Also known as ion trap · Molmer-Sorensen · motional modes · phonons · ion shuttling
Trapped ions are charged atoms held in electromagnetic traps and controlled with lasers or microwaves
[1, 2]. Qubits are stored in long-lived hyperfine or optical levels, and ions in
the same trap interact through their shared vibrational modes. This was the basis of the first proposal for a quantum
computer [3]. Ions combine excellent coherence and very high gate fidelities with comparatively slow
gates, which makes control of the motion the central problem.
Single-qubit control
Laser- and microwave-driven single-qubit gates reach errors of a few \(10^{-5}\) [4, 5]. Microwave near fields can also couple to the motion, which allows laser-free entangling
gates [6]. Composite and robust pulses suppress amplitude and frequency errors; see
Composite pulses and Robust & ensemble optimal control.
Entangling gates through the motion
Spin-dependent forces. The Mølmer–Sørensen gate uses a bichromatic field that entangles the ions’ internal
states through virtual excitation of the motion. The motion need not be fully controlled, so it works even with
ions in thermal motion [7, 8]. Laser-driven gates based on
spin-dependent forces have reached 99.9% fidelity [5].
Many modes. At the end of the gate, the ions must be disentangled from every motional mode, and longer chains
have more modes to close. Optimally shaped, segmented pulses address this in a five-ion chain
[9]. Frequency modulation of the driving force suppresses residual spin–motion entanglement and is
robust to frequency drifts [10]. Discrete phase shifts can decouple several modes and suppress drive
fluctuations [11]. Multitone drives give gates robust to several error sources
[12]. See Quantum gate synthesis.
Beyond the trap period. Standard gates are slow compared with the motional frequencies. Amplitude-shaped laser
pulses that drive the motion along designed trajectories gave entangling gates far faster than this limit
[13].
Shuttling
A scalable architecture moves ions between zones for storage, gates and readout [14]. The
“quantum CCD” architecture has been realized in practice [15]. Transport must be fast and must leave the
ion’s motion unexcited. Ions have been moved over hundreds of micrometres in 5 to 16 trap periods, gaining only about
0.1 motional quanta [16, 17], and ion chains have been split
[17]. Shuttling is a control problem in its own right. Numerical optimization, invariant-based
inverse engineering and geometric optimal control each work best in different regimes of length and time
[18]. See Shortcuts to adiabaticity.
Gates are slow compared with solid-state platforms, and speeding them up excites the motion.
Long chains have dense motional spectra, which makes gates harder to design and more sensitive to drifts.
Laser intensity and phase noise, beam pointing and heating of the motion limit fidelities.
Key papers
J. I. Cirac and P. ZollerQuantum Computations with Cold Trapped IonsPhys. Rev. Lett.74, 4091-4094 (1995)doi
The first proposal for quantum computing with trapped ions, using their shared motion as a bus.
D. Leibfried, R. Blatt, C. Monroe and D. WinelandQuantum dynamics of single trapped ionsRev. Mod. Phys.75, 281-324 (2003)doi
Review of the quantum dynamics and laser control of single trapped ions.
Klaus Mølmer and Anders SørensenMultiparticle Entanglement of Hot Trapped IonsPhys. Rev. Lett.82, 1835-1838 (1999)doi
The Mølmer–Sørensen gate, insensitive to the ions' thermal motion — the standard entangling gate.
T. Choi, S. Debnath, T. A. Manning, C. Figgatt, Z.-X. Gong, et al.Optimal Quantum Control of Multimode Couplings between Trapped Ion Qubits for Scalable EntanglementPhys. Rev. Lett.112, 190502 (2014)doi
Optimally shaped pulses that control many motional modes for entangling gates in a five-ion chain.
V. M. Schäfer, C. J. Ballance, K. Thirumalai, L. J. Stephenson, T. G. Ballance, et al.Fast quantum logic gates with trapped-ion qubitsNature555, 75-78 (2018)doi
Entangling gates faster than the trap period, driven by amplitude-shaped laser pulses.
