Publications

Realizing universal fault-tolerant quantum computation is a key goal in quantum information science^{1, 2, 34}. By encoding quantum information into logical qubits using quantum error correcting codes, physical errors can be detected and corrected, enabling a substantial reduction in logical error rates^{5, 6, 7, 8, 9, 1011}. However, the set of logical operations that can be easily implemented on these encoded qubits is often constrained^1,12, necessitating the use of special resource states known as magic states¹³ to implement universal, classically hard circuits¹⁴. A key method to prepare high-fidelity magic states is to perform distillation, creating them from multiple lower-fidelity inputs^13,15. Here we present the experimental realization of magic state distillation with logical qubits on a neutral-atom quantum computer. Our approach uses a dynamically reconfigurable architecture^8,16 to encode and perform quantum operations on many logical qubits in parallel. We demonstrate the distillation of magic states encoded in d = 3 and d = 5 colour codes, observing improvements in the logical fidelity of the output magic states compared with the input logical magic states. These experiments demonstrate a key building block of universal fault-tolerant quantum computation and represent an important step towards large-scale logical quantum processors.

Quantum simulations of many-body systems are among the most promising applications of quantum computers¹. In particular, models based on strongly correlated fermions are central to our understanding of quantum chemistry and materials problems², and can lead to exotic, topological phases of matter^3,4. However, owing to the non-local nature of fermions, such models are challenging to simulate with qubit devices⁵. Here we realize a digital quantum simulation architecture for two-dimensional fermionic systems based on reconfigurable atom arrays⁶. We utilize a fermion-to-qubit mapping based on Kitaevs model on a honeycomb lattice³, in which fermionic statistics are encoded using long-range entangled states⁷. We prepare these states efficiently using measurement⁸ and feedforward⁹, realize subsequent fermionic evolution through Floquet engineering^10,11 with tunable entangling gates¹² interspersed with atom rearrangement, and improve results with built-in error detection. Leveraging this fermion description of the Kitaev spin model, we efficiently prepare topological states across its complex phase diagram¹³ and verify the non-Abelian spin-liquid phase³ by evaluating an odd Chern number^14,15. We further explore this two-dimensional fermion system by realizing tunable dynamics and directly probing fermion exchange statistics. Finally, we simulate strong interactions and study the dynamics of the FermiHubbard model on a square lattice. These results pave the way for digital quantum simulations of complex fermionic systems for materials science, chemistry¹⁶ and high-energy physics¹⁷.

Understanding the collective quantum dynamics of non-equilibrium many-body systems is an outstanding challenge in quantum science. In particular, dynamics driven by quantum fluctuations are important for the formation of exotic quantum phases of matter¹, fundamental high-energy processes², quantum metrology^3,4 and quantum algorithms⁵. Here we use a programmable quantum simulator based on Rydberg atom arrays to experimentally study collective dynamics across a (2+1)-dimensional Ising quantum phase transition. After crossing the quantum critical point, we observe a gradual growth of correlations through coarsening of antiferromagnetically ordered domains⁶. By deterministically preparing and following the evolution of ordered domains, we show that the coarsening is driven by the curvature of domain boundaries, and find that the dynamics accelerate with proximity to the quantum critical point. We quantitatively explore these phenomena and further observe long-lived oscillations of the order parameter, corresponding to an amplitude (Higgs) mode⁷. These observations offer a viewpoint into emergent collective dynamics in strongly correlated quantum systems and non-equilibrium quantum processes.

