Physics
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Item Harnessing Quantum Systems for Sensing, Simulation, and Optimization(2024) Bringewatt, Jacob Allen; Gorshkov, Alexey V; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Quantum information science offers a remarkable promise: by thinking practically about how quantum systems can be put to work to solve computational and information processing tasks, we gain novel insights into the foundations of quantum theory and computer science. Or, conversely, by (re)considering the fundamental physical building blocks of computers and sensors, we enable new technologies, with major impacts for computational and experimental physics. In this dissertation, we explore these ideas through the lens of three different types of quantum hardware, each with a particular application primarily in mind: (1) networks of quantum sensors for measuring global properties of local field(s); (2) analog quantum computers for solving combinatorial optimization problems; and (3) digital quantum computers for simulating lattice (gauge) theories. For the setting of quantum sensor networks, we derive the fundamental performance limits for the sensing task of measuring global properties of local field(s) in a variety of physical settings (qubit sensors, Mach-Zehnder interferometers, quadrature displacements) and present explicit protocols that achieve these limits. In the process, we reveal the geometric structure of the fundamental bounds and the associated algebraic structure of the corresponding protocols. We also find limits on the resources (e.g. entanglement or number of control operations) required by such protocols. For analog quantum computers, we focus on the possible origins of quantum advantage for solving combinatorial optimization problems with an emphasis on investigating the power of adiabatic quantum computation with so-called stoquastic Hamiltonians. Such Hamiltonians do not exhibit a sign problem when classically simulated via quantum Monte Carlo algorithms, suggesting deep connections between the sign problem, the locality of interactions, and the origins of quantum advantage. We explore these connections in detail. Finally, for digital quantum computers, we consider the optimization of two tasks relevant for simulating lattice (gauge) theories. First, we investigate how to map fermionic systems to qubit systems in a hardware-aware manner that consequently enables an improved parallelization of Trotter-based time evolution algorithms on the qubitized Hamiltonian. Second, we investigate how to take advantage of known symmetries in lattice gauge theories to construct more efficient randomized measurement protocols for extracting purities and entanglement entropies from simulated states. We demonstrate how these protocols can be used to detect a phase transition between a trivial and a topologically ordered phase in $Z_2$ lattice gauge theory. Detecting this transition via these randomized methods would not otherwise be possible without relearning all symmetries.Item APPLICATIONS OF ARTIFICIAL NEURAL NETWORKS IN LEARNING QUANTUM SYSTEMS(2023) Pan, Ruizhi; Clark, Charles; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Quantum machine learning is an emerging field that combines techniques in the disciplines of machine learning (ML) and quantum physics. Research in this field takes three broad forms: applications of classical ML techniques to quantum physical systems, quantum computing and algorithms for classical ML problems, and new ideas inspired by the intersection of the two disciplines. We mainly focus on the power of artificial neural networks (NNs) in quantum-state representation and phase classification in this work. In the first part of the dissertation, we study NN quantum states which are used as wave-function ans{\" a}tze in the context of quantum many-body physics. While these states have achieved success in simulating low-lying eigenstates and short-time unitary dynamics of quantum systems and efficiently representing particular states such as those with a stabilizer nature, more rigorous quantitative analysis about their expressibility and complexity is warranted. Here, our analysis of the restricted Boltzmann machine (RBM) state representation of one-dimensional (1D) quantum spin systems provides new insight into their computational complexity. We define a class of long-range-fast-decay (LRFD) RBM states with quantifiable upper bounds on truncation errors and provide numerical evidence for a large class of 1D quantum systems that may be approximated by LRFD RBMs of at most polynomial complexities. These results lead us to conjecture that the ground states of a wide range of quantum systems may be exactly represented by LRFD RBMs or a variant of them, even in cases where other state representations become less efficient. At last, we provide the relations between multiple typical state manifolds. Our work proposes a paradigm for doing complexity analysis for generic long-range RBMs which naturally yields a further classification of this manifold. This paradigm and our characterization of their nonlocal structures may pave the way for understanding the natural measure of complexity for quantum many-body states described by RBMs and are generalizable for higher-dimensional systems and deep neural-network quantum states. In the second part, we use RBMs to investigate, in dimensions $D=1$ and $2$, the many-body excitations of long-range power-law interacting quantum spin models. We develop an energy-shift method to calculate the excited states of such spin models and obtain a high-precision momentum-resolved low-energy spectrum. This enables us to identify the critical exponent where the maximal quasiparticle group velocity transits from finite to divergent in the thermodynamic limit numerically. In $D=1$, the results agree with an analysis using the field theory and semiclassical spin-wave theory. Furthermore, we generalize the RBM method for learning excited states in nonzero-momentum sectors from 1D to 2D systems. At last, we analyze and provide all possible values ($3/2$, $2$ and $3$) of the critical exponent for 1D generic quadratic bosonic and fermionic Hamiltonians with long-range hoppings and pairings which serves for understanding the speed of information propagation in quantum systems. In the third part, we study deep NNs as phase classifiers. We analyze the phase diagram of a 2D topologically nontrivial fermionic model Hamiltonian with pairing terms at first and then demonstrate that deep NNs can learn the band-gap closing conditions only based on wave-function samples of several typical energy eigenstates, thus being able to identify the phase transition point without knowledge of Hamiltonians.