Demonstration of the trapped-ion quantum CCD computer architecture.

The trapped-ion quantum charge-coupled device (QCCD) proposal1,2 lays out a blueprint for a universal quantum computer that uses mobile ions as qubits. Analogous to a charge-coupled device (CCD) camera, which stores and processes imaging information as movable electrical charges in coupled pixels, a QCCD computer stores quantum information in the internal state of electrically charged ions that are transported between different processing zones using dynamic electric fields. The promise of the QCCD architecture is to maintain the low error rates demonstrated in small trapped-ion experiments3-5 by limiting the quantum interactions to multiple small ion crystals, then physically splitting and rearranging the constituent ions of these crystals into new crystals, where further interactions occur. This approach leverages transport timescales that are fast relative to the coherence times of the qubits, the insensitivity of the qubit states of the ion to the electric fields used for transport, and the low crosstalk afforded by spatially separated crystals. However, engineering a machine capable of executing these operations across multiple interaction zones with low error introduces many difficulties, which have slowed progress in scaling this architecture to larger qubit numbers. Here we use a cryogenic surface trap to integrate all necessary elements of the QCCD architecture-a scalable trap design, parallel interaction zones and fast ion transport-into a programmable trapped-ion quantum computer that has a system performance consistent with the low error rates achieved in the individual ion crystals. We apply this approach to realize a teleported CNOT gate using mid-circuit measurement6, negligible crosstalk error and a quantum volume7 of 26 = 64. These results demonstrate that the QCCD architecture provides a viable path towards high-performance quantum computers.

Emergent equilibrium in many-body optical bistability.

Many-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to ultracold Rydberg gases, establishing a fascinating interface between traditional many-body physics and the driven-dissipative, nonequilibrium setting of cavity QED. At this interface, the standard techniques and intuitions of both fields are called into question, obscuring issues as fundamental as the role of fluctuations, dimensionality, and symmetry on the nature of collective behavior and phase transitions. Here, we study the driven-dissipative Bose-Hubbard model, a minimal description of numerous atomic, optical, and solid-state systems in which particle loss is countered by coherent driving. Despite being a lattice version of optical bistability, a foundational and patently nonequilibrium model of cavity QED, the steady state possesses an emergent equilibrium description in terms of a classical Ising model. We establish this picture by making new connections between traditional techniques from many-body physics (functional integrals) and quantum optics (the system-size expansion). To lowest order in a controlled expansion-organized around the experimentally relevant limit of weak interactions-the full quantum dynamics reduces to nonequilibrium Langevin equations, which support a phase transition described by model A of the Hohenberg-Halperin classification. Numerical simulations of the Langevin equations corroborate this picture, revealing that canonical behavior associated with the Ising model manifests readily in simple experimental observables.

Exact sampling hardness of Ising spin models.

We study the complexity of classically sampling from the output distribution of an Ising spin model, which can be implemented naturally in a variety of atomic, molecular, and optical systems. In particular, we construct a specific example of an Ising Hamiltonian that, after time evolution starting from a trivial initial state, produces a particular output configuration with probability very nearly proportional to the square of the permanent of a matrix with arbitrary integer entries. In a similar spirit to boson sampling, the ability to sample classically from the probability distribution induced by time evolution under this Hamiltonian would imply unlikely complexity theoretic consequences, suggesting that the dynamics of such a spin model cannot be efficiently simulated with a classical computer. Physical Ising spin systems capable of achieving problem-size instances (i.e., qubit numbers) large enough so that classical sampling of the output distribution is classically difficult in practice may be achievable in the near future. Unlike boson sampling, our current results only imply hardness of exact classical sampling, leaving open the important question of whether a much stronger approximate-sampling hardness result holds in this context. The latter is most likely necessary to enable a convincing experimental demonstration of quantum supremacy. As referenced in a recent paper [A. Bouland, L. Mancinska, and X. Zhang, in Proceedings of the 31st Conference on Computational Complexity (CCC 2016),Leibniz International Proceedings in Informatics (Schloss Dagstuhl-Leibniz-Zentrum fur Informatik, Dagstuhl, 2016)], our result completes the sampling hardness classification of two-qubit commuting Hamiltonians.

Kaleidoscope of quantum phases in a long-range interacting spin-1 chain.

Motivated directly by recent trapped-ion quantum simulation experiments, we carry out a comprehensive study of the phase diagram of a spin-1 chain with XXZ-type interactions that decay as 1/rα , using a combination of finite and infinite-size DMRG calculations, spin-wave analysis, and field theory. In the absence of long-range interactions, varying the spin-coupling anisotropy leads to four distinct and well-studied phases: a ferromagnetic Ising phase, a disordered XY phase, a topological Haldane phase, and an antiferromagnetic Ising phase. If long-range interactions are antiferromagnetic and thus frustrated, we find primarily a quantitative change of the phase boundaries. On the other hand, ferromagnetic (nonfrustrated) long-range interactions qualitatively impact the entire phase diagram. Importantly, for α ≲ 3 long-range interactions destroy the Haldane phase, break the conformal symmetry of the XY phase, give rise to a new phase that spontaneously breaks a U(1) continuous symmetry, and introduce a possibly exotic tricritical point with no direct parallel in short-range interacting spin chains. Importantly, we show that the main signatures of all five phases found could be observed experimentally in the near future.

