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Fast and scalable quantum information processing with two-electron atoms in optical tweezer arrays

G. Pagano, F. Scazza, M. Foss-Feig

arXiv:1808.02503v2quant-phcond-mat.quant-gasphysics.atom-ph

TL;DR

High-fidelity two-qubit gates remain a challenge for neutral-atom quantum computing, and the paper proposes a programmable tweezer architecture that uses alkaline-earth-like atoms’ clock states to support operations on nuclear-spin qubits. The authors predict about 10% total gate error after 45 gates under an assumed 10^-3 transport infidelity, and identify cooling and entropy extraction as crucial tools for implementation.

  • Problem

    Scalable neutral-atom systems still face the challenge of implementing high-fidelity two-qubit entangling gates, and a complete spin-exchange-based universal architecture had not been implemented.

    Source: §I · p. 1

  • Method

    The paper proposes a programmable tweezer array of alkaline-earth-like atoms using nuclear spins as qubits and electronic clock states for auxiliary operations.

    Source: §I · p. 1, §II · p. 2

  • Results

    About 10% total gate error is predicted after 45 gates, assuming 10^-3 transport infidelity.

    Source: §1 · p. 6

  • Takeaways & Limitations

    Ground-state cooling and/or entropy extraction are crucial tools for implementing the architecture.

    Source: Appendix D · p. 12

    Increasing tweezer depth can suppress errors from motional excitation, but at the expense of a higher off-resonant scattering rate.

    Source: §1 · p. 6

Abstract

from arXiv · show

Atomic systems, ranging from trapped ions to ultracold and Rydberg atoms, offer unprecedented control over both internal and external degrees of freedom at the single-particle level. They are considered among the foremost candidates for realizing quantum simulation and computation platforms that can outperform classical computers at specific tasks. In this work, we describe a realistic experimental toolbox for quantum information processing with neutral alkaline-earth-like atoms in optical tweezer arrays. In particular, we propose a comprehensive and scalable architecture based on a programmable array of alkaline-earth-like atoms, exploiting their electronic clock states as a precise and robust auxiliary degree of freedom, and thus allowing for efficient all-optical one- and two-qubit operations between nuclear spin qubits. The proposed platform promises excellent performance thanks to high-fidelity register initialization, rapid spin-exchange gates and error detection in readout. As a benchmark and application example, we compute the expected fidelity of an increasing number of subsequent SWAP gates for optimal parameters, which can be used to distribute entanglement between remote atoms within the array.

I. INTRODUCTION

Scalable neutral-atom computing still faces the challenge of implementing high-fidelity two-qubit gates, and no complete spin-exchange universal architecture had been implemented. The paper proposes a programmable optical-tweezer architecture using alkaline-earth-like atoms and their clock-state spin exchange.

I. INTRODUCTION

  • Scalable, high-fidelity two-qubit entangling gates remain an outstanding challenge despite single-qubit manipulation fidelities above 99%.The introduction notes that Rydberg blockade is often used for two-qubit gates, while spin-exchange proposals had not yet yielded a complete universal architecture.Source: §I · p. 1
  • The proposal analyzes a realistic optical-tweezer architecture using spin-exchange gates among neutral alkaline-earth-like atoms, with gate fidelities above 99% and favorable scaling to large arrays.It aims to connect established neutral-atom quantum-information ideas with state-of-the-art experimental capabilities.Source: §I · p. 1
  • Alkaline-earth-like atoms combine long-lived clock states and a large elastic spin-exchange coupling, while nuclear spins are weakly sensitive to external fields.The atoms’ SU(N)-symmetric collisions add flexibility to quantum-information schemes.Source: §I · p. 1
  • The proposed register uses clock states as an auxiliary degree of freedom for one-qubit gates, spin-exchange gates, and shelved detection.The architecture is organized around programmable tweezers and practical individual-qubit addressing and detection.Source: §I · pp. 1–2, Figure 1 · p. 2

II. ARCHITECTURE

The architecture encodes qubits in nuclear spin states and uses electronic clock states as an auxiliary resource. A staggered array and state-selective transport bring neighboring atoms together for spin-exchange operations.