Suppressing errors is the central challenge for useful quantum computing¹, requiring quantum error correction (QEC)²⁶ for large-scale processing. However, the overhead in the realization of error-corrected logical qubits, in which information is encoded across many physical qubits for redundancy²⁴, poses substantial challenges to large-scale logical quantum computing. Here we report the realization of a programmable quantum processor based on encoded logical qubits operating with up to 280 physical qubits. Using logical-level control and a zoned architecture in reconfigurable neutral-atom arrays⁷, our system combines high two-qubit gate fidelities⁸, arbitrary connectivity^7,9, as well as fully programmable single-qubit rotations and mid-circuit readout¹⁰¹⁵. Operating this logical processor with various types of encoding, we demonstrate improvement of a two-qubit logic gate by scaling surface-code⁶ distance from d = 3 to d = 7, preparation of colour-code qubits with break-even fidelities⁵, fault-tolerant creation of logical GreenbergerHorneZeilinger (GHZ) states and feedforward entanglement teleportation, as well as operation of 40 colour-code qubits. Finally, using 3D [[8,3,2]] code blocks^16,17, we realize computationally complex sampling circuits¹⁸ with up to 48 logical qubits entangled with hypercube connectivity¹⁹ with 228 logical two-qubit gates and 48 logical CCZ gates²⁰. We find that this logical encoding substantially improves algorithmic performance with error detection, outperforming physical-qubit fidelities at both cross-entropy benchmarking and quantum simulations of fast scrambling^21,22. These results herald the advent of early error-corrected quantum computation and chart a path towards large-scale logical processors.

The ability to perform entangling quantum operations with low error rates in a scalable fashion is a central element of useful quantum information processing¹. Neutral-atom arrays have recently emerged as a promising quantum computing platform, featuring coherent control over hundreds of qubits^2,3 and any-to-any gate connectivity in a flexible, dynamically reconfigurable architecture⁴. The main outstanding challenge has been to reduce errors in entangling operations mediated through Rydberg interactions⁵. Here we report the realization of two-qubit entangling gates with 99.5% fidelity on up to 60 atoms in parallel, surpassing the surface-code threshold for error correction^6,7. Our method uses fast, single-pulse gates based on optimal control⁸, atomic dark states to reduce scattering⁹ and improvements to Rydberg excitation and atom cooling. We benchmark fidelity using several methods based on repeated gate applications^10,11, characterize the physical error sources and outline future improvements. Finally, we generalize our method to design entangling gates involving a higher number of qubits, which we demonstrate by realizing low-error three-qubit gates^12,13. By enabling high-fidelity operation in a scalable, highly connected system, these advances lay the groundwork for large-scale implementation of quantum algorithms¹⁴, error-corrected circuits⁷ and digital simulations¹⁵.

Many-body systems of quantum interacting particles in which time-reversal symmetry is broken give rise to a variety of rich collective behaviors and are, therefore, a major target of research in modern physics. Quantum simulators can potentially be used to explore and understand such systems, which are often beyond the computational reach of classical simulation. Of these, platforms with universal quantum control can experimentally access a wide range of physical properties. However, simultaneously achieving strong programmable interactions, strong time-reversal symmetry breaking, and high-fidelity quantum control in a scalable manner is challenging. Here, we realize quantum simulations of interacting, time-reversal-broken quantum systems in a universal trapped-ion quantum processor. Using a recently proposed, scalable scheme, we implement time-reversal-breaking synthetic gauge fields, shown for the first time in a trapped-ion chain, along with unique coupling geometries, potentially extendable to simulation of multidimensional systems. Our high-fidelity single-site resolution in control and measurement, along with highly programmable interactions, allow us to perform full state tomography of a ground state showcasing persistent current and to observe dynamics of a time-reversal-broken system with nontrivial interactions. Our results open a path toward simulation of time-reversal-broken many-body systems with a wide range of features and coupling geometries.

At radioactive ion beam (RIB) facilities, ions of short-lived radionuclides are cooled and bunched in buffer-gas-filled Paul traps to improve the ion-beam quality for subsequent experiments. To deliver even colder ions, beneficial to RIB experiments' sensitivity or accuracy, we employ Doppler and sympathetic cooling in a Paul trap cooler-buncher. The improved emittance of Mg⁺, K⁺, and O2⁺ ion beams is demonstrated by a reduced time-of-flight spread of the extracted ion bunches with respect to room-temperature buffer-gas cooling. Cooling externally-produced hot ions with energies of at least 7 eV down to a few Kelvin is achieved in a timescale of O(100 ms) by combining a low-pressure helium background gas with laser cooling. This is sufficiently short to cool short-lived radioactive ions. As an example of this technique's use for RIB research, the mass-resolving power in a multireflection time-of-flight mass spectrometer is shown to increase by up to a factor of 4.6 with respect to buffer-gas cooling. Simulations show good agreement with the experimental results and guide further improvements and applications. These results open a path to a significant emittance improvement and, thus, unprecedented ion-beam qualities at RIB facilities, achievable with standard equipment readily available. The same method provides opportunities for future high-precision experiments with radioactive cold trapped ions.

