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SESSION 9c: Frontiers of quantum information theory (Stiha Room)Chair: (Christopher Jackson (University of New Mexico)) | |
| 3:45pm-4:15pm | Lucas Brady, University of California Santa Barbara Evolution-time dependence in near-adiabatic quantum evolutions | Abstract. We expand upon the standard quantum adiabatic theorem, examining the time-dependence of quantum evolution in the near-adiabatic limit. We examine a Hamiltonian that evolves along some fixed trajectory from H0 to H1 in a total evolution-time T, and our goal is to determine how the final state of the system depends on T. If the system is initially started in a non-degenerate ground state, the adiabatic theorem says that in the limit of large T, the system will stay in the ground state. We examine the near-adiabatic limit where the system evolves slowly enough that most but not all of the final state is in the ground state, and we find that the probability of leaving the ground state oscillates in T with a frequency determined by the integral of the spectral gap along the trajectory of the Hamiltonian, so long as the gap is big. If the gap becomes exceedingly small, the final probability is the sum of oscillatory behavior determined by the integrals of the gap before and after the small gap. We confirm these analytic predictions with numerical evidence from barrier tunneling problems in the context of quantum adiabatic optimization. |
| 4:15pm-4:45pm | Anirban Narayan Chowdhury, University of New Mexico CQuIC Improved quantum algorithms using linear combination of unitaries | Abstract. The technique of implementing a linear combination of unitary (LCU) operators has led to significant improvements in the complexities of quantum algorithms for diverse problems such as Hamiltonian simulation and solving linear systems of equations. Here we combine LCU with a version of amplitude amplification to tackle two tasks that arise in the context of quantum algorithms for optimization problems - namely Gibbs state preparation, and that of implementing a reflection about eigenstates of a unitary operator. In both cases, we obtain improvements in resource requirements over earlier protocols that used quantum phase estimation (PE). The LCU approach for Gibbs state preparation has complexity that scales exponentially better in inverse precision and, for a certain class of Hamiltonians, polynomially better in terms of other parameters. We use similar ideas to approximate a reflection about an eigenstate of a given unitary using an LCU. Our implementation requires exponentially fewer ancilla qubits in terms of a precision parameter than a PE based approach, and has gate complexity that is comparable. Our analysis also improves upon the gate complexity of the PE-reflection by using an approximate quantum Fourier transform. Our results are useful as they reduce the resources needed by a large variety of existing quantum algorithms. We also prove a lower bound on the query complexity of implementing reflections. |
| 4:45pm-5:15pm | Alexander Meill, University of California San Diego Entanglement constraints in various symmetric subspaces | Abstract. We simplify the search for constraints on multi-partite entanglement by restricting the calculations to Hilbert spaces of 3-5 qubits which exhibit relevant symmetries. In 3 qubits we describe the space of achievable local unitary polynomial invariants among states which are fully symmetric under party relabeling. In 4 and 5 qubits we discuss pairwise concurrence relations in states which are invariant under cyclic permutation of the party labels. |
| 5:15pm-5:45pm | Ninnat Dangniam, University of New Mexico CQuIC Quasi-probabilities on a fermionic phase space | Abstract. Sometimes a classical simulation scheme of quantum processes given a restricted set of states and measurements can be naturally interpreted as a statistical simulation of positive quasi-probability distributions on a phase space. To explore the relation between classical simulatability and positivity of quasi-probabilities beyond the Wigner functions, we constructed quasi-probability representations on the compact phase space of fermionic Gaussian states (as opposed to coherent states in the usual Wigner phase space formulation) tailored to a classically simulatable problem of fermionic linear optics and found that fermionic Gaussian states possess negative quasi-probabilities. More generally, we showed that this construction due to Brif and Mann (Phys. Rev. A 59, 971 (1999)) is essentially unique given the group of quantum gates and an input state in the relevant representation. |
| 5:45pm-6:15pm | Siddhartha Das, Louisiana State University Robust quantum network architectures and topologies for entanglement distribution | Abstract. In this work [arXiv:1709.07404], we focus on two-dimensional quantum networks based on optical quantum technologies using dual-rail photonic qubits for the building of a fail-safe quantum internet. We lay out a quantum network architecture for entanglement distribution between distant parties using a Bravais lattice topology, with the technological constraint that quantum repeaters equipped with quantum memories are not easily accessible. We provide a robust protocol for simultaneous entanglement distribution between two distant groups of parties on this network. We also discuss a memory-based quantum network architecture that can be implemented on networks with an arbitrary topology. We examine networks with bow-tie lattice and Archimedean lattice topologies and use percolation theory to quantify the robustness of the networks. In particular, we provide figures of merit on the loss parameter of the optical medium that depend only on the topology of the network and quantify the robustness of the network against intermittent photon loss and intermittent failure of nodes. These figures of merit can be used to compare the robustness of different network topologies in order to determine the best topology in a given real-world scenario, which is critical in the realization of the quantum internet. |
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