A. Walther, F. Ziesel, T. Ruster, S. T. Dawkins, K. Ott, et al.Controlling Fast Transport of Cold Trapped IonsPhys. Rev. Lett.109, 080501 (2012)doi
Optimized fast transport of a ground-state-cooled ion over many wavefunction widths in a few trap periods.
References
D. Leibfried, R. Blatt, C. Monroe and D. WinelandQuantum dynamics of single trapped ionsRev. Mod. Phys.75, 281-324 (2003)doi
Colin D. Bruzewicz, John Chiaverini, Robert McConnell and Jeremy M. SageTrapped-ion quantum computing: Progress and challengesApplied Physics Reviews6, 021314 (2019)doi
J. I. Cirac and P. ZollerQuantum Computations with Cold Trapped IonsPhys. Rev. Lett.74, 4091-4094 (1995)doi
J. P. Gaebler, T. R. Tan, Y. Lin, Y. Wan, R. Bowler, et al.High-Fidelity Universal Gate Set for Be 9 + Ion QubitsPhys. Rev. Lett.117, 060505 (2016)doi
C. J. Ballance, T. P. Harty, N. M. Linke, M. A. Sepiol and D. M. LucasHigh-Fidelity Quantum Logic Gates Using Trapped-Ion Hyperfine QubitsPhys. Rev. Lett.117, 060504 (2016)doi
C. Ospelkaus, U. Warring, Y. Colombe, K. R. Brown, J. M. Amini, et al.Microwave quantum logic gates for trapped ionsNature476, 181-184 (2011)doi
Klaus Mølmer and Anders SørensenMultiparticle Entanglement of Hot Trapped IonsPhys. Rev. Lett.82, 1835-1838 (1999)doi
Anders Sørensen and Klaus MølmerEntanglement and quantum computation with ions in thermal motionPhys. Rev. A62, 022311 (2000)doi
T. Choi, S. Debnath, T. A. Manning, C. Figgatt, Z.-X. Gong, et al.Optimal Quantum Control of Multimode Couplings between Trapped Ion Qubits for Scalable EntanglementPhys. Rev. Lett.112, 190502 (2014)doi
Pak Hong Leung, Kevin A. Landsman, Caroline Figgatt, Norbert M. Linke, Christopher Monroe and Kenneth R. BrownRobust 2-Qubit Gates in a Linear Ion Crystal Using a Frequency-Modulated Driving ForcePhys. Rev. Lett.120, 020501 (2018)doi
Todd J. Green and Michael J. BiercukPhase-Modulated Decoupling and Error Suppression in Qubit-Oscillator SystemsPhys. Rev. Lett.114, 120502 (2015)doi
Yotam Shapira, Ravid Shaniv, Tom Manovitz, Nitzan Akerman and Roee OzeriRobust Entanglement Gates for Trapped-Ion QubitsPhys. Rev. Lett.121, 180502 (2018)doi
V. M. Schäfer, C. J. Ballance, K. Thirumalai, L. J. Stephenson, T. G. Ballance, et al.Fast quantum logic gates with trapped-ion qubitsNature555, 75-78 (2018)doi
D. Kielpinski, C. Monroe and D. J. WinelandArchitecture for a large-scale ion-trap quantum computerNature417, 709-711 (2002)doi
J. M. Pino, J. M. Dreiling, C. Figgatt, J. P. Gaebler, S. A. Moses, et al.Demonstration of the trapped-ion quantum CCD computer architectureNature592, 209-213 (2021)doi
A. Walther, F. Ziesel, T. Ruster, S. T. Dawkins, K. Ott, et al.Controlling Fast Transport of Cold Trapped IonsPhys. Rev. Lett.109, 080501 (2012)doi
R. Bowler, J. Gaebler, Y. Lin, T. R. Tan, D. Hanneke, et al.Coherent Diabatic Ion Transport and Separation in a Multizone Trap ArrayPhys. Rev. Lett.109, 080502 (2012)doi
H A Fürst, M H Goerz, U G Poschinger, M Murphy, S Montangero, et al.Controlling the transport of an ion: classical and quantum mechanical solutionsNew J. Phys.16, 075007 (2014)doi
C. Flühmann, T. L. Nguyen, M. Marinelli, V. Negnevitsky, K. Mehta and J. P. HomeEncoding a qubit in a trapped-ion mechanical oscillatorNature566, 513-517 (2019)doi
