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Demonstration of multi-qubit entanglement and algorithms on a programmable neutral atom quantum computer
T. M. Graham, Y. Song, J. Scott, C. Poole, L. Phuttitarn, K. Jooya, P. Eichler, X. Jiang, A. Marra, B. Grinkemeyer, M. Kwon, M. Ebert, J. Cherek, M. T. Lichtman, M. Gillette, J. Gilbert, D. Bowman, T. Ballance, C. Campbell, E. D. Dahl, O. Crawford, N. S. Blunt, B. Rogers, T. Noel, M. Saffman
TL;DR
The paper addresses whether neutral-atom arrays can support programmable gate-model quantum computation with scalable qubits, long coherence, and high-fidelity logic. It implements native microwave, laser, and Rydberg-mediated gates to demonstrate GHZ preparation, quantum phase estimation, and QAOA MaxCut. The experiments establish programmable circuit capability while showing that gate errors and finite qubit resources limit present algorithmic performance and precision.
Problem
The work addresses the need to operate quantum computers at scale with long coherence times and high-fidelity logic while preserving interactions needed for computation.
Method
The authors use a two-dimensional neutral-atom array with scanned optical addressing and a native gate set of global microwave rotations, local RZ rotations, and CZ entangling gates.
Results
The platform created GHZ states up to six qubits and demonstrated quantum phase estimation and QAOA MaxCut circuits, including a four-qubit hydrogen-energy estimate of −1.06 Ha.
Takeaways & Limitations
The results demonstrate a programmable circuit-model neutral-atom quantum computer and provide capabilities relevant to entanglement-enhanced sensing, quantum phase estimation, and hybrid quantum-classical algorithms.
Takeaways & Limitations
Current two-qubit gate fidelity limits algorithmic performance, while phase-estimation precision is limited by qubit count, basis-set choice, and circuit approximations.
Abstract
from arXiv · showhide
Gate model quantum computers promise to solve currently intractable computational problems if they can be operated at scale with long coherence times and high fidelity logic. Neutral atom hyperfine qubits provide inherent scalability due to their identical characteristics, long coherence times, and ability to be trapped in dense multi-dimensional arrays\cite{Saffman2010}. Combined with the strong entangling interactions provided by Rydberg states\cite{Jaksch2000,Gaetan2009,Urban2009}, all the necessary characteristics for quantum computation are available. Here we demonstrate several quantum algorithms on a programmable gate model neutral atom quantum computer in an architecture based on individual addressing of single atoms with tightly focused optical beams scanned across a two-dimensional array of qubits. Preparation of entangled Greenberger-Horne-Zeilinger (GHZ) states\cite{Greenberger1989} with up to 6 qubits, quantum phase estimation for a chemistry problem\cite{Aspuru-Guzik2005}, and the Quantum Approximate Optimization Algorithm (QAOA)\cite{Farhi2014} for the MaxCut graph problem are demonstrated. These results highlight the emergent capability of neutral atom qubit arrays for universal, programmable quantum computation, as well as preparation of non-classical states of use for quantum enhanced sensing.
GHZ STATE PREPARATION
The platform prepares and characterizes neutral-atom GHZ states using native microwave, local laser, and Rydberg-mediated gates, demonstrating entanglement up to six qubits while exposing coherence limits that worsen with system size.
- GHZ STATE PREPARATION: GHZ states with up to N = 6 qubits were created using global microwave, local RZ, and CZ gates.State fidelity was evaluated from computational-basis populations and parity-oscillation coherence.
- GHZ STATE PREPARATION: The work reports the first neutral-atom GHZ states with N > 2 encoded on long-lived hyperfine ground-state qubits.Earlier neutral-atom GHZ states used ground–Rydberg transitions with coherence lifetimes below 2 µs for N ≥ 4.
- GHZ STATE PREPARATION: Parity-oscillation frequency showed the expected N scaling, providing a coherence-based signature of the prepared GHZ states.Parity was measured after analysis rotations and computed from even- versus odd-parity probabilities.
- GHZ STATE PREPARATION: GHZ coherence time followed a 1/N scaling caused by correlated, non-Markovian dephasing from magnetic-field noise, trap-intensity fluctuations, and atomic motion.The experiments used blue-detuned traps and m = 0 clock states, yet this scaling was still observed.
- GHZ STATE PREPARATION: Dynamical decoupling improved single-qubit coherence beyond 1 s and increased GHZN coherence time by more than a factor of five.The achievable optimized GHZ coherence scaling was left for future studies.