II. ARCHITECTURE

  • Nuclear spin states serve as memory qubits, while the electronic degree of freedom supports coherent manipulation, measurement, and state-selective transport.The proposed atoms are 173Yb or 87Sr, with clock-state lifetimes exceeding 20 seconds.Source: §II · p. 2
  • Magic-wavelength tweezers give |g⟩ and |e⟩ atoms equal trapping potentials, so optical-qubit manipulation is independent of the trapping potential.The stated wavelengths are approximately 465 nm for 173Yb and 497 nm for 87Sr.Source: §II · p. 2
  • Alternating |g⟩ and |e⟩ atoms across the array ensures that each neighboring exchange gate involves one atom of each state and avoids inelastic collisions between |e⟩ atoms.This requires initialization in a staggered electronic-state configuration.Source: §II · p. 2
  • The computational basis uses two adjacent nuclear-spin states from the 2F + 1 available states for either clock state.The selected states are mF = −F and −F+1, with F = 5/2 for 173Yb or F = 9/2 for 87Sr.Source: §II · p. 2
  • A moving tune-out-wavelength tweezer selectively merges |g⟩ atoms with neighboring |e⟩ atoms, and a circularly polarized beam supplies the spin-dependent shift used to time exchange.The auxiliary shift is provided by a beam closely detuned from the 1S0 → 3P1 transition.Source: §II · pp. 2–3

A. One-qubit gate

One-qubit rotations are performed on an optical clock qubit mapped from the nuclear-spin qubit and then mapped back. Spin-selective clock pulses and differential shifts provide the state selectivity.

A. One-qubit gate

  • Two spin-selective clock π-pulses map the nuclear qubit to the optical qubit and back, enclosing a π-polarized clock pulse that performs the rotation.For |g⟩ atoms the mapping uses σ− light; for |e⟩ atoms it uses σ+ light.Source: A. One-qubit gate · p. 3
  • One-qubit operation speed is set by the clock Rabi frequency Ω0, while transition selectivity between mF states is limited by the differential energy shift hδeg.A spin-dependent light shift can separate nuclear-spin states within the |g⟩ manifold.Source: A. One-qubit gate · p. 3
  • A spin-dependent light shift can separate |↓⟩ and |↑⟩ by about h × 1 MHz, allowing one-qubit operations on a microsecond scale in principle.A quantization magnetic field can also produce a differential Zeeman shift, with species-specific coefficients given for 173Yb and 87Sr.Source: A. One-qubit gate · p. 3

B. Two-qubit exchange gate

The two-qubit gate uses coherent spin exchange between |g⟩ and |e⟩ atoms merged into one tweezer. A timed SWAP operation relies on the exchange interaction, while transport fidelity is a relevant motional constraint.

B. Two-qubit exchange gate

  • The gate uses coherent spin exchange between |g⟩ and |e⟩ atoms occupying the motional ground state of the same tweezer.The interaction strength is determined by the difference between triplet and singlet scattering lengths.Source: B. Two-qubit exchange gate · p. 3
  • A SWAP gate is realized by merging two atoms and allowing spin-exchange dynamics for ∆tgate = h/(8Vex).The exchange interaction strength Vex is set by the difference between triplet and singlet scattering lengths.Source: B. Two-qubit exchange gate · p. 3
  • A locally adiabatic transport profile gives final infidelity of order 10^-3 in about 14 µs for 173Yb.The figure compares naive and locally adiabatic ramping and specifies a 2 µm separation for the adjacent tweezers.Source: Figure 4 · p. 4

1. Perturbative interactions

The proposal models exchange gates and transport as a combined process, accounting for coherent exchange errors, motional heating, and spin decoherence. Under the stated assumptions, transport infidelity dominates degradation over repeated gates.

1. Perturbative interactions

  • A state-dependent transport tweezer merges neighboring atoms without moving the magic-wavelength tweezers, and an optical switch delays exchange until transport is complete.The locally adiabatic protocol varies confinement and position in separate stages; transport infidelity can reach about 10^-3 on a timescale of ∼3 · 2π/ωtw, but requires timing precision below 10 ns and excursions beyond the strict harmonic regime.Source: §1 · pp. 4–5
  • The two-qubit evolution can be decomposed into a SWAP and phase gate, while sequential SWAPs can distribute entanglement between remote atoms.The modeled state comprises four basis states |gσ, eσ′⟩, with interactions treated perturbatively for 87Sr; the approximation may break down for 173Yb.Source: §1 · pp. 4–5
  • About 10% total gate error is predicted after 45 gates when single-transport infidelity is 10^-3.For 40 consecutive SWAP gates, the calculated infidelity is minimized near VOS/h = 250 kHz.Source: Figure 5 · p. 5, §1 · p. 6
  • Transport-stage exchange oscillations and sensitivity of the differential phase to intensity and beam-pointing fluctuations are additional sources of gate error.For a vibrational gap near 100 kHz, about 3 nm transport-tweezer pointing stability is required to stabilize the differential phase to fractional accuracy 10^-2.Source: §1 · pp. 5–6
  • Increasing optical-switch laser power suppresses unwanted exchange oscillations but increases motional heating and direct spin decoherence.Deeper tweezers can suppress motional-heating errors, at the expense of higher off-resonant scattering.Source: §1 · p. 6

2. Strong interactions

The treatment computes singlet and triplet interaction energies in magic-wavelength tweezers, but the perturbative model does not apply straightforwardly to 173Yb. Alternative gate configurations may avoid that complexity, with a pointing-sensitivity trade-off for one option.

