Quantum Computers of Atoms

99.5 Percent

In 2023 a team from Harvard and MIT reported in Nature two-qubit entangling gates (CZ gates) at 99.5 % fidelity on up to 60 rubidium atoms at once: about one error in 200. The best neutral-atom two-qubit gates before had reached about 97.5 %, and the first CNOT gate between two atoms, in 2010, 73 %. At 99.5 % the gates clear the threshold that surface-code error correction needs.

Late in 2023 the same machine encoded 48 logical qubits on 128 atoms, in codes that can detect errors but not correct them. In 2025 a Caltech group loaded more than 6,100 caesium atoms into about 12,000 tweezers, the largest array at the time, though that experiment ran no two-qubit gates. A preprint of April 2026 reports two-qubit gates at 99.854 %.

Two-qubit gates 99.5 % (2023) · 48 logical qubits (2023) · more than 6,100 atoms (2025)

A Cold Cloud

It begins with a cloud of cold atoms. At the heart of the glass vacuum cell, laser beams press on the atoms from every side while the field of two coils herds them together, chilling them to within a hair of absolute zero: a magneto-optical trap, or MOT. In the Harvard machine the cloud holds millions of rubidium-87 atoms; Caltech’s is about 1.6 mm across.

The 1997 Nobel Prize in Physics went to “methods to cool and trap atoms with laser light”. How a MOT works is told in the plate on Bose–Einstein condensation. Here the cloud is only raw material: the tweezers lift atoms out of it one at a time.

MOT: light and a magnetic field · millions of ⁸⁷Rb atoms · a cloud about 1.6 mm across (Caltech)

Light That Holds an Atom

An objective of high numerical aperture squeezes a laser beam to a point, and the light is brightest there. If its wavelength is a little longer than the one the atom absorbs, the atom is drawn to the brightest spot, as if into a small pit made of light: an optical tweezer. Typical tweezers use near-infrared light of 808 to 850 nm, focused to a radius of about 1 µm, in a pit about 1 mK deep (as a temperature).

In 1986 a focused laser beam trapped atoms for the first time: about 500 sodium atoms. In 2001 a team in France, with an objective of numerical aperture 0.7, shrank the spot below a micrometre, and single atoms went in: the pit had room for only one. Half of the 2018 Nobel Prize in Physics went to optical tweezers “and their application to biological systems”.

a focus about 1 µm in radius · about 1 mK deep · 808⁠–⁠850 nm

One or None

A tweezer loads from the cold cloud by chance. Its spot is so small that when a second atom wanders in, the two collide violently in the light (a light-assisted collision) and both are thrown out. Each tweezer ends up with one atom or none, half an atom on average: the collisional blockade.

In practice loading runs at 50⁠–⁠60 %; in 2025 Harvard’s machine reached 75 % with a different cooling method (gray molasses). For every tweezer to be full at once, each one must get lucky: with 100 tweezers at 50 %, the chance is 0.5¹⁰⁰, about 7.9 × 10⁻³¹.

Each tweezer: 0 or 1 atom · 0.5 on average · 0.5¹⁰⁰ ≈ 7.9 × 10⁻³¹

A Photo, Then the Gaps

The way round it is a photograph. Under imaging light the atoms fluoresce, and a camera sees which tweezers hold one and which are empty; a computer works out the moves, and a set of moving tweezers picks atoms up and sets them into the gaps, until the array has no holes. What runs here is the page’s toy version: load, photograph, fill, one atom at a time along straight paths; real machines often move whole rows and columns at once.

In 2016 a Harvard team assembled lines of more than 50 atoms this way in under 400 ms, and a team in France arrays of about 50 atoms in two dimensions, sorted in under 50 ms. In 2025 a team at the University of Science and Technology of China used AI to compute holograms in real time and a fast spatial light modulator to move all the atoms at once: 2,024 atoms in 60 ms (45 × 45 = 2,025 sites, nearly without defects).

Photo → plan → fill · 2016: about 50 atoms · 2025: 2,024 atoms in 60 ms

Two Levels

Each atom is one qubit. The Harvard machine uses rubidium-87, whose ground state splits into two hyperfine levels 6.834 682 610 904 GHz apart: in the lower level (F = 1) the state with magnetic quantum number zero is the qubit’s 0, and its counterpart in the upper level (F = 2) is the 1. These are called clock states: to first order a magnetic field cannot move them, so they keep a quantum state for a long time. Raman laser light turns all the atoms at once, and single-qubit gates reach 99.97 % fidelity.