METHODS
The apparatus combines a two-dimensional neutral-atom trap array, cooling and rearrangement, fluorescence-based state readout, and coherence-preserving qubit control. Coherence measurements characterize atom lifetimes, Ramsey dephasing, and dynamical-decoupling performance.
- A 2D blue-detuned optical trap array was combined with cooling below 5 µK and tweezer-based atomic rearrangement.
- Atoms were rearranged into sites separated by 9 µm to reduce optical crosstalk during circuit operations.
- Fluorescence imaging determined atom occupancy, while removing f = 4 atoms mapped dark and bright signals to |1⟩ and |0⟩.
- Atom lifetimes reached ∼10 s at the 1/e population-decay point, while the qubit T1 time was ∼4 s.
- Ramsey coherence was typically 3.5 ms, improved to 8 ms with optimized cooling, ∼50 ms with dynamical decoupling, and ∼1 s using XY8.
2 . Quantum gate set
The platform implements programmable quantum circuits using global microwave rotations, local laser-controlled single-qubit rotations, and Rydberg-mediated entangling gates. Optical trap engineering and scanning beams support individual addressing across the array.
- A universal gate set used global microwave Rφ(θ) rotations, focused-laser RZ(θ) rotations, and Rydberg-mediated CZ gates.
- The CZ gate used simultaneous two-atom excitation to the 75s1/2 Rydberg state with beams focused to 3 µm waists.
- 92.7(13)% raw Bell-state fidelity was measured for the CZ gate, increasing to ∼95.5% after SPAM correction.
- The apparatus generated crossed optical trap-line arrays using diffractive optics and AODs driven by multiple radio-frequency tones.
- Arrays reached 24×24 lines, with atoms trapped in 15×15 arrays and 196 sites; the reported work used a 7×7 array.
C. Trap array analysis
The trap-array analysis models confinement and localization from line spacing, beam waist, aspect ratio, light shifts, and temperature, then compares predictions with measured trap properties. At the operating point, perpendicular confinement is weaker than in-plane confinement.
- The analytical model assumes ideal uniform-intensity lines with Gaussian transverse profiles and uses spacing d, waist w, and aspect ratio s = d/w.
- Measured trap vibration frequencies were 19 kHz radially and 4 kHz axially for d = 3 µm, s = 3, Ud = kB × 300 µK, and Ta = 5 µK.
- At s = 3, the transverse and axial effective trapping intensities were It/Id = 1.17 and It,z(zmax)/Id = 0.91, respectively.
- The confinement barrier was about 20% lower perpendicular to the array plane at the operating point.
- The model relates trap geometry and light shifts to spring constants, vibration frequencies, and thermal localization variances.
- Microwave spectroscopy verified intensity balancing; the six GHZ sites spanned 144 Hz in qubit frequency, and the N = 6 circuit lasted 180 µs.
D. Qubit addressing and crosstalk
Individual addressing uses tightly focused Gaussian beams, with spacing and beam waist chosen to suppress neighboring-site illumination. Measured crosstalk remained below 0.01 for both addressing wavelengths, while smaller waists introduce alignment and motion sensitivities.
- Single-site operations use focused Gaussian beams whose ideal focal-plane intensity decays as I(r) = I0e−2d2/w2.
- With d = 9 µm and w = 3 µm, the ideal intensity crosstalk was e−18 = 1.5×10−8.
- The measured crosstalk of the 459 nm beam at 9 µm spacing was ≪0.01.
- The measured crosstalk of the 1040 nm beam was also ≪0.01 at 9 µm spacing.
- Reducing beam waist lowers crosstalk but increases sensitivity to optical alignment and atom motion.
E. Two-qubit simultaneous addressing
The architecture uses scanned optical beams and frequency-compensated two-photon addressing to control multiple sites, while dual-site operation faces crosstalk constraints.
- E. Two-qubit simultaneous addressing: Two-photon addressing cancels scan-angle-dependent frequency shifts, allowing resonance at multiple atomic locations with one laser system.The two photons’ frequency shifts are arranged to cancel each other.
- E. Two-qubit simultaneous addressing: The beam-steering geometry maps acoustic modulation frequencies to beam positions and imposes a resonance condition for simultaneous addressing.The implementation selects opposite diffraction orders and matches beam positions before imposing fa1 + fa2 = 0.
- E. Two-qubit simultaneous addressing: Identical scanned-beam sizes can also be engineered by relating the AOD and output-plane waists.The passage introduces the output-plane waist relation for beams with waists wj at the AOD.