2. Strong interactions

  • In the pseudopotential approximation, singlet and triplet interaction energies can be computed exactly when small trap anharmonicities are ignored.The treatment assumes isotropic confinement, achievable by retro-reflecting tweezer light to increase axial confinement.Source: §2 · p. 6
  • For 87Sr, Vex/h = 6 kHz and Vd/h = 15 kHz at the end of the transport-tweezer ramp, supporting a perturbative treatment.The supplied passage reports these interaction energies as much lower than in the strong-interaction case.Source: §2 · p. 6
  • For 173Yb, the triplet interaction nearly reaches the vibrational gap while the singlet remains perturbative up to 150 kHz, invalidating the preceding simple Hamiltonian.The resulting exchange dynamics couple spin and motion because the singlet and triplet motional wavefunctions differ significantly.Source: §2 · p. 7
  • Keeping the transport tweezer on during exchange can preserve small atom overlap, while omitting the OS beam makes the singlet-triplet basis diagonal for all tweezer configurations.The OS-beam-free approach can in principle yield an extremely fast 173Yb gate, but is sensitive to pointing fluctuations during transport.Source: §2 · p. 7

IV. REGISTER INITIALIZATION

Register preparation starts with single atoms in a one-dimensional tweezer array, followed by spin polarization, motional ground-state cooling, and staggered clock-state preparation. Cooling performance differs by species, and residual motional excitations can be identified and removed.

IV. REGISTER INITIALIZATION

  • For 87Sr, sideband cooling reaches n0 ≃0.99 at 10 quanta/ms, whereas 173Yb reaches n0 ≃0.98 at ∼0.7 quanta/ms with clock-transition cooling.The Yb scheme uses 3P0→3D1 repumping light to broaden the clock transition; cooling in both species is limited by heating from 3P1 deconfinement in magic-wavelength tweezers.Source: §IV · p. 7
  • The array is loaded from a low-temperature narrow-line MOT, rearranged to uniform spacing, optically pumped to |g↓⟩, and cooled to the motional ground state.The initial loading yields at least half of tweezers singly occupied; spacing d ≃3λm balances negligible crosstalk with short transport distances.Source: §IV · p. 7
  • For Yb, the cooling figure depicts a repumper detuned by ∆aux from 3P0→3D1 to quench 3P0 and enhance cooling on 1S1→3P0.The figure compares ground-state cooling schemes for 87Sr and 173Yb.Source: Figure 6 · p. 7
  • Motional excitations reduce exchange energy and gate fidelity, so post-cooling 3P0 imaging can identify and remove atoms excited by the final red-sideband clock pulse.The array can then be rearranged, extracting entropy from the system.Source: §IV · pp. 7–8
  • After ground-state cooling, clock-beam addressing prepares the staggered |e⟩−|g⟩ configuration, with tweezer-induced frequency shifts available to avoid crosstalk.The OS or transport tweezer beams can shift the targeted atom into resonance.Source: §IV · p. 8

V. READ-OUT

Readout maps nuclear-spin states onto electronic clock states, then detects |g⟩ atoms by fluorescence. A subsequent clock pulse can also measure the |e⟩ population to improve statistics and isolate preparation and readout errors.

V. READ-OUT

  • A clock π-pulse maps nuclear-spin states to |g⟩ or |e⟩ according to trap parity, making |g⟩ detection equivalent to nuclear-spin detection.Bright and dark signals correspond to opposite spin states in odd versus even tweezers.Source: §V · p. 8
  • Fluorescence on the strong |g⟩→|d⟩ transition enables single-atom-resolved detection, with several hundred photons scattered in about 100 µs.A few hundred EMCCD counts suffice to distinguish bright occupied traps from empty ones.Source: §V · p. 8
  • Sub-Doppler molasses or sideband cooling during imaging can extend collection beyond 1000 photons per atom without atom losses.The passage describes these as options when larger fluorescence signals are needed to increase detection fidelity.Source: §V · p. 8
  • Because |g⟩ detection ideally leaves |e⟩ atoms undisturbed, a second clock π-pulse can measure |e⟩ population and help separate preparation from readout errors.Source: §V · p. 8

VI. CONCLUSIONS AND OUTLOOK

The paper proposes a tweezer-array platform for fermionic alkaline-earth-like atoms, combining nuclear-spin qubits with clock-state control and spin-exchange gates. It identifies prospects for parallel entanglement and simulation, while noting that strongly interacting transport protocols remain open.

