} Consider two neutral atoms in their respective ground states. When they are close to each other, their interaction potential is dominated by van Der Waals force $V\_\{qq\}\; \backslash approx\; \backslash frac\{\; \backslash mu\_\{B\}^\{2\}\}\{R^\{6\}\}$ where $\backslash mu\_\{B\}$ is the Bohr Magneton and $R$ is the distance between the atoms. This interaction is very weak, around $10^\{-5\}$ Hz for $R\; =\; 10\; \backslash mu\; m$. When one of the atoms is put into a Rydberg state (state with very high principal quantum number), the interaction between the two atoms is dominated by second order dipole-dipole interaction which is also weak. When both of the atoms are excited to a Rydberg state, then the resonant dipole-dipole interaction becomes $V\_\{rr\}\; =\; \backslash frac\{(n^\{2\}e\; a\_\{0\})^\{2\}\}\{R^\{3\}\}$ where $a\_\{0\}$ is the Bohr radius. This interaction is around $100$MHz at $R=10\backslash mu\; m$, around twelve orders of magnitude larger. This interaction potential induces a blockade, where-in, if one atom is excited to a Rydberg state, the other nearby atoms cannot be excited to a Rydberg state because the two-atom Rydberg state is far detuned. This phenomenon is called the Rydberg blockade. Rydberg mediated gates make use of this blockade as a control mechanism to implement two qubit controlled gates.

Let's consider the physics induced by the this blockade. Suppose we are considering two isolated neutral atoms in a magneto-optical trap. Ignoring the coupling of hyperfine levels that make the qubit and motional degrees of freedom, the Hamiltonian of this system can be written as:

$H\; =\; H\_\{1\}\; +\; H\_\{2\}\; +\; V\_\{rr\}\; |r\; \backslash rangle\; \_\{1\}\; \backslash langle\; r|\; \backslash otimes\; |r\; \backslash rangle\; \_\{2\}\; \backslash langle\; r|)$

File:RydbergAtomsHamiltonian.jpg

where, $H\_\{i\}\; =\; \backslash frac\{1\}\{2\}((\backslash Omega\; |1\; \backslash rangle\; \_\{i\}\; \backslash langle\; r|\; +\; \backslash Omega^\{*\}\; |r\; \backslash rangle\; \_\{i\}\; \backslash langle\; 1|)\; -\; \backslash Delta\; |r\; \backslash rangle\; \_\{i\}\; \backslash langle\; r|$ is the Hamiltonian of i-th atom,

$\backslash Omega$ is the Rabi frequency of coupling between the Rydberg states and the $|\; 1\; \backslash rangle$ state and $\backslash Delta$ is the detuning (see figure to the right for level diagram). When $|V\_\{rr\}|\; >>\; |\backslash Omega|,\; |\backslash Delta|$, we are in the so-called Rydberg Blockade regime. In this regime, the $|rr\; \backslash rangle$ state is highly detuned from the rest of the system and thus is effectively decoupled. For the rest of this article, we consider only the Rydberg Blockade regime.

The physics of this Hamiltonian can be divided into several subspaces depending on the initial state. The $|00\; \backslash rangle$ state is decoupled and does not evolve. Suppose only the i-th the atom is in $|\; 1\backslash rangle$ state ($|10\backslash rangle$, $|01\backslash rangle$), then the Hamiltonian is given by $H\_\{i\}$. This Hamiltonian is the standard two-level Rabi hamiltonian. It characterizes the "light shift" in a two level system and has eigenvalues $E\_\{LS\}^\{(1)\}\; =\; \backslash frac\{1\}\{2\}(\backslash Delta\; \backslash pm\; \backslash sqrt\{\backslash Omega^\{2\}\; +\backslash Delta^\{2\}\})$.

