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Item MANY-BODY ENTANGLEMENT DYNAMICS AND COMPUTATION IN QUANTUM SYSTEMS WITH POWER-LAW INTERACTIONS(2022) Guo, Andrew; Gorshkov, Alexey V; Swingle, Brian; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Quantum many-body systems with long-range interactions—such as those that decay as a power-law in the distance between particles—are promising candidates for quantum information processors. Due to their high degree of connectivity, they are potentially capable of generating entanglement more quickly than systems limited to local interactions, which may lead to faster computational speeds. The questions of the nature of the speed-ups they can achieve—as well as how to program these long-range systems to achieve such speed-ups—are, therefore, of prime theoretical interest. To understand the nature of the speed-ups achievable, it is natural to consider the dual question, which is what are the fundamental speed limits in quantum many-body systems? Given that most systems relevant to quantum computation operate in the non-relativistic regime—where information typically propagates at velocities far below the threshold set by the speed of light—the absence of an absolute speed limit seems to allow for unbounded rates of information transfer. However, in 1972, Lieb and Robinson restored a notion of locality in systems with local interactions by proving a bound that led to light-cone-like regions outside which information propagation is exponentially suppressed. The question of whether similar bounds could be proven for long-range systems has remained open—until recently. In this thesis, we will describe results related to the now-fuller picture of the fundamental rates of information propagation in power-law-interacting systems. First, we consider the regime of ``strongly long-range'' interactions, for which velocities can grow unboundedly with system size. We will present Lieb-Robinson-type bounds for these systems and also outline a protocol that can transfer quantum states as fast as these bounds will allow. We will also discuss the implications of these bounds for quantum information scrambling. The second part of the thesis will study how protocols for transferring quantum states quickly can be used to perform multi-qubit gates. In particular, we will demonstrate how the power of long-range interactions allows one to implement the unbounded fanout gate asymptotically faster than systems with local interactions. This result also implies the hardness of simulating the dynamics of long-range systems evolving for superlogarithmic times, and demonstrates the potential for insights from quantum many-body physics to lead to a more powerful toolbox for quantum computation. Finally, we will address the question of fundamental speed limits in quantum systems that are open to the environment. A priori, it may seem surprising that such speed limits may exist, since non-unitary processes may break locality constraints. However, we show that under certain assumptions such as linearity and Markovianity of the bath, one can restore a notion of locality using Lieb-Robinson-type bounds. We use the resulting bounds to constrain the entanglement structure of the steady states of open long-range systems, a first step towards proving the area law for such systems.Item Generation and Uses of Distributed Entanglement in Quantum Information(2019) Eldredge, Zachary David; Rolston, Steven L; Gorshkov, Alexey V; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this thesis, we focus on the questions of how quantum entanglement can be generated between two or more spatially separated systems and, once generated, how it can be applied in quantum technology. First we will discuss a protocol, which we conjecture to be optimal in some regimes, that quickly creates entangled states across long distances in systems with power-law interactions. We will discuss how this protocol compares with currently known bounds on entangled state generation and how it might be implemented in a three-dimensional lattice of Rydberg atoms. Next, we will turn our attention to more general questions of how the Lieb-Robinson bound and other limitations on entanglement can be used to inform the design of quantum computers. Quantum computers will be required to create entanglement if they are to realize significant advantages over classical computers, meaning that the generation of entanglement is an important question. First, we will discuss the implications of the Lieb-Robinson bound on graph descriptions of quantum computer architectures, and how the relevant graph parameter (diameter) compares to likely cost functions for architectures, such as maximum graph degree and total number of necessary connections. We will present a proposed graph architecture, the hierarchical product, which we believe provides excellent balance between these considerations. We will then introduce new methods of evaluating graphs that allow us to include quantum architectures capable of measurement and feedback operations. After doing so, we will show that the generation of entanglement entropy becomes a limit on computation. We will show that, for several possible physical models of computation, the generation of entanglement can