VI. CONCLUSIONS AND OUTLOOK

  • The authors present the neutral-atom architecture as a realistic platform within reach of state-of-the-art atomic physics experiments.Source: §VI · p. 8
  • The proposed platform combines robust nuclear qubits, an auxiliary optical qubit, state-dependent tweezer transport, and fast spin-exchange entangling operations.The exchange gates are described as largely insensitive to beam pointing and intensity fluctuations; extending locally adiabatic transport protocols to strongly interacting atoms remains open.Source: §VI · p. 8
  • Parallel entangling gates on different pairs with virtually no crosstalk could produce multipartite entangled states in O(N) operations.The paper identifies cluster states as a route to one-way quantum computing algorithms.Source: §VI · p. 8
  • The platform is also proposed for digital quantum simulation and studies of RKKY and spin-orbital interactions in minimal lattice models.A tunable-wavelength optical lattice would provide flexibility for realizing two-orbital lattice Hamiltonians on demand.Source: §VI · p. 8
  • The architecture could be extended to Rydberg-mediated two-qubit gates by applying a state-dependent phase to clock-excited neighboring atoms.Single-photon access to Rydberg s-states from 3P0 yields higher Rabi frequencies than in alkalis, allowing fast operations and mitigating decoherence.Source: §VI · pp. 8–9

Appendix A: Motional ground state fidelity during transport

The appendix models tweezer transport as a time-dependent harmonic potential and computes the probability that an initially ground-state atom remains in the instantaneous ground state. It also checks how the Gaussian tweezer’s anharmonicity changes transport infidelity.

Appendix A: Motional ground state fidelity during transport

  • The transport potential combines the magic-wavelength trap with a tweezer that traps only the g atom, and is approximated as a harmonic potential with time-dependent frequency and center.The model describes the atom’s evolution using a time-dependent quadratic Hamiltonian and an operator expansion in the initial annihilation and creation operators.Source: Appendix A · p. 9
  • The calculation obtains the evolution coefficients from equations of motion, maps them to displacement and squeezing parameters, and evaluates the overlap with the instantaneous ground state.The persistence probability is the probability that an atom initially in the ground state remains in the instantaneous ground state after the tweezer manipulation.Source: Appendix A · p. 9
  • The Gaussian potential produces nearly the same transport dynamics as the harmonic approximation on timescales of tens of µs, with only a slight delay of infidelity dips in the diabatic regime.At ∼20 µs, maximum trajectory deviations are ∼10% of the beam waist, corresponding to harmonic-potential corrections at the ∼1% level.Source: Appendix A · p. 10

Appendix B: Optical switch and associated scattering rates

The appendices quantify optical-switch scattering and decoherence, then examine how imperfect cooling affects repeated SWAP gates. They identify ground-state cooling and/or entropy extraction as crucial tools for the architecture.

Appendix B: Optical switch and associated scattering rates

  • For the optical switch, σ− polarization and large detuning reduce Raman and Rayleigh scattering; the stated rates are Γ↑↓/(2π) ≃ 5 × 10^-7 VOS/h and Γel/2π ≃ 1 × 10^-7 VOS/h.These rates use δOS = 45 GHz for 173Yb or 5 GHz for 87Sr from the 3P1 F′ = F + 1 state.Source: Appendix B · pp. 10–11

Appendix C: Decoherence dynamics

  • The decoherence model uses a master equation with a Lindbladian, including scattering effects and motional heating; Raman scattering affects states |2⟩ and |4⟩, while heating is modeled as non-trace-preserving decay.The stated total scattering rate is Γtot = Γ↑ + Γ↓.Source: Appendix C · p. 11

Appendix D: Impact of imperfect cooling

  • Imperfect ground-state cooling degrades single-gate fidelity linearly with the excited-state population, while repeated SWAP gates further reduce fidelity as atoms are pumped into a mixture of symmetric and antisymmetric motional states.The analysis numerically computes fidelity for 40 repeated two-qubit SWAP gates and restricts consideration to one shared motional excitation.Source: Appendix D · pp. 11–12

Appendix E: Wavelengths for 173Yb and 87Sr

  • The wavelength tables summarize required wavelengths and scattering rates for 173Yb and 87Sr under specified trap-frequency, beam-waist, detection-intensity, and optical-switch conditions.The table captions give species-specific assumptions for the trap frequencies and optical-switch detunings.Source: Table I · p. 12, Table II · p. 12
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