Caltech’s 6,100-atom array uses caesium-133, with a coherence time of 12.6 s. The hyperfine frequency of caesium-133’s ground state, 9 192 631 770 Hz, is what defines the second; clocks built on atomic levels are in the plate on the optical lattice clock. Superconducting qubits are artificial atoms made of circuits, in the plate on superconducting qubits; these qubits are natural atoms, each one identical to the next.

⁸⁷Rb: 6.834 682 610 904 GHz · clock states · single-qubit gates 99.97 %

The Rydberg Blockade

Atoms in their ground state barely interact. To make two qubits feel each other, a laser lifts an atom’s electron to a very high level, with a principal quantum number n in the tens: a Rydberg atom. The Harvard machine uses two beams, at 420 nm and 1013 nm, to excite rubidium to n = 53. The radius of the electron’s orbit grows roughly as n², to about 150 nm at n = 53 (an order of magnitude), far larger than the atom in its ground state.

Between two Rydberg atoms the van der Waals interaction goes as C₆/R⁶, and C₆ grows roughly as n¹¹. When two atoms are closer than the blockade radius, once one is excited the other cannot be: the laser no longer matches the energy of both excited together. The radius depends on n and on how strongly the laser drives: about 9 µm for the 70S state at a Rabi frequency Ω = 2π × 2 MHz, for example. The idea was proposed in 2000, named in 2001, and first seen with two single atoms in 2009.

V = C₆/R⁶ · C₆ ∝ n¹¹ · 70S, Ω = 2π × 2 MHz: R_b ≈ 9 µm

One Pulse, Many Gates

Move two atoms to about 2 µm apart and their interaction is about 2π × 450 MHz, far above the laser’s Rabi frequency of 2π × 4.6 MHz: an almost perfect blockade. One laser pulse of 270 ns then excites only atoms in state 1, and the result is a CZ gate: when both atoms are in state 1, their joint phase flips sign. The tweezers are switched off for a few hundred nanoseconds during the pulse, so their light does not disturb the Rydberg state.

The same pulse lights every gate site, so every pair runs its gate at once; the sites sit at least 10 µm apart and leave each other alone. In 2023 the gates ran at 99.54 % on 20 atoms in parallel and 99.48 % on 60; later, up to 160 qubits ran gates at once, at 99.3⁠–⁠99.5 %. The 420 nm light comes from an 840 nm titanium-sapphire laser, frequency-doubled; titanium-sapphire lasers also appear in the plate on attosecond pulses.

about 2 µm · 2π × 450 MHz ≫ Ω = 2π × 4.6 MHz · 270 ns · 60 atoms in parallel

Cell and Objective, Cut Open

The atoms hang in a glass vacuum cell that holds almost nothing else: from the atoms’ lifetime Caltech estimated about 7 × 10⁻¹² mbar in theirs, some 7 × 10⁻¹⁵ of the pressure of the air. One end of the cell joins the stainless-steel vacuum system, and the trap’s coils sit on either side. With a corner of the glass and the coils cut away, the array of atoms inside comes into view.

The objective sits outside the cell, looking in through the glass. Cut open, it is a stack of lenses growing larger towards the back; the lenses in the section are schematic, not any maker’s design. The one objective does two jobs: it focuses the tweezers’ light into the middle of the cell, and it gathers the light the atoms give off and passes it to the camera.

about 7 × 10⁻¹² mbar (Caltech’s estimate) · the objective outside the cell

Numerical Aperture 0.65

An objective’s power to gather light is its numerical aperture, NA. The Harvard and Caltech machines both use objectives of NA 0.65, a cone of light with a half-angle of about 40.5°. The larger the NA, the smaller the focus and the closer the tweezers can sit: the two atoms in a Harvard gate site are only about 2 µm apart because of it.

Caltech’s objective sees a field 1.5 mm across, holding all of its roughly 12,000 tweezers. In 2001, when single atoms were first loaded, the objective was nine spherical lenses of NA 0.7, inside the ultra-high vacuum, with a working distance of 10 mm.

NA 0.65 · half-angle about 40.5° · a field 1.5 mm across (Caltech)

A Picture of Phase

The still array of tweezers comes from a spatial light modulator: a liquid-crystal-on-silicon screen whose pixels change only the light’s phase, never its brightness. The screen shows a computed pattern of phase, a hologram; a laser beam reflects off it, the objective focuses it, and in the focal plane hundreds or thousands of spots appear, in whatever pattern was asked for.