Julio T. Barreiro, Markus Müller, Philipp Schindler, Daniel Nigg, Thomas Monz, et al.An open-system quantum simulator with trapped ionsNature470, 486-491 (2011)doi
Y. Lin, J. P. Gaebler, F. Reiter, T. R. Tan, R. Bowler, et al.Dissipative production of a maximally entangled steady state of two quantum bitsNature504, 415-418 (2013)doi
Johannes Roßnagel, Samuel T. Dawkins, Karl N. Tolazzi, Obinna Abah, Eric Lutz, et al.A single-atom heat engineScience352, 325-329 (2016)doi
Thomas Monz, Philipp Schindler, Julio T. Barreiro, Michael Chwalla, Daniel Nigg, et al.14-Qubit Entanglement: Creation and CoherencePhys. Rev. Lett.106, 130506 (2011)doi
Martin Ringbauer, Michael Meth, Lukas Postler, Roman Stricker, Rainer Blatt, et al.A universal qudit quantum processor with trapped ionsNat. Phys.18, 1053-1057 (2022)doi
Recent papers
420 tracked papers since 2000 are classified
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Massive mechanical oscillators couple directly to forces, accelerations and gravity, making them attractive probes of new physics and of quantum mechanics at macroscopic scales. Pushing sensitivities beyond the standard quantum limit for signals of unknown phase requires non-Gaussian quantum states, whose metrological advantage has so far been confined to lighter systems such as trapped ions. Here we operate a microgram-scale acoustic mode of a high-overtone bulk acoustic wave resonator as a phase-insensitive quantum-enhanced sensor. A transmon qubit prepares the mode in Fock states of up to seven phonons by optimal control, and resolves its phonon-number distribution after interaction with a weak resonant signal. Bayesian analysis yields a Fisher information five times the vacuum value, a 7.0 dB gain in signal-amplitude sensitivity over any classical probe state, irrespective of its energy, currently limited by state preparation infidelities. We then train a neural network on the measured sensor response to perform Bayesian estimation without any analytical model of the system, showing the same sensitivity gain with half the systematic bias. Our results establish acoustic resonators prepared in non-Gaussian states as quantum-enhanced probes for high-frequency gravitational waves, dark matter and wave-function collapse.
Scaling trapped-ion optical clocks to hundreds of ions remains a major challenge due to inhomogeneous frequency shifts in large ion crystals. Here, we propose a circular surface-trap architecture for a multi-ion optical clock with hundreds of ions. The rotational symmetry of the ion crystal suppresses the main sources of inhomogeneity, quadrupole shift.We investigate the feasibility of a clock based on a ring crystal of 400 $^{40}\mathrm{Ca}^{+}$ ions and propose a suitable experimental setup configuration. We have shown that circular configuration of ions leads to suppression by two orders of magnitude of the quadrupole shift comparing to the linear trap. Combined with stray-field compensation and dynamical decoupling techniques, this architecture provides a pathway toward multi-ion optical clocks with fractional frequency uncertainty at the $10^{-18}$ level and an expected 20-fold improvement in frequency stability compared to single ion clocks.