Quantum computers are expected to achieve a significant speed-up over classical computers in solving a range of computational problems. Chains of ions held in a linear Paul trap are a promising platform for constructing such quantum computers, due to their long coherence times and high quality of control. Here, we report on the construction of a small five-qubit universal quantum computer using 88Sr+ ions in a radio-frequency (rf) trap. All basic operations, including initialization, quantum logic operations, and readout, are performed with high fidelity. Selective two-qubit and single-qubit gates, implemented using a narrow-line-width laser, comprise a universal gate set, allowing realization of any unitary on the quantum register. We review the main experimental tools and describe in detail unique aspects of the computer: the use of robust entangling gates and the development of a quantum coherent feedback system through electron-multiplying CCD camera acquisition. The latter is necessary for carrying out quantum error-correction protocols in future experiments.

In some quantum computing architectures, entanglement of an arbitrary number of qubits can be generated in a single operation. This property has many potential applications, and may specifically be useful for quantum error correction (QEC). Stabilizer measurements can then be implemented using a single multiqubit gate instead of several two-qubit gates, thus reducing circuit depth. In this study, the toric code is used as a benchmark to compare the performance of two-qubit and five-qubit gates within parity-check circuits. We consider trapped ion qubits that are controlled via Raman transitions, where the primary source of error is assumed to be spontaneous photon scattering. We show that a five-qubit Molmer-Sorensen gate offers an approximately 40% improvement over two-qubit gates in terms of the fault tolerance threshold. This result indicates an advantage of using multiqubit gates in the context of QEC.

In recent years, arrays of atomic ions in a linear radio-frequency trap have proven to be a particularly successful platform for quantum simulation. However, a wide range of quantum models and phenomena have, so far, remained beyond the reach of such simulators. In this work we introduce a technique that can substantially extend this reach using an external field gradient along the ion chain and a global, uniform driving field. The technique can be used to generate both static and time-varying synthetic gauge fields in a linear chain of trapped ions, and enables continuous simulation of a variety of coupling geometries and topologies, including periodic boundary conditions and high-dimensional Hamiltonians. We describe the technique, derive the corresponding effective Hamiltonian, propose a number of variations, and discuss the possibility of scaling to quantum-advantage-sized simulators. Additionally, we suggest several possible implementations and briefly examine two: the Aharonov-Bohm ring and the frustrated triangular ladder.

The prevalent approach to executing quantum algorithms on quantum computers is to break down the algorithms to a concatenation of universal gates, typically single and two-qubit gates. However such a decomposition results in long gate sequences which are exponential in the qubit register size. Furthermore, gate fidelities tend to decrease when acting in larger qubit registers. Thus high-fidelity implementations in large qubit registers are still a prominent challenge. Here we propose and investigate multiqubit entangling gates for trapped ions. Our gates couple many qubits at once, allowing us to decrease the total number of gates used while retaining a high gate fidelity. Our method employs all of the normal modes of motion of the ion chain, which allows us to operate outside of the adiabatic regime and at rates comparable to the secular ion-trapping frequency. Furthermore we extend our method for generating Hamiltonians which are suitable for quantum analog simulations, such as a nearest-neighbor spin Hamiltonian or the Su-Schrieffer-Heeger Hamiltonian.

Atomic isotope shifts (ISs) are the isotope-dependent energy differences between atomic electron energy levels. These shifts have an important role in atomic and nuclear physics, and have been recently suggested as unique probes of physics beyond the standard model under the condition that they are determined significantly more precisely than the current state of the art. In this Letter, we present a simple and robust method for measuring ISs by taking advantage of Hilbert subspaces that are insensitive to common-mode noise yet sensitive to the IS. Using this method we evaluate the IS of the 5S(1/2) 4D(5/2) transition between Sr-86(+) and Sr-88(+) with a 1.6 x 10(-11) relative uncertainty to be 570 264 063.435(5)(8) (statistical)(systematic) Hz. Furthermore, we detect a relative difference of 3.46(23) x 10(-8) between the orbital g factors of the electrons in the 4D(5/2) level of the two isotopes. Our method is relatively easy to implement and is indifferent to element or isotope, paving the way for future tabletop searches for new physics, posing interesting prospects for testing quantum many-body calculations, and for the study of nuclear structure.