If both atoms are in the excited state $|11\; \backslash rangle$ the effective system evolves in the subspace of $\backslash \{|1r\; \backslash rangle,\; |r1\; \backslash rangle,\; |11\; \backslash rangle\; \backslash \}$. It is convenient to rewrite the Hamiltonian in terms of bright $|b\backslash rangle\; =\; \backslash frac\{1\}\{\backslash sqrt\{2\}\}(|r1\backslash rangle\; +\; |1r\backslash rangle)$ and dark $|d\backslash rangle\; =\; \backslash frac\{1\}\{\backslash sqrt\{2\}\}(|r1\backslash rangle\; -\; |1r\backslash rangle)$ basis states, along with $|\; 11\; \backslash rangle$. In this basis, the Hamiltonian is given by

$H\; =\; -\backslash Delta(|b\backslash rangle\; \backslash langle\; b|\; +\; |d\backslash rangle\; \backslash langle\; d|)\; +\; \backslash frac\{\backslash sqrt\{2\}\}\{2\}(\backslash Omega\; |b\backslash rangle\; \backslash langle\; 11|\; +\; \backslash Omega^\{*\}\; |11\backslash rangle\; \backslash langle\; b|)$.

File:RydbergHamiltonianSubspaces.jpg

Note that the dark state is decoupled from the bright state and the $|11\backslash rangle$ state. Thus we can ignore it and the effective evolution reduces to a two-level system consisting of the bright state and $|11\backslash rangle$ state. In this basis, the dressed eigenvalues and eigenvectors of the hamiltonian are given by:

$E\_\{LS\}^\{(2)\}\; =\; \backslash frac\{1\}\{2\}(\backslash Delta\; \backslash pm\; \backslash sqrt\{2\backslash Omega^\{2\}\; +\backslash Delta^\{2\}\})$

$|\; \backslash tilde\{11\}\; \backslash rangle\; =\; \backslash cos\; (\backslash theta/2)|\; 11\; \backslash rangle\; +\; \backslash sin\; (\backslash theta/2)|\; b\; \backslash rangle$

$|\; \backslash tilde\{b\}\; \backslash rangle\; =\; \backslash cos\; (\backslash theta/2)|\; b\; \backslash rangle\; -\; \backslash sin\; (\backslash theta/2)|\; 11\backslash rangle$,

where, $\backslash theta$ depends on the Rabi frequency and detuning.

We will make use of these considerations in the gates below. The level diagrams of these subspaces have been shown in the figure above.

We can use the Rydberg blockade to implement a controlled-phase gate by applying standard Rabi pulses between the $|1\backslash rangle$ and $|r\backslash rangle$ levels. Consider the following protocol:

File:JakschGate.jpg

1. Apply $\backslash pi$ pulse to control atom (red).
2. Apply $2\; \backslash pi$ pulse the target atom (brown).
3. Apply $\backslash pi$ pulse to control atom again (red).

The figure on the right shows what this pulse sequence does. When the state is $|00\; \backslash rangle$, both levels are uncoupled from the Rydberg states and so the pulses do nothing. When either of the atoms is in $|0\; \backslash rangle$ state, the other one picks up a $-1$ phase due to the $2\; \backslash pi$ pulse. When the state is $|11\; \backslash rangle$, the second atom is off-resonant to its Rydberg state and thus does not pick up any phase, however the first one does. The truth table of this gate is given below. This is equivalent to a controlled-z gate up-to a local rotation to the hyperfine levels.

The adiabatic gate was introduced as an alternative to the Jaksch gate.{{cite journal |last1=Keating |first1=Tyler |last2=Cook |first2=Robert L. |last3=Hankin |first3=Aaron M. |last4=Jau |first4=Yuan-Yu |last5=Biedermann |first5=Grant W. |last6=Deutsch |first6=Ivan H. |title=Robust quantum logic in neutral atoms via adiabatic Rydberg dressing |journal=Physical Review A |date=28 January 2015 |volume=91 |issue=1 |pages=012337 |doi=10.1103/PhysRevA.91.012337 |url=https://journals.aps.org/pra/abstract/10.1103/PhysRevA.91.012337|arxiv=1411.2622 |bibcode=2015PhRvA..91a2337K }} It is global and symmetric and thus it does not require locally focused lasers. Moreover, the Adiabatic Gate prevents the problem of spurious phase accumulation when the atom is in Rydberg state. In the Adiabatic Gate, instead of doing fast pulses, we dress the atom with an adiabatic pulse sequence that takes the atom on a trajectory around the Bloch sphere and back. The levels pick up a phase on this trip due to the so-called "light shift" induced by the lasers. The shapes of pulses can be chosen to control this phase.

