Neural network-based machine learning has recently proven successful for many complex applications ranging from image recognition to precision medicine. However, its direct application to problems in ...quantum physics is challenging due to the exponential complexity of many-body systems. Motivated by recent advances in realizing quantum information processors, we introduce and analyse a quantum circuit-based algorithm inspired by convolutional neural networks, a highly effective model in machine learning. Our quantum convolutional neural network (QCNN) uses only O(log(N)) variational parameters for input sizes of N qubits, allowing for its efficient training and implementation on realistic, near-term quantum devices. To explicitly illustrate its capabilities, we show that QCNNs can accurately recognize quantum states associated with a one-dimensional symmetry-protected topological phase, with performance surpassing existing approaches. We further demonstrate that QCNNs can be used to devise a quantum error correction scheme optimized for a given, unknown error model that substantially outperforms known quantum codes of comparable complexity. The potential experimental realizations and generalizations of QCNNs are also discussed.
We analyze quantum dynamics of strongly interacting, kinetically constrained many-body systems. Motivated by recent experiments demonstrating surprising long-lived, periodic revivals after quantum ...quenches in Rydberg atom arrays, we introduce a manifold of locally entangled spin states, representable by low-bond dimension matrix product states, and derive equations of motion for them using the time-dependent variational principle. We find that they feature isolated, unstable periodic orbits, which capture the recurrences and represent nonergodic dynamical trajectories. Our results provide a theoretical framework for understanding quantum dynamics in a class of constrained spin models, which allow us to examine the recently suggested explanation of "quantum many-body scarring" Nat. Phys. 14, 745 (2018)NPAHAX1745-247310.1038/s41567-018-0137-5, and establish a possible connection to the corresponding phenomenon in chaotic single-particle systems.
The physical realization ofZ2topological order as encountered in the paradigmatic toric code has proven to be an elusive goal. We predict that this phase of matter can be realized in a ...two-dimensional array of Rydberg atoms placed on the ruby lattice, at specific values of the Rydberg blockade radius. First, we show that the blockade model—also known as a “PXP” model—realizes a monomer-dimer model on the kagome lattice with a single-site kinetic term. This model can be interpreted as aZ2gauge theory whose dynamics is generated by monomer fluctuations. We obtain its phase diagram using the numerical density matrix renormalization group method and find a topological quantum liquid (TQL) as evidenced by multiple measures including (i) a continuous transition between two featureless phases, (ii) a topological entanglement entropy ofln2as measured in various geometries, (iii) degenerate topological ground states, and (iv) the expected modular matrix from ground state overlap. Next, we show that the TQL persists upon including realistic, algebraically decaying van der Waals interactionsV(r)∼1/r6for a choice of lattice parameters. Moreover, we can directly access topological loop operators, including the Fredenhagen-Marcu order parameter. We show how these can be measured experimentally using a dynamic protocol, providing a “smoking gun” experimental signature of the TQL phase. Finally, we show how to trap an emergent anyon and realize different topological boundary conditions, and we discuss the implications for exploring fault-tolerant quantum memories.
Quantum phases of Rydberg atoms on a kagome lattice Samajdar, Rhine; Ho, Wen Wei; Pichler, Hannes ...
Proceedings of the National Academy of Sciences - PNAS,
01/2021, Letnik:
118, Številka:
4
Journal Article
Recenzirano
Odprti dostop
We analyze the zero-temperature phases of an array of neutral atoms on the kagome lattice, interacting via laser excitation to atomic Rydberg states. Density-matrix renormalization group calculations ...reveal the presence of a wide variety of complex solid phases with broken lattice symmetries. In addition, we identify a regime with dense Rydberg excitations that has a large entanglement entropy and no local order parameter associated with lattice symmetries. From a mapping to the triangular lattice quantum dimer model, and theories of quantum phase transitions out of the proximate solid phases, we argue that this regime could contain one or more phases with topological order. Our results provide the foundation for theoretical and experimental explorations of crystalline and liquid states using programmable quantum simulators based on Rydberg atom arrays.