- E. Two-qubit simultaneous addressing: Simultaneous addressing supports pairs in the same row or column, but diagonal pairs generate undesired beams at the rectangle’s other corners.Spatial light modulators are identified as a possible way to relax this constraint.
- E. Two-qubit simultaneous addressing: 9 µm qubit spacing reduced dual-site addressing crosstalk to ≪0.01 because 1% spillover could otherwise cause large control errors.A modified beam-scanning system was expected to enable smaller spacings by using exactly the same frequencies at both sites.
F. Rydberg lasers
The Rydberg-laser system combines two-photon excitation, cavity-based frequency stabilization, and intensity stabilization, achieving narrow spectral features and measured coherence parameters.
- F. Rydberg lasers: Rydberg excitation uses 459 nm light from 6s1/2 to 7p1/2 and approximately 1040 nm light from 7p1/2 to 75s1/2.The 459 nm beam is produced by frequency doubling a Ti:Sa system, while the 918 nm source is frequency stabilized.
- F. Rydberg lasers: The 918 nm laser is locked to a high-finesse ULE reference cavity, with AOM, frequency-doubling, and intensity-stabilization stages completing the optical system.The intensity stabilization uses an AOM noise eater and a slower waveplate-polarizer loop.
- F. Rydberg lasers: The calculated T∗2 analysis uses atom temperature and magnetic-field noise, with measured coherence of 3.5 ms indicating a temperature near 5 µK.The stated magnetic-noise estimate is σ < 20 mG.
- F. Rydberg lasers: Three feedback loops cover fast, medium, and slow frequency corrections through an EOM, fast piezo, and slow piezo.The fast loop spans 100 kHz–10 MHz, while the medium loop covers DC–100 kHz.
- F. Rydberg lasers: Servo resonance peaks remain below −50 dBC for frequencies more than 20 kHz from the carrier.Laser noise was measured with a fiber-based self-heterodyne system using a 10 km delay line.
QUBIT COHERENCE
Qubit coherence is modeled through magnetic, trap-intensity, and motional dephasing, with measurements and trap design indicating millisecond-scale coherence and reduced intensity-noise sensitivity.
- QUBIT COHERENCE: The apparatus exhibited trapped-atom lifetimes of approximately 10 s and qubit T1 of approximately 4 s.The |0⟩→|1⟩ and |1⟩→|0⟩ transitions had approximately equal lifetimes.
- QUBIT COHERENCE: 34 mechanisms contribute to transverse coherence loss through magnetic noise, trap-light intensity noise, and atomic motion.These mechanisms produce time-dependent differential shifts or dephasing of the qubit transition.
- QUBIT COHERENCE: The measured average T∗2 across six GHZ-preparation sites was 3.5 ms, and the inferred atomic temperature was approximately 5 µK.Independent temperature measurements were similar but typically 1–2 µK higher.
- QUBIT COHERENCE: Blue-detuned trapping reduced atoms’ sensitivity to trap-intensity noise by a factor of 22 relative to the trapping-potential intensity.The estimate suggests trap-intensity noise was not significant even with free-running trap lasers.
- QUBIT COHERENCE: The circuit platform combines global microwave rotations, local RZ and Rφ gates, and CZ gates, with local rotations synthesized from global and local controls.CZ gates use Rydberg interactions, and local Hadamard rotations provide a CNOT construction.
ONE-QUBIT GATE FIDELITY
One-qubit gate performance was characterized with randomized benchmarking across the array and at the sites used for GHZ and algorithm experiments.
- ONE-QUBIT GATE FIDELITY: Global microwave rotation gates previously achieved 0.998 fidelity in randomized benchmarking.The present experiment increased the Rabi frequency to 76.5 kHz using a higher-power microwave amplifier.
- ONE-QUBIT GATE FIDELITY: Global Rφ(θ) gate performance was measured across all sites of a 7 × 7 = 49-qubit array using Clifford-group randomized benchmarking.The characterization reported SPAM error per qubit and gate fidelity.
- ONE-QUBIT GATE FIDELITY: Local RZ(θ) gates are sensitive to slow pulse-intensity fluctuations and variations in intensity caused by atomic position.The rotation angle depends on the integrated intensity experienced by the atom.
- ONE-QUBIT GATE FIDELITY: Local RZ(θ) and Rφ(θ) gate performance was characterized at the six sites used for GHZ preparation and algorithm demonstrations.The same randomized-benchmarking procedure reported SPAM error per qubit and gate fidelity.