If both atoms are in the $|00\backslash rangle$ state, nothing happens so $|00\backslash rangle\; \backslash rightarrow\; |\; 00\backslash rangle$. If one of them is in the $|0\backslash rangle$ state, the other atom picks up a phase due to light shift: $|01\backslash rangle\; \backslash rightarrow\; e^\{i\backslash phi\_\{1\}\}|\; 01\backslash rangle$ and similarly $|10\backslash rangle\; \backslash rightarrow\; e^\{i\backslash phi\_\{1\}\}|\; 10\backslash rangle$ with:

$\backslash phi\_\{1\}\; =\; \backslash int\; E\_\{LS\}^\{(1)\}\; (t)\; dt\; =\; \backslash int\; \backslash frac\{1\}\{2\}(\backslash Delta(t)\; -\backslash sqrt\{\backslash Omega^\{2\}(t)\; +\; \backslash Delta^\{2\}\; (t)\})\; dt$.

When both of the atoms are in $|1\backslash rangle$ states, the atoms pick up a phase due to the two-atom light shift as seen by the eigenvalues of Hamiltonian above, then $|11\backslash rangle\; \backslash rightarrow\; e^\{i\backslash phi\_\{2\}\}|\; 11\backslash rangle$ with

$\backslash phi\_\{2\}\; =\; \backslash int\; E\_\{LS\}^\{(2)\}\; (t)\; dt\; =\; \backslash int\; \backslash frac\{1\}\{2\}(\backslash Delta(t)\; -\backslash sqrt\{2\backslash Omega^\{2\}(t)\; +\; \backslash Delta^\{2\}\; (t)\})\; dt$.

Note that this light shift is not equal to twice the single atom light shifts. The single atom light-shifts are then cancelled by a global pulse that implements $U\; =\; \backslash exp(-i\backslash phi\_\{1\}\; |1\; \backslash rangle\; \backslash langle\; 1|)$ to get rid of the single qubit light shifts. The truth table for this gate is given to the right. This protocol leaves a total phase of $\backslash int\; (E\_\{LS\}^\{(2)\}(t)\; -\; 2E\_\{LS\}^\{(1)\}(t))\; dt$ phase on the $|11\backslash rangle$ state. We can choose the pulses so that this phase equals $\backslash pi$, making it a controlled-Z gate. An extension to this gate was introduced to make it robust against errors in reference.{{cite journal |last1=Mitra |first1=Anupam |last2=Martin |first2=Michael J. |last3=Biedermann |first3=Grant W. |last4=Marino |first4=Alberto M. |last5=Poggi |first5=Pablo M. |last6=Deutsch |first6=Ivan H. |title=Robust M\o{}lmer-S\o{}rensen gate for neutral atoms using rapid adiabatic Rydberg dressing |journal=Physical Review A |date=20 March 2020 |volume=101 |issue=3 |pages=030301 |doi=10.1103/PhysRevA.101.030301 |url=https://journals.aps.org/pra/abstract/10.1103/PhysRevA.101.030301|arxiv=1911.04045 }}