The realization of strong interactions between individual photons is a long-standing goal of both fundamental and technological significance. Scientists have known for over half a century that light ...fields can interact inside nonlinear optical media, but the nonlinearity of conventional materials is negligible at the light powers associated with individual photons. Nevertheless, remarkable advances in quantum optics have recently culminated in the demonstration of several methods for generating optical nonlinearities at the level of individual photons. Systems exhibiting strong photon-photon interactions enable a number of unique applications, including quantum-by-quantum control of light fields, single-photon switches and transistors, all-optical deterministic quantum logic, and the realization of strongly correlated states of light and matter.
The quantum approximate optimization algorithm (QAOA) is a hybrid quantum-classical variational algorithm designed to tackle combinatorial optimization problems. Despite its promise for near-term ...quantum applications, not much is currently understood about the QAOA’s performance beyond its lowest-depth variant. An essential but missing ingredient for understanding and deploying the QAOA is a constructive approach to carry out the outer-loop classical optimization. We provide an in-depth study of the performance of the QAOA on MaxCut problems by developing an efficient parameter-optimization procedure and revealing its ability to exploit nonadiabatic operations. Building on observed patterns in optimal parameters, we propose heuristic strategies for initializing optimizations to find quasioptimalp-level QAOA parameters inOpoly(p)time, whereas the standard strategy of random initialization requires2O(p)optimization runs to achieve similar performance. We then benchmark the QAOA and compare it with quantum annealing, especially on difficult instances where adiabatic quantum annealing fails due to small spectral gaps. The comparison reveals that the QAOA can learn via optimization to utilize nonadiabatic mechanisms to circumvent the challenges associated with vanishing spectral gaps. Finally, we provide a realistic resource analysis on the experimental implementation of the QAOA. When quantum fluctuations in measurements are accounted for, we illustrate that optimization is important only for problem sizes beyond numerical simulations but accessible on near-term devices. We propose a feasible implementation of large MaxCut problems with a few hundred vertices in a system of 2D neutral atoms, reaching the regime to challenge the best classical algorithms.
We describe the zero-temperature phase diagram of a model of a two-dimensional square-lattice array of neutral atoms, excited into Rydberg states and interacting via strong van der Waals ...interactions. Using the density-matrix renormalization group algorithm, we map out the phase diagram and obtain a rich variety of phases featuring complex density wave orderings, upon varying lattice spacing and laser detuning. While some of these phases result from the classical optimization of the van der Waals energy, we also find intrinsically quantum-ordered phases stabilized by quantum fluctuations. These phases are surrounded by novel quantum phase transitions, which we analyze by finite-size scaling numerics and Landau theories. Our work highlights Rydberg quantum simulators in higher dimensions as promising platforms to realize exotic many-body phenomena.
The ability to engineer parallel, programmable operations between desired qubits within a quantum processor is key for building scalable quantum information systems
. In most state-of-the-art ...approaches, qubits interact locally, constrained by the connectivity associated with their fixed spatial layout. Here we demonstrate a quantum processor with dynamic, non-local connectivity, in which entangled qubits are coherently transported in a highly parallel manner across two spatial dimensions, between layers of single- and two-qubit operations. Our approach makes use of neutral atom arrays trapped and transported by optical tweezers; hyperfine states are used for robust quantum information storage, and excitation into Rydberg states is used for entanglement generation
. We use this architecture to realize programmable generation of entangled graph states, such as cluster states and a seven-qubit Steane code state
. Furthermore, we shuttle entangled ancilla arrays to realize a surface code state with thirteen data and six ancillary qubits
and a toric code state on a torus with sixteen data and eight ancillary qubits
. Finally, we use this architecture to realize a hybrid analogue-digital evolution
and use it for measuring entanglement entropy in quantum simulations
, experimentally observing non-monotonic entanglement dynamics associated with quantum many-body scars
. Realizing a long-standing goal, these results provide a route towards scalable quantum processing and enable applications ranging from simulation to metrology.
We propose and analyze a deterministic protocol to generate two-dimensional photonic cluster states using a single quantum emitter via time-delayed quantum feedback. As a physical implementation, we ...consider a single atom or atom-like system coupled to a 1D waveguide with a distant mirror, where guided photons represent the qubits, while the mirror allows the implementation of feedback. We identify the class of many-body quantum states that can be produced using this approach and characterize them in terms of 2D tensor network states.
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