be bounded by simple graph properties. We demonstrate a connection between worst-case scenarios for entanglement generation and a graph quantity called the Cheeger constant or isoperimetric number, which we evaluate for several proposed quantum computing architectures. Finally, we will look at the scenario of quantum sensing. In particular, we will examine protocols for quantum function estimation, where quantum sensors are available to measure all of the inputs to the function. We will demonstrate that entangled sensors are more capable than non-entangled ones by first deriving a new lower bound on measurement error and then presenting protocols that saturate these bounds. We will first do so for linear functions of the measured quantities and then extend this to general functions using a two-step linearizing protocol.Item Engineering a Quantum Many-body Hamiltonian with Trapped Ions(2016) Lee, Aaron Christopher; Monroe, Christopher; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)While fault-tolerant quantum computation might still be years away, analog quantum simulators offer a way to leverage current quantum technologies to study classically intractable quantum systems. Cutting edge quantum simulators such as those utilizing ultracold atoms are beginning to study physics which surpass what is classically tractable. As the system sizes of these quantum simulators increase, there are also concurrent gains in the complexity and types of Hamiltonians which can be simulated. In this work, I describe advances toward the realization of an adaptable, tunable quantum simulator capable of surpassing classical computation. We simulate long-ranged Ising and XY spin models which can have global arbitrary transverse and longitudinal fields in addition to individual transverse fields using a linear chain of up to 24 Yb+ 171 ions confined in a linear rf Paul trap. Each qubit is encoded in the ground state hyperfine levels of an ion. Spin-spin interactions are engineered by the application of spin-dependent forces from laser fields, coupling spin to motion. Each spin can be read independently using state-dependent fluorescence. The results here add yet more tools to an ever growing quantum simulation toolbox. One of many challenges has been the coherent manipulation of individual qubits. By using a surprisingly large fourth-order Stark shifts in a clock-state qubit, we demonstrate an ability to individually manipulate spins and apply independent Hamiltonian terms, greatly increasing the range of quantum simulations which can be implemented. As quantum systems grow beyond the capability of classical numerics, a constant question is how to verify a quantum simulation. Here, I present measurements which may provide useful metrics for large system sizes and demonstrate them in a system of up to 24 ions during a classically intractable simulation. The observed values are consistent with extremely large entangled states, as much as ~95% of the system entangled. Finally, we use many of these techniques in order to generate a spin Hamiltonian which fails to thermalize during experimental time scales due to a meta-stable state which is often called prethermal. The observed prethermal state is a new form of prethermalization which arises due to long-range interactions and open boundary conditions, even in the thermodynamic limit. This prethermalization is observed in a system of up to 22 spins. We expect that system sizes can be extended up to 30 spins with only minor upgrades to the current apparatus. These results emphasize that as the technology improves, the techniques and tools developed here can potentially be used to perform simulations which will surpass the capability of even the most sophisticated classical techniques, enabling the study of a whole new regime of quantum many-body physics.Item Timing the State of Light with Anomalous Dispersion and a Gradient Echo Memory(2013) Clark, Jeremy; Rolston, Steven L; Lett, Paul D; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)We study the effects of anomalous dispersion on the continuous-variable entanglement of EPR states (generated using four-wave mixing in 85Rb) by sending one part of the state through a fast-light medium and measuring the state's quantum mutual information. We observe an advance in the maximum of the quantum mutual information between modes. In contrast, due to uncorrelated noise added by a small phase-insensitive gain, we do not observe any statistically significant advance in the leading edge of the mutual information. We also study the storage and retrieval of multiplexed optical signals in a Gradient Echo Memory (GEM) at relevant four-wave mixing frequencies in 85Rb. Temporal multiplexing capabilities are demonstrated by storing multiple classical images in the memory simultaneously and observing the expected first-in last-out order of recall without obvious cross-talk. We also develop a technique wherein selected portions of an image written into the memory can be spatially targeted for readout and erasure on demand. The effect of diffusion on the quality of the recalled images is characterized. Our results indicate that Raman-based atomic memories may serve as a flexible platform for the storage and retrieval of multiplexed optical signals.