A. Dephasing from low frequency intensity noise
Shot-to-shot optical intensity fluctuations produce phase uncertainty that grows with pulse area and reduce Rabi oscillation amplitude. Feedback stabilizes the optical power, making this contribution negligible relative to measured gate error.
- A. Dephasing from low frequency intensity noise: Shot-to-shot intensity variations cause dephasing of qubit rotations through fluctuations in the pulse phase.The phase uncertainty increases with the target phase θ0, reducing oscillation amplitude.
- A. Dephasing from low frequency intensity noise: 3.1% array-averaged SPAM error and 2.2×10^-3 average Clifford-gate error were measured across the 49-qubit array.At the six sites used for demonstrations, average SPAM error was 2.5% and average RZ(θ), Rφ(θ) error per gate was 7.5 × 10^-3.
- A. Dephasing from low frequency intensity noise: 10^-4 expected error for a π pulse is negligible compared with the observed gate fidelity error of ∼0.01 for a π pulse.Optical power is periodically sampled and stabilized using feedback to a waveplate and polarizer.
B. Dephasing from atom position variations
Atomic motion makes each shot sample a slightly different optical intensity, producing an exponential decay of Rabi amplitude with pulse length. The measured and simulated figure of merit agree closely.
- B. Dephasing from atom position variations: Atomic motion causes position-dependent intensity variations while its ∼1/(20 kHz) timescale is long compared with the gate time.The intensity can therefore be treated as constant during each gate.
- B. Dephasing from atom position variations: 0.0046 error per π pulse follows from the measured figure of merit fτ, defined using the 1/e Rabi-amplitude decay time.The resulting amplitude decay is exponential with pulse length.
- B. Dephasing from atom position variations: fτ = 46 was obtained in numerical simulation using experimental parameters.The simulation is presented alongside the measured shot-to-shot power variation in Fig. SM-6.
C. Light scattering
Spontaneous scattering from the 7p1/2 level contributes a calculable gate error. At the operating detuning, this contribution is comparable to position-induced error and can be reduced with larger detuning.
- C. Light scattering: The scattering error is negligible for |0⟩, while the |1⟩ state has the quoted nonzero scattering probability.The detuning from 7p1/2 is small compared with the qubit frequency.
- C. Light scattering: 0.0042 scattering error is estimated for a π pulse using Δ = 2π × 760 MHz and τ7p1/2 = 155 ns.The estimate uses the detuned-drive excited-state population and a coherence-decay prefactor.
- C. Light scattering: Larger detuning can reduce the spontaneous-scattering error.The complete estimated error budget is ϵintensity = 0.0001, ϵposition = 0.0040, and ϵscatter = 0.0042.
SM-V. CZ GATE TUNING AND CHARACTERIZATION
The symmetric CZ gate uses paired detuned Rydberg pulses and local phase compensation to implement canonical two-qubit control. Characterization across separations and qubit pairs establishes high, though SPAM-sensitive, Bell-state and gate fidelities.
- SM-V. CZ GATE TUNING AND CHARACTERIZATION: Two detuned Rydberg pulses drive the |11⟩ state through a 2π rotation, while compensation pulses correct residual |10⟩ and |01⟩ phases.The relative phase between Rydberg pulses and local RZ corrections are calibrated to produce a canonical CZ gate.
- SM-V. CZ GATE TUNING AND CHARACTERIZATION: 0.927(0.013) maximum Bell-state fidelity was measured without SPAM correction, while the average across gate pairs was 0.90.Bell-state populations and parity were used for the characterization.
- SM-V. CZ GATE TUNING AND CHARACTERIZATION: 2.5% average SPAM error per qubit is dominated by atom loss during readout and imperfect optical pumping.Simply subtracting SPAM errors from raw infidelity overestimates corrected gate fidelity; a two-qubit process analysis is used instead.
- SM-V. CZ GATE TUNING AND CHARACTERIZATION: 0.914(0.014) and 0.927(0.013) Bell-state fidelities were measured at 3 µm and 9 µm spacing, respectively.The corresponding blockade shifts were 1.03 GHz and 3.0 MHz.
- SM-V. CZ GATE TUNING AND CHARACTERIZATION: 2.2–3.1% SPAM error contributes to measured Bell-state infidelity, yielding SPAM-corrected average fidelity between 0.921 and 0.931.The correction does not include biases from blowaway-based measurement in the |1⟩ state.