Logical quantum processor based on reconfigurable atom arrays.

Suppressing errors is the central challenge for useful quantum computing1, requiring quantum error correction (QEC)2-6 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 redundancy2-4, 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 connectivity7,9, as well as fully programmable single-qubit rotations and mid-circuit readout10-15. 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 Greenberger-Horne-Zeilinger (GHZ) states and feedforward entanglement teleportation, as well as operation of 40 colour-code qubits. Finally, using 3D [[8,3,2]] code blocks16,17, 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 scrambling21,22. These results herald the advent of early error-corrected quantum computation and chart a path towards large-scale logical processors.

High-fidelity parallel entangling gates on a neutral-atom quantum computer.

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 qubits2,3 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 correction6,7. 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 applications10,11, 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 gates12,13. 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.

Quadrupole Shift Cancellation Using Dynamic Decoupling.

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 sqrt[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 ^{88}Sr^{+} 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.

Precision Measurement of Atomic Isotope Shifts Using a Two-Isotope Entangled State.

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 ^{86}Sr^{+} and ^{88}Sr^{+} with a 1.6×10^{-11} relative uncertainty to be 570 264 063.435(5)(8) (statistical)(systematic) Hz. Furthermore, we detect a relative difference of 3.46(23)×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.

Toward Heisenberg-Limited Rabi Spectroscopy.

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 ^{88}Sr^{+} 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.

Robust Entanglement Gates for Trapped-Ion Qubits.

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 Mølmer-Sørensen gate by using multitone drives. We experimentally implemented several of the proposed gates on ^{88}Sr^{+} ions trapped in a linear Paul trap and verified their resilience.

Fast Dynamical Decoupling of the Mølmer-Sørensen Entangling Gate.

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 sqrt[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 π/2, independently of the number of pulses applied. We experimentally demonstrate the robustness of our entangling gate with fast dynamical decoupling to σ_{z} noise using ions in a Paul trap.