Trapped ion quantum computing based on the quantum charge coupled device (QCCD) architecture uses functional zoning and ion transport to enable high fidelity computation and all to all qubit connectivity. As trapped ion quantum processing units (QPU) scale, 90° X-junction turns account for an increasing fraction of total transport time. Frequent junction crossings, therefore, make transport speed and final phonon excitation direct determinants of quantum algorithm execution efficiency. However, complex electric fields in X-junctions complicate waveform design, making it difficult to achieve high speed and low final phonon excitation simultaneously. Here, we develop a waveform design method for low-phonon-excitation high-speed X-junction(LHX-T) transport. It integrates low barrier pseudopotential channel design using multiple radio frequency (Multi-RF), multidimensional shortcut to adiabaticity dynamics, and constrained DC voltage optimization over the entire transport sequence. This framework connects waveform design, control, and computational validation, with smooth multichannel waveforms computed rapidly through a Karush-Kuhn-Tucker(KKT) linear system. The resulting waveform transports a single $^{171}Yb^+$ ion through a 90° turn in $5μs$ at an average speed of 14.6 m/s. Over 50 consecutive round trips, the final equivalent coherent phonon number consistently stays below 0.001, with no noticeable accumulation over time. System level evaluations at the QCCD scale show that the median duration of a single execution cycle is reduced by about $30\%$ across various circuit types. The fraction of execution time spent on transport decreases from approximately $70\%$ to $55\%$. This approach offers a means of designing fast ion transport waveforms with low phonon excitation for scalable QCCD based QPUs and provides a technical basis for efficient execution of quantum algorithms.
Bosonic quantum error correction represents a route towards significant hardware overhead reduction for fault-tolerant quantum computation. However, controlling quantum harmonic oscillators that encode the quantum information comes with its own challenges. In many platforms such as superconducting circuits and trapped ions, the bosonic degree of freedom is controlled by an ancillary qubit whose decay during a qubit-oscillator gate propagates to the oscillator as a continuous error. Such errors generally lie beyond the scope of errors that the bosonic code is capable of correcting. We introduce the continuous-variable flag: an auxiliary oscillator coupled to the ancilla whose phase-space position encodes the continuous error corrupting the storage mode. After the gate, a heterodyne measurement of the flag estimates this continuous-variable error and a subsequent feedback control undoes it up to a bosonic code stabilizer. The scheme requires no new ingredients, as the flag is driven by the same dispersive coupling, displacements and rotations that implement the gates it is supposed to protect. We construct sequences protecting conditional rotations to all orders in ancilla decay with one flag, and conditional displacements to first order with one flag and to all orders with two. Simulations with realistic circuit-QED parameters predict more than three orders of magnitude fewer logical errors for the parity measurement of a four-component cat code, and a finite-energy GKP logical lifetime near its noiseless-ancilla bound. By discretizing continuous-variable errors, the flags introduced in this work are a useful tool for any hybrid oscillator-qubit processor, and open the route towards fault-tolerant simulation and computation with bosonic modes.
Scaling quantum control for atoms, ions, and solid-state emitters requires gigahertz-frequency spectral control of high-power visible light in a volume-manufacturable platform. Silicon nitride photonics provides high power handling and CMOS-foundry compatibility but has no intrinsic mechanism for high-speed modulation. Integration with piezoelectric materials enables acousto-optic phase modulation, and mechanical resonant enhancement has made it efficient at gigahertz frequencies. However, a single resonance restricts the modulation waveform to a single tone, imposing Bessel-function sideband amplitudes and limiting frequency-shifting efficiency to 33.9%. Here we engineer a silicon nitride acousto-optic microstructure to support harmonically spaced resonances at 1.14 GHz and 2.28 GHz, each strongly optomechanically coupled to a 730 nm guided optical mode, so that tailored non-sinusoidal modulation waveforms can be resonantly synthesized. By piezoelectrically controlling the two mechanical amplitudes and their relative phase, we demonstrate 50% conversion to one sideband (1.5x the single-tone theoretical maximum), a flat seven-line comb, and a frequency shift with 60 dB carrier and 53 dB image suppression - to our knowledge the highest reported for an integrated modulator. The devices are fabricated in a 200 mm CMOS foundry, and we measure 91.7% yield without post-fabrication tuning across 36 devices from three wafers. We also show how the technique can be straightforwardly scaled to three or more harmonics. This result overcomes the trade-off between resonant enhancement and spectral programmability, with important consequences including improved single-qubit gate efficiency for hyperfine qubits.