Alexander Holevo publishes a paper showing that nqubits can carry more than n classical bits of information, but at most n classical bits are accessible (a result known as "Holevo's theorem" or "Holevo's bound").
R. P. Poplavskii publishes "Thermodynamical models of information processing" (in Russian)[4] which shows the computational infeasibility of simulating quantum systems on classical computers, due to the superposition principle.
Roman Stanisław Ingarden, a Polish mathematical physicist, publishes the paper "Quantum Information Theory" in Reports on Mathematical Physics, vol. 10, pp. 43–72, 1976 (The paper was submitted in 1975). It is one of the first attempts at creating a quantum information theory, showing that Shannon information theory cannot directly be generalized to the quantum case, but rather that it is possible to construct a quantum information theory, which is a generalization of Shannon's theory, within the formalism of a generalized quantum mechanics of open systems and a generalized concept of observables (the so-called semi-observables).
Paul Benioff describes the first quantum mechanical model of a computer. In this work, Benioff showed that a computer could operate under the laws of quantum mechanics by describing a Schrödinger equation description of Turing machines, laying a foundation for further work in quantum computing. The paper[5] was submitted in June 1979 and published in April 1980.
Yuri Manin briefly motivates the idea of quantum computing.[6]
At the first Conference on the Physics of Computation, held at the Massachusetts Institute of Technology (MIT) in May,[8]Paul Benioff and Richard Feynman give talks on quantum computing. Benioff's built on his earlier 1980 work showing that a computer can operate under the laws of quantum mechanics. The talk was titled “Quantum mechanical Hamiltonian models of discrete processes that erase their own histories: application to Turing machines”.[9] In Feynman's talk, he observed that it appeared to be impossible to efficiently simulate an evolution of a quantum system on a classical computer, and he proposed a basic model for a quantum computer.[10]
Yoshihisa Yamamoto and K. Igeta propose the first physical realization of a quantum computer, including Feynman's CNOT gate.[16] Their approach uses atoms and photons and is the progenitor of modern quantum computing and networking protocols using photons to transmit qubits and atoms to perform two-qubit operations.
Bikas K. Chakrabarti & collaborators from Saha Institute of Nuclear Physics, Kolkata, India, propose that quantum fluctuations could help explore rugged energy landscapes by escaping from local minima of glassy systems having tall but thin barriers by tunneling (instead of climbing over using thermal excitations), suggesting the effectiveness of quantum annealing over classical simulated annealing.[18][19]
David Deutsch and Richard Jozsa propose a computational problem that can be solved efficiently with the deterministic Deutsch–Jozsa algorithm on a quantum computer, but for which no deterministic classical algorithm is possible. This was perhaps the earliest result in the computational complexity of quantum computers, proving that they were capable of performing some well-defined computational task more efficiently than any classical computer.
Ethan Bernstein and Umesh Vazirani propose the Bernstein–Vazirani algorithm. It is a restricted version of the Deutsch–Jozsa algorithm where instead of distinguishing between two different classes of functions, it tries to learn a string encoded in a function. The Bernstein–Vazirani algorithm was designed to prove an oracle separation between complexity classes BQP and BPP.
Research groups at Max Planck Institute of Quantum Optics (Garching)[21][22] and shortly after at NIST (Boulder)[23] experimentally realize the first crystallized strings of laser-cooled ions. Linear ion crystals constitute the qubit basis for most quantum computing and simulation experiments with trapped ions.
Peter Shor, at AT&T's Bell Labs in New Jersey, publishes Shor's algorithm. It would allow a quantum computer to factor large integers quickly. It solves both the factoring problem and the discrete log problem. The algorithm can theoretically break many of the cryptosystems in use today. Its invention sparked a tremendous interest in quantum computers.
Isaac Chuang and Yoshihisa Yamamoto propose a quantum-optical realization of a quantum computer to implement Deutsch's algorithm.[24] Their work introduced dual-rail encoding for photonic qubits.
Lov Grover, at Bell Labs, invents the quantum database search algorithm. The quadratic speedup is not as dramatic as the speedup for factoring, discrete logs, or physics simulations. However, the algorithm can be applied to a much wider variety of problems. Any problem that can be solved by random, brute-force search, may take advantage of this quadratic speedup in the number of search queries.
