Spring 2020

The recent advances in qubit manufacturing and coherent control of synthetic quantum matter are leading to a new generation of intermediate scale quantum hardware, with promising progress towards simulation of quantum matter and materials. In order to enhance the capabilities of this class of quantum devices, some of the more arduous experimental tasks can be off-loaded to classical algorithms running on conventional computers.

Demonstrating a superpolynomial quantum speedup using feasible schemes has become a key near-term goal in the field of quantum simulation and computation. The most prominent schemes for "quantum supremacy" such as boson sampling or random circuit sampling are based on the task of sampling from the output distribution of a certain randomly chosen unitary. But to convince a skeptic of a successful demonstration of quantum supremacy, one must verify that the sampling device produces the correct outcomes.

The first part of this talk will introduce generalized Jordan–Wigner transformation on arbitrary triangulation of any manifold in 2d, 3d, and general dimensions. This gives a duality between all fermionic systems and a new class of Z2 lattice gauge theories. This map preserves the locality and has an explicit dependence on the second Stiefel–Whitney class and a choice of spin structure on the manifold. In the Euclidean picture, this mapping is equivalent to introducing topological terms (Chern-Simon term in 2d or the Steenrod square term in general) to the Euclidean action.

The quantum adiabatic theorem governs the evolution of a wavefunction under a slowly time-varying Hamiltonian.

Resource theories have mushroomed in quantum information theory over the past decade. Resource theories are simple models for situations in which constraints limit the operations performable and the systems accessible. In a fixed-temperature environment, for instance, the first law of thermodynamics constrains operations to preserve energy, and thermal states can be prepared easily.  Scores of resource-theory theorems have been proved. Can they inform science beyond quantum information theory? Can resource theories answer pre-existing questions about the real physical world?

We derive general results relating revivals in the dynamics of quantum many-body systems to the entanglement properties of energy eigenstates. For a lattice system of N sites initialized in a low-entangled and short-range correlated state, our results show that a perfect revival of the state after a time at most poly(N) implies the existence of "quantum many-body scars", whose number grows at least as the square root of N up to poly-logarithmic factors.

The past decade has seen a dramatic increase in the degree, quality, and sophistication of control over quantum-mechanical interactions available between artificial degrees of freedom in a variety of experimental platforms. The geometrical structure of these interactions, however, remains largely constrained by the underlying rectilinear geometry of three-dimensional Euclidean space.

Can a quantum computer help us analyze a large classical data set? Data stored classically cannot be queried in superposition, which rules out direct Grover searches, and it can often be classically accessed with some level of parallelism, which would negate the advantage of Grover even if it were possible.