Spring 2020

The position states of the harmonic oscillator describe the location of a particle moving on the real line. Similarly, the phase difference between two superconductors on either side of a Josephson junction takes values in the configuration space of a particle on a circle. More generally, many physical systems can be described by a basis of "position states," describing a particle moving on a more general configuration or state space. Most of this space is usually ignored due to the energy cost required to pin a particle to a precise "position".

The AdS/CFT correspondence is a concrete instance of holographic duality, where a bulk theory of quantum gravity in d+1 dimensions can emerge from a conformal field theory (CFT) in d dimensions. In particular, we expect the semi-classical spacetime of d+1 dimensions to emerge from the entanglement patterns of certain quantum states in the CFT. Therefore, it is crucial to understand what kind of states encode such spacetime geometries and how to explicitly reconstruct these geometries from quantum entanglement.

"Mana" is a measure of the degree to which a state cannot be approximated the result of Clifford gates; consequently, it can measure both the difficulty of state preparation on a quantum computer, and the degree to which entanglement is non-Bell-pair. I will show numerical calculations of the mana of ground states of the one-dimensional Z3 Potts model, chosen for convenience, in which we find that the mana is extensive and peaked at the phase transition.

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.

Quantum dots formed in silicon heterostructures have emerged as a promising candidate for creating qubits, the building blocks of quantum computing. Their small size, ease of control, and compatibility with modern semiconductor processes make them especially enticing. However, the intrinsic near-degeneracy (valley splitting) of the conduction band electrons that form these quantum dots poses a serious concern for the viability of these qubits, but may also hold the solution.

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.

I will present our recent advances in the formal verification of post-quantum security. Our framework includes a logic for reasoning about quantum programs (qRHL, quantum relational Hoare logic) and a tool for computer-aided verification in qRHL. We have used this framework to verify the post-quantum security of the Fujisaki-Okamoto transform for building encryption schemes. I will give an overview of the logical foundations and of our experiences when verifying a real-life cryptosystem.

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.

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.

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