The first experimental demonstration of a quantum algorithm is reported. A working 2-qubit NMR quantum computer was used to solve Deutsch's problem by Jonathan A. Jones and Michele Mosca at Oxford University and shortly after by Isaac L. Chuang at IBM's Almaden Research Center, in California, and Mark Kubinec and the University of California, Berkeley together with coworkers at Stanford University and MIT.[33]
The first working 3-qubit NMR computer is reported.
Bruce Kane proposes a silicon-based nuclear spin quantum computer, using nuclear spins of individual phosphorus atoms in silicon as the qubits and donor electrons to mediate the coupling between qubits.[34]
Daniel Gottesman and Emanuel Knill independently prove that a certain subclass of quantum computations can be efficiently emulated with classical resources (Gottesman–Knill theorem).[37]
Samuel L. Braunstein and collaborators show that none of the bulk NMR experiments performed to date contain any entanglement; the quantum states being too strongly mixed. This is seen as evidence that NMR computers would likely not yield a benefit over classical computers. It remains an open question, however, whether entanglement is necessary for quantum computational speedup.[38]
Gabriel Aeppli, Thomas Felix Rosenbaum and colleagues demonstrate experimentally the basic concepts of quantum annealing in a condensed matter system.
Arun K. Pati and Samuel L. Braunstein prove the quantum no-deleting theorem. This is dual to the no-cloning theorem which shows that one cannot delete a copy of an unknown qubit. Together with the stronger no-cloning theorem, the no-deleting theorem has the implication that quantum information can neither be created nor be destroyed.
The first execution of Shor's algorithm at IBM's Almaden Research Center and Stanford University is demonstrated. The number 15 was factored using 1018 identical molecules, each containing seven active nuclear spins.
Noah Linden and Sandu Popescu prove that the presence of entanglement is a necessary condition for a large class of quantum protocols. This, coupled with Braunstein's result (see 1999 above), called the validity of NMR quantum computation into question.[40]
Emanuel Knill, Raymond Laflamme, and Gerard Milburn show that optical quantum computing is possible with single-photon sources, linear optical elements, and single-photon detectors, establishing the field of linear optical quantum computing.
The Quantum Information Science and Technology Roadmapping Project, involving some of the main participants in the field, lays out the Quantum computation roadmap.
A group led by Gerhard Birkl (now at TU Darmstadt) demonstrates the first 2D array of optical tweezers with trapped atoms for quantum computation with atomic qubits.[43]
The first implementation of a CNOT quantum gate, according to the Cirac–Zoller proposal, is reported by a team at the University of Innsbruck led by Rainer Blatt.[47]
Physicists at the University of Innsbruck show deterministic quantum-state teleportation between a pair of trapped calcium ions.[48]
The first five-photon entanglement is demonstrated by Jian-Wei Pan's team at the University of Science and Technology of Chin; the minimal number of qubits required for universal quantum error correction.[49]
Two teams of physicists measure the capacitance of a Josephson junction for the first time. The methods could be used to measure the state of quantum bits in a quantum computer without disturbing the state.[50]
The Materials Science Department of Oxford University, England cage a qubit in a "buckyball" (a molecule of buckminsterfullerene) and demonstrated quantum "bang-bang" error correction.[52]
Vlatko Vedral of the University of Leeds and colleagues at the universities of Porto and Vienna find that the photons in ordinary laser light can be quantum mechanically entangled with the vibrations of a macroscopic mirror.[54]
Samuel L. Braunstein at the University of York along with the University of Tokyo and the Japan Science and Technology Agency give the first experimental demonstration of quantum telecloning.[55]
Professors at the University of Sheffield develop a means to efficiently produce and manipulate individual photons at high efficiency at room temperature.[56]
A new error checking method is theorized for Josephson junction computers.[57]
A two-dimensional ion trap is developed for quantum computing.[59]
Seven atoms are placed in a stable line, a step on the way to constructing a quantum gate, at the University of Bonn.[60]
A team at Delft University of Technology in the Netherlands creates a device that can manipulate the "up" or "down" spin-states of electrons on quantum dots.[61]
Tai-Chang Chiang, at Illinois at Urbana–Champaign, finds that quantum coherence can be maintained in mixed-material systems.[66]