The adiabatic gate is global but it is slow (due to adiabatic condition). The Levine-Pichler gate was introduced as a fast diabatic substitute to the global Adiabatic Gate.{{cite journal |last1=Levine |first1=Harry |last2=Keesling |first2=Alexander |last3=Semeghini |first3=Giulia |last4=Omran |first4=Ahmed |last5=Wang |first5=Tout T. |last6=Ebadi |first6=Sepehr |last7=Bernien |first7=Hannes |last8=Greiner |first8=Markus |last9=Vuletić |first9=Vladan |last10=Pichler |first10=Hannes |last11=Lukin |first11=Mikhail D. |title=Parallel Implementation of High-Fidelity Multiqubit Gates with Neutral Atoms |journal=Physical Review Letters |date=22 October 2019 |volume=123 |issue=17 |pages=170503 |doi=10.1103/PhysRevLett.123.170503 |pmid=31702233 |url=https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.123.170503|arxiv=1908.06101 |bibcode=2019PhRvL.123q0503L |hdl=1721.1/136494.2 }} This gate uses carefully chosen pulse sequences to perform a controlled-phase gate.

In this protocol, we apply the following pulse sequence:

1. Apply pulse of length $\backslash tau\; =\; 2\; \backslash pi/\backslash sqrt\{\backslash Delta^\{2\}\; +\; 2\backslash Omega^\{2\}\}$ with Rabi frequency $\backslash Omega$ (red).
2. Apply another pulse of length $\backslash tau\; =\; 2\; \backslash pi/\backslash sqrt\{\backslash Delta^\{2\}\; +\; 2\backslash Omega^\{2\}\}$ but with a phase shifted Rabi frequency $\backslash Omega\; \backslash rightarrow\; e^\{-i\; \backslash xi\}\; \backslash Omega$ (brown).

File:PitchlerGate.jpg

The intuition of this gate is best understood in terms of the picture given above. When the state of the system is $|11\backslash rangle$, the pulses send the state around the Bloch sphere twice and accumulates a net phase $\backslash phi\_\{2\}\; =\; \backslash frac\{4\; \backslash pi\; \backslash Delta\}\{\backslash sqrt\{\backslash Delta^\{2\}\; +2\; \backslash Omega^\{2\}\}\}$. When one of the atoms is in $|0\backslash rangle$ state, the other atom does not go around the Bloch sphere fully after the first pulse due to the mismatch in Rabi frequency. The second pulse corrects for this effect by rotating the state around a different axis. This puts the atom back into the $|1\backslash rangle$ state with a net phase $\backslash phi\_\{1\}$, which can be calculated easily. The pulses can be chosen to make $e^\{i\backslash phi\_\{2\}\}\; =e^\{i(2\backslash phi\_\{1\}+\backslash pi)\}$. Doing so makes this gate equivalent to a controlled-z gate up-to a local rotation. The truth table of Levine-Pichler gate is given on the right. This gate has been improved using the methods of quantum optimal controls recently.{{cite journal |last1=Pagano |first1=Alice |last2=Weber |first2=Sebastian |last3=Jaschke |first3=Daniel |last4=Pfau |first4=Tilman |last5=Meinert |first5=Florian |last6=Montangero |first6=Simone |last7=Büchler |first7=Hans Peter |title=Error budgeting for a controlled-phase gate with strontium-88 Rydberg atoms |journal=Physical Review Research |date=11 July 2022 |volume=4 |issue=3 |pages=033019 |doi=10.1103/PhysRevResearch.4.033019 |url=https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.4.033019|arxiv=2202.13849 |bibcode=2022PhRvR...4c3019P }}{{cite journal |last1=Jandura |first1=Sven |last2=Pupillo |first2=Guido |title=Time-Optimal Two- and Three-Qubit Gates for Rydberg Atoms |journal=Quantum |date=13 May 2022 |volume=6 |pages=712 |doi=10.22331/q-2022-05-13-712 |url=https://quantum-journal.org/papers/q-2022-05-13-712/|arxiv=2202.00903 |bibcode=2022Quant...6..712J }}

Entangling gates in state-of-the art neutral atom quantum computing platforms have been implemented with up-to .995 quantum fidelity.

• Superconducting quantum computing
• Trapped-ion quantum computer

{{reflist}}

{{Quantum information}}

Category:Quantum computing

Category:Quantum information science