We present a method that uses radio-frequency pulses to cancel the quadrupole shift in optical clock transitions. Quadrupole shifts are an inherent inhomogeneous broadening mechanism in trapped ion crystals and impose one of the limitations forcing current optical ion clocks to work with a single probe ion. Canceling this shift, at each interrogation cycle of the ion frequency, reduces the complexity in using N>1 ions in clocks, thus allowing for a reduction of the instability in the clock frequency by N according to the standard quantum limit. Our sequence relies on the tensorial nature of the quadrupole shift, and thus also cancels other tensorial shifts, such as the tensor ac stark shift. We experimentally demonstrate our sequence on three and seven Sr88+ ions trapped in a linear Paul trap, using correlation spectroscopy. We show a reduction of the quadrupole shift difference between ions to the ≈10 mHz level where other shifts, such as the relativistic second-order Doppler shift, are expected to limit our spectral resolution. In addition, we show that using radio-frequency dynamic decoupling we can also cancel the effect of first-order Zeeman shifts.

We report the frequency noise suppression of a 674nm diode laser by phase-locking it to a 1560nm cavity-stabilized laser, using a commercial optical frequency comb. By phase-locking the frequency comb to the narrow reference at telecom wavelength we were able to phase-coherently distribute the reference stability across the optical spectrum. Subsequently, we used one of the comb teeth as an optical reference for a 674nm external cavity diode laser. We demonstrated the locked 674nm laser frequency stability by comparing it to an independent cavity-stabilized laser of the same wavelength and by performing spectroscopic measurements on a dipole-forbidden narrow optical transition in a single $^{88}$Sr$^+$ ion. These measurements indicated a fast laser linewidth of 19Hz and 16Hz, respectively.

High-fidelity two-qubit entangling gates play an important role in many quantum information processing tasks and are a necessary building block for constructing a universal quantum computer. Such high-fidelity gates have been demonstrated on trapped-ion qubits; however, control errors and noise in gate parameters may still lead to reduced fidelity. Here we propose and demonstrate a general family of two-qubit entangling gates which are robust to different sources of noise and control errors. These gates generalize the renowned Molmer-Sorensen gate by using multitone drives. We experimentally implemented several of the proposed gates on Sr-88(+) ions trapped in a linear Paul trap and verified their resilience.

The use of entangled states was shown to improve the fundamental limits of spectroscopy to beyond the standard-quantum limit. Here, rather than probing the free evolution of the phase of an entangled state with respect to a local oscillator, we probe the evolution of an initially separable two-atom register under an Ising spin Hamiltonian with a transverse field. The resulting correlated spin-rotation spectrum is twice as narrow as that of an uncorrelated rotation. We implement this ideally Heisenberg-limited Rabi spectroscopy scheme on the optical-clock electric-quadrupole transition of Sr-88(+) using a two-ion crystal. We further show that depending on the initial state, correlated rotation can occur in two orthogonal subspaces of the full Hilbert space, yielding entanglement-enhanced spectroscopy of either the average transition frequency of the two ions or their difference from the mean frequency. The use of correlated spin rotations can potentially lead to new paths for clock stability improvement.

Engineering entanglement between quantum systems often involves coupling through a bosonic mediator, which should be disentangled from the systems at the operation's end. The quality of such an operation is generally limited by environmental and control noise. One of the prime techniques for suppressing noise is by dynamical decoupling, where one actively applies pulses at a rate that is faster than the typical time scale of the noise. However, for boson-mediated gates, current dynamical decoupling schemes require executing the pulses only when the boson and the quantum systems are disentangled. This restriction implies an increase of the gate time by a factor of root N, with N being the number of pulses applied. Here we propose and realize a method that enables dynamical decoupling in a boson-mediated system where the pulses can be applied while spin-boson entanglement persists, resulting in an increase in time that is at most a factor of pi/2, independently of the number of pulses applied. We experimentally demonstrate the robustness of our entangling gate with fast dynamical decoupling to sigma(z) noise using ions in a Paul trap.