Cristophe Boehme, University of Utah, demonstrates the feasibility of reading data using the nuclear spin on a silicon-phosphorus Kane quantum computer.[67]
Chip constructed by D-Wave Systems Inc. designed to operate as a 128-qubit superconducting adiabatic quantum optimization processor, mounted in a sample holder (2009)
NIST demonstrates multiple computing operations on qubits.[141]
The first large-scale topological cluster state quantum architecture is developed for atom-optics.[142]
A combination of all of the fundamental elements required to perform scalable quantum computing through the use of qubits stored in the internal states of trapped atomic ions is shown.[143]
Researchers at University of Bristol demonstrate Shor's algorithm on a silicon photonic chip.[144]
Quantum Computing with an Electron Spin Ensemble is reported.[145]
A so-called photon machine gun is developed for quantum computing.[146]
The first universal programmable quantum computer is unveiled.[147]
Scientists electrically control quantum states of electrons.[148]
Google collaborates with D-Wave Systems on image search technology using quantum computing.[149]
A method for synchronizing the properties of multiple coupled CJJ rf-SQUID flux qubits with a small spread of device parameters due to fabrication variations is demonstrated.[150]
Universal Ion Trap Quantum Computation with decoherence free qubits is realized.[151]
The first chip-scale quantum computer is reported.[152]
D-Wave claimed to have developed quantum annealing and introduced their product called D-Wave One. The company claims this is the first commercially available quantum computer.[177]
Repetitive error correction was demonstrated in a quantum processor.[178]
Diamond quantum computer memory was demonstrated.[179]
Coherence time of 39 minutes at room temperature (and 3 hours at cryogenic temperatures) was demonstrated for an ensemble of impurity-spin qubits in isotopically purified silicon.[201]
Extension of time for a qubit maintained in superimposed state for ten times longer than what has ever been achieved before was reported.[202]
The first resource analysis of a large-scale quantum algorithm using explicit fault-tolerant, error-correction protocols was developed for factoring.[203]
Researchers in Japan and Austria published the first large-scale quantum computing architecture for a diamond-based system.[208]
Scientists at the University of Innsbruck performed quantum computations on a topologically encoded qubit which was encoded in entangled states distributed over seven trapped-ion qubits.[209]
Scientists transferred data by quantum teleportation over a distance of 10 feet (3.0 meters) with zero percent error rate; a vital step towards a quantum Internet.[210][211]
Physicists led by Rainer Blatt joined forces with scientists at the Massachusetts Institute of Technology (MIT), led by Isaac Chuang, to efficiently implement Shor's algorithm in an ion-trap-based quantum computer.[217]
IBM released the Quantum Experience, an online interface to their superconducting systems. The system is immediately used to publish new protocols in quantum information processing.[218][219]
Google, using an array of 9 superconducting qubits developed by the Martinis group and UCSB, simulated a hydrogen molecule.[220]
Scientists in Japan and Australia invented a quantum version of a Sneakernet communications system.[221]
D-Wave Systems Inc. announced general commercial availability of the D-Wave 2000Q quantum annealer, which it claimed has 2000 qubits.[222]
A blueprint for a microwave trapped ion quantum computer was published.[223]
IBM unveiled a 17-qubit quantum computer—and a better way of benchmarking it.[224]
Scientists built a microchip that generates two entangled qudits each with 10 states, for 100 dimensions total.[225]
Microsoft revealed Q#, a quantum programming language integrated with its Visual Studio development environment. Programs can be executed locally on a 32-qubit simulator, or a 40-qubit simulator on Azure.[226]
IBM revealed a working 50-qubit quantum computer that can maintain its quantum state for 90 microseconds.[227]
The first teleportation using a satellite, connecting ground stations over a distance of 1400 km apart was announced.[228] Previous experiments were at Earth, at shorter distances.
MIT scientists reported the discovery of a new triple-photon form of light.[230][231]
Oxford researchers successfully use a trapped-ion technique, where they placed two charged atoms in a state of quantum entanglement to speed up logic gates by a factor of 20 to 60 times, as compared with the previous best gates, translated to 1.6 microseconds long, with 99.8% precision.[232]
QuTech successfully tested a silicon-based 2-spin-qubit processor.[233]
Google announced the creation of a 72-qubit quantum chip, called "Bristlecone",[234] achieving a new record.