Caltech uses two modulators, one with 1061 nm light and one with 1055 nm, making about 12,000 tweezers 7.2 µm apart, about 1.4 mW each at the atoms, from 130 W of fibre amplifiers. The screens are water-cooled to 22 °C, and the holograms optimised with a weighted Gerchberg–Saxton algorithm. The phase pattern at the top right is this page’s simple sum of one plane wave per spot, not that algorithm.

phase only · about 12,000 tweezers, 7.2 µm apart (Caltech, 2025)

Tweezers That Move

To move atoms, some tweezers must move. An acousto-optic deflector is a crystal in which a radio-frequency signal sets up a sound wave; the wave bends light like a grating, more at higher frequencies, and several frequencies at once split one beam into several. Two deflectors are crossed, one for x and one for y, and two voltage waveforms weave a whole grid, each row and each column one frequency.

A step of 0.49 MHz in frequency moved the spot 2.6 µm in Harvard’s 2016 line of atoms. Sweep a frequency and its spots glide; rows and columns never cross. For a hand-off a moving tweezer deepens to about twice the depth of a still one and carries the atom away; a move between gates takes about 200 µs. The deflectors’ bandwidth limits the grid: it set the 250 µm width of Harvard’s zones.

one tone per row · 0.49 MHz ↔ 2.6 µm · about 200 µs a move

A Fluorescence Photo

An atom is far too small to show its shape; all that can be seen is its light. Imaging light makes each atom absorb and re-emit photons over and over (780 nm for rubidium, 852 nm for caesium); the same objective gathers some of that light, a dichroic mirror separates it from the tweezers’ light, and it goes to the camera. In the photo each atom is a bright dot and an empty tweezer stays dark.

The 2016 experiments used electron-multiplying CCD cameras. Harvard now uses a CMOS camera, chosen for its fast readout; Caltech uses a quantitative CMOS (qCMOS) camera, exposes each image for 80 ms, keeps 99.98952 % of the atoms through it, and tells full from empty with 99.99374 % accuracy. To read some qubits partway through a computation, Harvard moves them aside and images them in 500 µs, at about 99.8 %.

80 ms · survival 99.98952 % · accuracy 99.99374 % (Caltech, 2025)

Three Zones

Atoms that move let a machine have zones. Harvard’s logical processor has three: a storage zone where idle qubits wait, free of gate errors; an entangling zone about 250 µm wide and 35 µm tall, evenly lit by the Rydberg beams, where the gates happen; and a readout zone about 100 µm away, where qubits to be read are moved and photographed without disturbing the rest.

Entanglement travels with the atoms: in 2022 entangled pairs were pulled 110 µm apart, and the entanglement showed no visible harm. In 2023, 48 logical qubits were encoded in [[8,3,2]] codes on 128 atoms and ran 228 logical two-qubit gates; such codes only detect errors, and the results improve by discarding the flagged runs. In 2025, in experiments with up to 448 atoms, a distance-5 surface code did 2.14 times better than distance 3.

storage · entangling · readout · entangling zone 250 × 35 µm · readout about 100 µm away

What Still Holds It Back

Atoms get lost. Now and then a stray gas molecule in the vacuum knocks one out, and how long atoms last in the tweezers depends on the machine: about 10 s in Harvard’s of 2023, about 23 minutes in Caltech’s; a whole array of N atoms stays complete for only 1/N of that. In the 2025 error-correction experiments about half the errors were lost atoms. One answer is to refill while computing: in 2025 another machine fed in 300,000 atoms a second and kept an array of more than 3,000 atoms going for over two hours.

The gates are not the slow part: a CZ gate takes 270 ns, the same order as the gates of superconducting qubits; moving atoms (about 200 µs a move) and photographing them (0.5 to 10 ms) are. In 2025 one round of surface-code correction took 4.45 ms, against 1.1 µs on Google’s superconducting chip Willow, about 4,000 times longer; the authors estimate that per logical step their methods are only some 10⁠–⁠20 times slower, an estimate rather than a measurement. Error correction itself is told in the plate on superconducting qubits.

about half the errors are lost atoms · one round of correction 4.45 ms, superconducting 1.1 µs

Taken Apart

The glass cell and its coils, the vacuum system, the objective, the dichroic and the camera, the spatial light modulator, the acousto-optic deflectors, the beam combiner, the tweezer laser and the Rydberg lasers, lifted apart one by one.

The part the pointer rests on (a tap, on a phone) lifts out on its own and takes its name, while the rest fade.