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 A Programmable Five Qubit Quantum Computer Using Trapped Atomic Ions(2016) Debnath, Shantanu; Monroe, Christopher R; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Quantum computers can solve certain problems more efficiently compared to conventional classical methods. In the endeavor to build a quantum computer, several competing platforms have emerged that can implement certain quantum algorithms using a few qubits. However, the demonstrations so far have been done usually by tailoring the hardware to meet the requirements of a particular algorithm implemented for a limited number of instances. Although such proof of principal implementations are important to verify the working of algorithms on a physical system, they further need to have the potential to serve as a general purpose quantum computer allowing the flexibility required for running multiple algorithms and be scaled up to host more qubits. Here we demonstrate a small programmable quantum computer based on five trapped atomic ions each of which serves as a qubit. By optically resolving each ion we can individually address them in order to perform a complete set of single-qubit and fully connected two-qubit quantum gates and alsoperform efficient individual qubit measurements. We implement a computation architecture that accepts an algorithm from a user interface in the form of a standard logic gate sequence and decomposes it into fundamental quantum operations that are native to the hardware using a set of compilation instructions that are defined within the software. These operations are then effected through a pattern of laser pulses that perform coherent rotations on targeted qubits in the chain. The architecture implemented in the experiment therefore gives us unprecedented flexibility in the programming of any quantum algorithm while staying blind to the underlying hardware. As a demonstration we implement the Deutsch-Jozsa and Bernstein-Vazirani algorithms on the five-qubit processor and achieve average success rates of 95 and 90 percent, respectively. We also implement a five-qubit coherent quantum Fourier transform and examine its performance in the period finding and phase estimation protocol. We find fidelities of 84 and 62 percent, respectively. While maintaining the same computation architecture the system can be scaled to more ions using resources that scale favorably (O(N^2)) with the number of qubits N.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 A Modular Quantum System of Trapped Atomic Ions(2015) Hucul, David Alexander; Monroe, Christopher R; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Scaling up controlled quantum systems to involve large numbers of qubits remains one of the outstanding challenges of quantum information science. One path toward scalability is the use of a modular architecture where adjacent qubits may be entangled with applied electromagnetic fields, and remote qubits may be entangled using photon interference. Trapped atomic ion qubits are one of the most promising platforms for scaling up quantum systems by combining long coherence times with high fidelity entangling operations between proximate and remote qubits. In this thesis, I present experimental progress on combining entanglement between remote atomic ions separated by 1 meter with near-eld entanglement between atomic ions in the same ion trap. I describe the experimental improvements to increase the remote entanglement rate by orders of magnitude to nearly 5 per second. This is the first experimental demonstration where the remote entanglement rate exceeds the decoherence rate of the entangled qubits. The flexibility of creating remote entanglement through photon interference is demonstrated by using the interference of distinguishable photons without sacrificing remote entanglement rate or fidelity. Next I describe the use of master clock in combination with a frequency comb to lock the phases of all laser-induced interactions between remote ion traps while removing optical phase stability requirements. The combination of both types of entanglement gates to create a small quantum network are described. Finally, I present ways to mitigate cross talk between photonic and memory qubits by using different trapped ion species. I show preliminary work on performing state detection of nuclear spin 0 ions by using entanglement between atomic ion spin and photon polarization. These control techniques may be important for building a large-scale modular quantum system.Item Quantum Information Processing with Trapped Ion Chains(2014) Manning, Timothy Andrew; Monroe, Christopher R; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Trapped atomic ion systems are currently the most advanced platform for quantum information processing. Their long coherence times, pristine state initialization and detection, and precisely controllable and versatile interactions make them excellent quantum systems for experiments in quantum computation and quantum simulation. One of the more promising schemes for quantum computing consists of performing single and multi-qubit quantum gates on qubits in a linear ion crystal. Some of the key challenges of scaling such a system are the individual addressing of arbitrary subsets of ions and controlling the growing complexity of motional mode interactions as the number of qubits increases or when the gates are performed faster. Traditional entangling quantum gates between ion qubits use laser pulses to couple the qubit states to the collective motion of the crystal, thereby generating a spin-spin interaction that can produce entanglement between selected qubits. The intrinsic limitations on the performance of gates using this method can be alleviated by applying optimally shaped pulses instead of pulses with constant amplitude. This thesis explains the theory behind this pulse shaping scheme and how it is implemented on a chain of Yb ions held in a linear radiofrequency `Paul' trap. Several experiments demonstrate the technique in chains of two, three, and five ions using various types of pulse shapes. A tightly focused individual addressing beam allows us to apply the entangling gates to a target pair of ions, and technical issues related to such tight focusing are discussed. Other advantages to the pulse shaping scheme include a robustness against detuning errors and the possibility of suppressing undesirable coupling due to optical spillover on neighboring ions. Combined with ion shuttling, we harness these features to perform sequential gates to different qubit pairs in order to create genuine tripartite entangled states and demonstrate the programmable quantum information processing capability of our system.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.