Intel began testing a silicon-based spin-qubit processor manufactured in the company's D1D fab in Oregon.[235]
Intel confirmed development of a 49-qubit superconducting test chip, called "Tangle Lake".[236]
Japanese researchers demonstrated universal holonomic quantum gates.[237]
An integrated photonic platform for quantum information with continuous variables was documented.[238]
On December 17, 2018, the company IonQ introduced the first commercial trapped-ion quantum computer, with a program length of over 60 two-qubit gates, 11 fully connected qubits, 55 addressable pairs, one-qubit gate error of <0.03% and two-qubit gate error of <1.0%.[239][240]
IBM Q System One (2019), the first circuit-based commercial quantum computer
IBM unveiled its first commercial quantum computer, the IBM Q System One,[244] designed by UK-based Map Project Office and Universal Design Studio and manufactured by Goppion.[245]
Austrian physicists demonstrated self-verifying, hybrid, variational quantum simulation of lattice models in condensed matter and high-energy physics using a feedback loop between a classical computer and a quantum co-processor.[246]
Griffith University, UNSW and UTS, in partnership with seven universities in the United States, develop noise cancelling for quantum bits via machine learning, taking quantum noise in a quantum chip down to 0%.[247][248]
Google revealed its Sycamore processor, consisting of 53 qubits. A paper by Google's quantum computer research team was briefly available in late September 2019, claiming the project had reached quantum supremacy.[251][252][253] Google also developed a cryogenic chip for controlling qubits from within a dilution refrigerator.[254]
20 April – UNSW Sydney develops a way of producing 'hot qubits' – quantum devices that operate at 1.5 kelvin.[256]
11 March – UNSW perform electric nuclear resonance to control single atoms in electronic devices.[257]
23 April – University of Tokyo and Australian scientists create and successfully test a solution to the quantum wiring problem, creating a 2D structure for qubits. Such structure can be built using existing integrated circuit technology and has considerably lower cross-talk.[258]
11 February – Quantum engineers report that they created artificial atoms in silicon quantum dots for quantum computing and that artificial atoms with a higher number of electrons can be more stable qubits than previously thought possible. Enabling silicon-based quantum computers may make it possible to reuse the manufacturing technology of "classical" modern-day computer chips among other advantages.[261][262]
14 February – Quantum physicists develop a novel single-photon source which may allow bridging of semiconductor-based quantum-computers that use photons by converting the state of an electron spin to the polarisation of a photon. They showed that they can generate a single photon in a controlled way without the need for randomly formed quantum dots or structural defects in diamonds.[263][264]
25 February – Scientists visualize a quantum measurement: by taking snapshots of ion states at different times of measurement via coupling of a trapped ion qutrit to the photon environment, they showed that the changes of the degrees of superpositions, and therefore of probabilities of states after measurement, happens gradually under the measurement influence.[265][266]
Working IQM Quantum Computer installed in Espoo, Finland in 20202 March – Scientists report achieving repeated quantum nondemolition measurements of an electron's spin in a silicon quantum dot: measurements that do not change the electron's spin in the process.[267][268]
11 March – Quantum engineers report to have controlled the nucleus of a single atom using only electric fields. This was first suggested to be possible in 1961 and may be used for silicon quantum computers that use single-atom spins without needing oscillating magnetic fields. This may be especially useful for nanodevices, for precise sensors of electric and magnetic fields, as well as for fundamental inquiries into quantum nature.[269][270]
19 March – A US Army laboratory announces that its scientists analysed a Rydberg sensor's sensitivity to oscillating electric fields over an enormous range of frequencies—from 0 to 10^12 Hz (the spectrum to 0.3 mm wavelength). The Rydberg sensor may potentially be used to detect communications signals as it could reliably detect signals over the entire spectrum and compare favourably with other established electric field sensor technologies, such as electro-optic crystals and dipole antenna-coupled passive electronics.[271][272]
23 March – Researchers report that they corrected for signal loss in a prototype quantum node that can catch, store and entangle bits of quantum information. Their concepts could be used for key components of quantum repeaters in quantum networks and extend their longest possible range.[273][274]
15 April – Researchers demonstrate a proof-of-concept silicon quantum processor unit cell which works at 1.5 kelvin – many times warmer than common quantum processors that are being developed. The finding may enable the integration of classical control electronics with a qubit array and substantially reduce costs. The cooling requirements necessary for quantum computing have been called one of the toughest roadblocks in the field.[275][276][277][278]