Topological phases with long-range interactions.

Topological phases of matter are primarily studied in systems with short-range interactions. In nature, however, nonrelativistic quantum systems often exhibit long-range interactions. Under what conditions topological phases survive such interactions, and how they are modified when they do, is largely unknown. By studying the symmetry-protected topological phase of an antiferromagnetic spin-1 chain with 1/r α interactions, we show that two very different outcomes are possible, depending on whether or not the interactions are frustrated. While unfrustrated long-range interactions can destroy the topological phase for α ≲ 3, the topological phase survives frustrated interactions for all α > 0. Our conclusions are based on strikingly consistent results from large-scale matrix-product-state simulations and effective-field-theory calculations, and we expect them to hold for more general interacting spin systems. The models we study can be naturally realized in trapped-ion quantum simulators, opening the prospect for experimental investigation of the issues confronted here.

Entangling two transportable neutral atoms via local spin exchange.

To advance quantum information science, physical systems are sought that meet the stringent requirements for creating and preserving quantum entanglement. In atomic physics, robust two-qubit entanglement is typically achieved by strong, long-range interactions in the form of either Coulomb interactions between ions or dipolar interactions between Rydberg atoms. Although such interactions allow fast quantum gates, the interacting atoms must overcome the associated coupling to the environment and cross-talk among qubits. Local interactions, such as those requiring substantial wavefunction overlap, can alleviate these detrimental effects; however, such interactions present a new challenge: to distribute entanglement, qubits must be transported, merged for interaction, and then isolated for storage and subsequent operations. Here we show how, using a mobile optical tweezer, it is possible to prepare and locally entangle two ultracold neutral atoms, and then separate them while preserving their entanglement. Ground-state neutral atom experiments have measured dynamics consistent with spin entanglement, and have detected entanglement with macroscopic observables; we are now able to demonstrate position-resolved two-particle coherence via application of a local gradient and parity measurements. This new entanglement-verification protocol could be applied to arbitrary spin-entangled states of spatially separated atoms. The local entangling operation is achieved via spin-exchange interactions, and quantum tunnelling is used to combine and separate atoms. These techniques provide a framework for dynamically entangling remote qubits via local operations within a large-scale quantum register.

Quantum simulation. Two-dimensional superexchange-mediated magnetization dynamics in an optical lattice.

The interplay of magnetic exchange interactions and tunneling underlies many complex quantum phenomena observed in real materials. We study nonequilibrium magnetization dynamics in an extended two-dimensional (2D) system by loading effective spin-1/2 bosons into a spin-dependent optical lattice and use the lattice to separately control the resonance conditions for tunneling and superexchange. After preparing a nonequilibrium antiferromagnetically ordered state, we observe relaxation dynamics governed by two well-separated rates, which scale with the parameters associated with superexchange and tunneling. With tunneling off-resonantly suppressed, we observe superexchange-dominated dynamics over two orders of magnitude in magnetic coupling strength. Our experiment will serve as a benchmark for future theoretical work as the detailed dynamics of this 2D, strongly correlated, and far-from-equilibrium quantum system remain out of reach of current computational techniques.

Two-particle quantum interference in tunnel-coupled optical tweezers.

The quantum statistics of atoms is typically observed in the behavior of an ensemble via macroscopic observables. However, quantum statistics modifies the behavior of even two particles. Here, we demonstrate near-complete control over all the internal and external degrees of freedom of two laser-cooled (87)Rb atoms trapped in two optical tweezers. This controllability allows us to observe signatures of indistinguishability via two-particle interference. Our work establishes laser-cooled atoms in optical tweezers as a promising route to bottom-up engineering of scalable, low-entropy quantum systems.

Suppressing the loss of ultracold molecules via the continuous quantum Zeno effect.

We investigate theoretically the suppression of two-body losses when the on-site loss rate is larger than all other energy scales in a lattice. This work quantitatively explains the recently observed suppression of chemical reactions between two rotational states of fermionic KRb molecules confined in one-dimensional tubes with a weak lattice along the tubes [Yan et al., Nature (London) 501, 521 (2013)]. New loss rate measurements performed for different lattice parameters but under controlled initial conditions allow us to show that the loss suppression is a consequence of the combined effects of lattice confinement and the continuous quantum Zeno effect. A key finding, relevant for generic strongly reactive systems, is that while a single-band theory can qualitatively describe the data, a quantitative analysis must include multiband effects. Accounting for these effects reduces the inferred molecule filling fraction by a factor of 5. A rate equation can describe much of the data, but to properly reproduce the loss dynamics with a fixed fillingfraction for all lattice parameters we develop a mean-field model and benchmark it with numerically exacttime-dependent density matrix renormalization group calculations.