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High ground state overlap via quantum embedding methods
Get PDFQuantum computers can accurately compute ground state energies using phase estimation, but this requires a guiding state that has significant overlap with the true ground state. For large molecules and extended materials, it becomes difficult to find guiding states with good ground state overlap for growing molecule sizes. Additionally, the required number of qubits and quantum gates may become prohibitively large. One approach for dealing with these challenges is to use a quantum embedding method, which allows a reduction to one or multiple smaller quantum cores embedded in a larger quantum region. In such situations, it is unclear how the embedding method affects the hardness of constructing good guiding states. In this work, we therefore investigate the preparation of guiding states in the context of quantum embedding methods. We extend previous work on quantum impurity problems, a framework in which we can rigorously analyze the embedding of a subset of orbitals. While there exist results for optimal active orbital space selection in terms of energy minimization, we rigorously demonstrate how the same principles can be used to define selected orbital spaces for state preparation in terms of the overlap with the ground state. Moreover, we perform numerical studies of molecular systems relevant to biochemistry, one field in which quantum embedding methods are required due to the large size of biomacromolecules such as proteins and nucleic acids. We investigate two different embedding strategies which can exhibit qualitatively different orbital entanglement. In all cases, we demonstrate that the easy-to-obtain mean-field state will have a sufficiently high overlap with the target state to perform quantum phase estimation
Lossy-and-constrained extended non-local games with applications to quantum cryptography
Get PDFExtended non-local games are a generalization of monogamy-of-entanglement games, played by two quantum parties and a quantum referee that performs a measurement on their local quantum system. Along the lines of the NPA hierarchy, the optimal winning probability of those games can be upper bounded by a hierarchy of semidefinite programs (SDPs) converging to the optimal value. Here, we show that if one extends such games by considering constraints and loss, motivated by experimental errors and loss through quantum communication, the convergence of the SDPs to the optimal value still holds. We give applications of this result, and we compute SDPs that show tighter security of protocols for relativistic bit commitment, quantum key distribution, and quantum position verification
Parallel composition of constraint automata
No full textIn this paper, we introduce the parallel composition of Constraint Automata (CA), a variant of the original composition of Constraint Automata better suited to compactly represent highly concurrent compositional models, such as Reo. By relegating the crux of composition to run-time, our parallel composition maintains the integrity of the constituent parts of a composite model, allowing dynamic modification of CA models. We discuss the run-time structure of the parallel composition with its implementation in Maude, and the notion of maximality for a composite transition with respect to various criteria. We show the utility of parallel composition in formal analysis through Maude search queries
Concurrent rules machines
No full textCyber-Physical systems interact with their environment in complex ways. In addition to exchanging information with other systems, they affect and are affected by their physical/natural environment. Their components run concurrently and may be physically distributed, participating in both synchronous and asynchronous interactions. Existing formal models typically model closed systems, or limited interactions among system components. In this paper we introduce the Concurrent Rules Machine (CRM), a formal model of system behavior that makes explicit interaction with the environment. We define an algebra of operations for CRM composition and decomposition along with equational properties. We illustrate our ideas with a simple cyber-physical system example