16 April – Scientists prove the existence of the Rashba effect in bulk perovskites. Previously researchers have hypothesized that the materials' extraordinary electronic, magnetic and optical properties – which make it a commonly used material for solar cells and quantum electronics – are related to this effect which to date had not been proven to be present in the material.[279][280]
8 May – Researchers report to have developed a proof-of-concept of a quantum radar using quantum entanglement and microwaves which may potentially be useful for the development of improved radar systems, security scanners and medical imaging systems.[281][282][283]
15 June – Scientists report the development of the smallest synthetic molecular motor, consisting of 12 atoms and a rotor of 4 atoms, shown to be capable of being powered by an electric current using an electron scanning microscope and moving even with very low amounts of energy due to quantum tunneling.[292][293][294]
17 June – Quantum scientists report the development of a system that entangled two photon quantum communication nodes through a microwave cable that can send information in between without the photons being sent through, or occupying, the cable. On 12 June it was reported that they also, for the first time, entangled two phonons as well as erase information from their measurement after the measurement had been completed using delayed-choice quantum erasure.[295][296][297][298]
18 June – Honeywell announces a quantum computer with a quantum volume of 64, the highest at the time.[299]
13 August – Universal coherence protection is reported to have been achieved in a solid-state spin qubit, a modification that allows quantum systems to stay operational (or "coherent") for 10,000 times longer than before.[300][301]
26 August – Scientists report that ionizing radiation from environmental radioactive materials and cosmic rays may substantially limit the coherence times of qubits if they are not shielded adequately.[302][303][304]
Google Sycamore quantum computer processor in 201928 August – Quantum engineers working for Google report the largest chemical simulation on a quantum computer – a Hartree–Fock approximation with a Sycamore computer paired with a classical computer that analyzed results to provide new parameters for a 12-qubit system.[305][306][307]
2 September – Researchers present an eight-user city-scale quantum communication network, located in Bristol, England, using already deployed fibres without active switching or trusted nodes.[308][309]
9 September – Xanadu offers a cloud quantum computing service, offering a photonic quantum computer.[310]
3 December – Chinese researchers claim to have achieved quantum supremacy, using a photonic peak 76-qubit system (43 average) known as Jiuzhang, which performed calculations at 100 trillion times the speed of classical supercomputers.[313][314][315]
29 October – Honeywell introduces a subscription for a quantum computing service, known as quantum computing as a service,, with an ion trap quantum computer.[316]
12 December – At the IEEE International Electron Devices Meeting (IEDM), IMEC shows an RF multiplexer chip that operates at temperatures as low as a few milikelvins, designed for quantum computers. Researchers from the Chalmers University of Technology developed a cryogenic low-noise amplifier (LNA) for amplifying signals from qubits, made of indium phosphide (InP) high-electron-mobility transistors (HEMTs).[317]
21 December – Publication of research of "counterfactual quantum communication" – whose first achievement was reported in 2017 – by which information can be exchanged without any physical particle traveling between observers and without quantum teleportation.[318] The research suggests that this is based on some form of relation between the properties of modular angular momentum.[319][320][321]
6 January – Chinese researchers report that they have built the world's largest integrated quantum communication network, combining over 700 optical fibers with two QKD-ground-to-satellite links for a total distance between nodes of the network of networks of up to ~4,600 km.[322][323]
15 January – Researchers in China report the successful transmission of entangled photons between drones, used as nodes for the development of mobile quantum networks or flexible network extensions, marking the first work in which entangled particles were sent between two moving devices.[326][327]
27 January – BMW announces the use of a quantum computer for the optimization of supply chains.[328]
28 January – Swiss and German researchers report the development of a highly efficient single-photon source for quantum IT with a system of gated quantum dots in a tunable microcavity which captures photons released from these excited "artificial atoms".[329][330]
3 February – Microsoft starts offering a cloud quantum computing service, called Azure Quantum.[331]
11 March – Honeywell announces a quantum computer with a quantum volume of 512.[334]
