Sophia E. Economou

Periodically driven quantum systems exhibit many fascinating phenomena absent in equilibrium systems, but their simulation is more challenging than that of static systems. Consequently, quantum simulation of these systems offers greater opportunity for achieving quantum advantage. To build the foundation for simulating time-periodic Hamiltonians, we utilize the Floquet-Hilbert space formalism to transform the Hamiltonian into a time-independent form and provide its Pauli decomposition. Within this formalism, we develop a hybrid quantum-classical algorithm, Floquet-ADAPT-VQE, that produces three key quantities that govern periodically driven quantum dynamics: the quasienergy, the associated Floquet eigenstates, and expectation values of observables with respect to these eigenstates. The latter is achieved by applying a fixed-depth quantum circuit to an initial Floquet eigenstate—an efficient construction made possible by the Floquet-Hilbert space formalism. We also identify a suitable auxiliary initial state whose squared Floquet energy is independent of the number of auxiliary qubits as well as the driving frequency, which leads to better convergence with fewer ADAPT iterations. We demonstrate our algorithm by performing numerical simulations on a periodically driven XYZ model with a magnetic field. We also explore potential applications of our algorithm for studying various non-equilibrium phenomena in periodically driven systems.

Scaling quantum networks to long distances necessitates the development of advanced Quantum Repeater (QR) technologies. Depending on the error mitigation mechanisms adopted to suppress loss and errors, QRs are typically classified into memory-based or all-photonic QRs; and each type of QR may be best suited for a specific type of underlying quantum technology, a particular scale of quantum networks, or a specific regime of operational parameters. This paper presents a comparative theoretical and simulation-based analysis of first-generation memory-based trapped-ion QRs and networks, and all-photonic entanglement-based QRs and networks. Our model incorporates a wide range of realistic parameters and noise sources to evaluate performance trade-offs. Major research findings of this study include: (a) the entanglement rate does not necessarily scale with the number of quantum repeaters. Although adding repeaters in a chain helps to reduce photon loss in quantum links, it also introduces overheads that can be attributed to imperfect photon collection, inefficient quantum frequency conversion, and limited detector efficiency. The entanglement rate only improves when the distance between QRs exceeds a certain threshold, specifically, when the reduction in photon loss in quantum links gained by adding QRs outweighs the inherent overheads they introduce. (b) Without quantum error correction and entanglement purification, the entanglement fidelity decreases with the number of QRs, regardless of the chain distance. Finally, the theoretical models and simulation software package developed in this study provide a versatile framework for the design and evaluation of future QR technologies, protocols, and architectures.

The adaptive derivative-assembled problem-tailored variational quantum eigensolver (ADAPT-VQE) provides a promising approach for simulating highly correlated quantum systems on quantum devices, as it strikes a balance between hardware efficiency, trainability, and accuracy. Although ADAPT-VQE avoids many of the shortcomings of other VQEs, it is sometimes hindered by a phenomenon known as gradient troughs. This refers to a non-monotonic convergence of the gradients, which may become very small even though the minimum energy has not been reached. This results in difficulties finding the right operators to add to the ansatz, due to the limited number of shots and statistical uncertainties, leading to stagnation in the circuit structure optimization. In this paper, we propose ways to detect and mitigate this phenomenon. Leveraging the non-commutative algebra of the ansatz, we develop heuristics for determining where to insert new operators into the circuit. We find that gradient troughs are more likely to arise when the same locations are used repeatedly for new operator insertions. Our novel protocols, which add new operators in different ansatz positions, allow us to escape gradient troughs and thereby lower the measurement cost of the algorithm. This approach achieves an effective balance between cost and efficiency, leading to faster convergence without compromising the low circuit depth and gate count of ADAPT-VQE.

Developing and deploying advanced Quantum Repeater (QR) technologies will be necessary to scale quantum networks to longer distances. Depending on the error mitigation mechanisms adopted to suppress loss and errors, QRs are typically classified into memory-based or all-photonic QRs; and each type of QR may be best suited for a specific type of underlying quantum technology, a particular scale of quantum networks, or a specific regime of operational parameters. We perform theoretical analysis and simulations of quantum repeaters and networks to investigate the relative performance and resource requirements of different quantum network paradigms. Our results will help guide the optimization of quantum hardware and components and shed light on the role of a robust control plane. We present our research findings on theoretical analysis and simulations of memory-based first-generation trapped-ion quantum repeaters and networks, and all-photonic entanglement-based quantum repeaters and networks. We study the relative performance in terms of entanglement generation rate and fidelity, as well as the resource requirements of these two different quantum network paradigms.

Photonic graph states are important for measurement- and fusion-based quantum computing, quantum networks, and sensing. They can in principle be generated deterministically by using emitters to create the requisite entanglement. Finding ways to minimize the number of entangling gates between emitters and understanding the overall optimization complexity of such protocols is crucial for practical implementations. Here, we address these issues using graph theory concepts. We develop optimizers that minimize the number of entangling gates, reducing them by up to 75% compared to naive schemes for moderately sized random graphs. While the complexity of optimizing emitter-emitter CNOT counts is likely NP-hard, we are able to develop heuristics based on strong connections between graph transformations and the optimization of stabilizer circuits. These patterns allow us to process large graphs and still achieve a reduction of up to 66% in emitter CNOTs, without relying on subtle metrics such as edge density. We find the optimal emission orderings and circuits to prepare unencoded and encoded repeater graph states of any size, achieving global minimization of emitter and CNOT resources despite the average NP-hardness of both optimization problems. We further study the locally equivalent orbit of graphs. Although enumerating orbits is #P complete for arbitrary graphs, we analytically calculate the size of the orbit of repeater graphs and find a procedure to generate the orbit for any repeater size. Finally, we inspect the entangling gate cost of preparing any graph from a given orbit and show that we can achieve the same optimal CNOT count across the orbit.