13 April – In a preprint, an astronomer describes for the first time how one could search for quantum communicationtransmissions sent by extraterrestrial intelligence using existing telescope and receiver technology. He also provides arguments for why future searches of SETI should also target interstellar quantum communications.[335][336]
17 June – Austrian, German and Swiss researchers present a quantum computing demonstrator fitting into two 19-inch racks, the world's first quality standards-meeting compact quantum computer.[343][344]
29 June – IBM demonstrates a quantum advantage.[345]
1 July – Rigetti develops a method to join several quantum processor chips together.[346]
7 July – American researchers present a programmable quantum simulator that can operate with 256 qubits,[347][348] and on the same date and journal another team presents a quantum simulator of 196 Rydeberg atoms trapped in optical tweezers.[349]
25 October – Chinese researchers report that they have developed the world's fastest programmable quantum computers. The photon-based Jiuzhang 2 is claimed to calculate a task in one millisecond, that otherwise would have taken a conventional computer 30 trillion years to complete. Additionally, Zuchongzhi 2 is a 66-qubit programmable superconducting quantum computer that was claimed to be the world's fastest quantum computer that can run a calculation task one million times more complex than Google's Sycamore, as well as being 10 million times faster.[350][351]
16 November – IBM claims that it has created a 127 quantum bit processor, 'IBM Eagle', which according to a report is the most powerful quantum processor known. According to the report, the company had not yet published an academic paper describing its metrics, performance or abilities.[354][355]
14 April – The Quantinuum System Model H1-2 doubles its performance claiming to be the first commercial quantum computer to pass quantum volume 4096.[359]
26 May – A universal set of computational operations on fault-tolerant quantum bits is demonstrated by a team of experimental physicists in Innsbruck, Austria.[360]
21 July – A universal qudit quantum processor is demonstrated with trapped ions.[365]
15 August – Nature Materials publishes the first work showing optical initialization and coherent control of nuclear spin qubits in 2D materials (an ultrathin hexagonal boron nitride).[366]
24 August – Nature publishes the first research related to a set of 14 photons entangled with high efficiency and in a defined way.[367]
26 August – Created photon pairs at several different frequencies using optical ultra-thin resonant metasurfaces made up of arrays of nanoresonators is reported.[368]
29 August – Physicists at the Max Planck Institute for Quantum Optics deterministically generate entangled graph states of up to 14 photons using a trapped rubidium atom in an optical cavity.[369]
2 September – Researchers from The University of Tokyo and other Japanese institutions develop a systematic method that applies optimal control theory (GRAPE algorithm) to identify the theoretically optimal sequence from among all conceivable quantum operation sequences. It is necessary to complete the operations within the time that the coherent quantum state is maintained.[370]
30 September – Researchers at University of New South Wales achieve a coherence time of two milliseconds, 100 times higher than the previous benchmark in the same quantum processor.[371]
9 November – IBM presents its 433-qubit 'Osprey' quantum processor, the successor to its Eagle system.[372][373]
1 December – The world's first portable quantum computer enters into commerce in Japan. With three variants, topping out at 3 qubits, they are meant for education. They are based on nuclear magnetic resonance (NMR), "NMR has extremely limited scaling capabilities" and dimethylphosphite.[374][375][376]
17 February - Fusion-based quantum computation is proposed[379]
27 March – India's first quantum computing-based telecom network link is inaugurated.[380]
14 June – IBM computer scientists report that a quantum computer produced better results for a physics problem than a conventional supercomputer.[381][382]
21 June – Microsoft declares that it is working on a topological quantum computer based on Majorana fermions, with the aim of arriving within 10 years at a computer capable of carrying out at least one million operations per second with an error rate of one operation every 1,000 billion (corresponding to 11 uninterrupted days of calculation).[383]
13 October – Researchers at TU Darmstadt publish the first experimental demonstration of a qubit array with more than 1,000 qubits:[384][385] A 3,000-site atomic array based on a 2D configuration of optical tweezers[386] holds up to 1,305 atomic qubits.
24 October – Atom Computing announces that it has "created a 1,225-site atomic array, currently populated with 1,180 qubits",[387] based on Rydberg atoms.[388]
4 December – IBM presents its 1121-qubit ‘Condor’ quantum processor, the successor to its Osprey and Eagle systems.[389][390] The Condor system was the culmination of IBM's multi-year ‘Roadmap to Quantum Advantage’ seeking to break the 1,000 qubit threshold.[391]
6 December – A group led by Misha Lukin at Harvard University realises a programmable quantum processor based on logical qubits using reconfigurable neutral atom arrays.[392]
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