This series consists of talks in the area of Quantum Information Theory.
We study the robustness of quantum information stored in
the degenerate ground space of a local, frustration-free Hamiltonian with
commuting terms on a 2D spin lattice. On one hand, a macroscopic energy barrier
separating the distinct ground states under local transformations would protect
the information from thermal fluctuations. On the other hand, local topological
order would shield the ground space from static perturbations.
Self-testing a multipartite quantum state means verifying
the existence of the state based on the outcomes of unknown or untrusted
measurements.
This concept is important in device-independent quantum
cryptography.
The minimal dimension of the Hilbert space that hosts states of an entangled pair of photons can be extremely high. The process of spontaneous parametric down-conversion (SPDC) is a possible way of producing highly entangled photon pairs, in both the spatial and temporal parts of the wave function. However, the most common approximations that are used in the analytical treatment of SPDC hinder the possibility of noticing further structures of the single joint modes.
Winter's measurement compression theorem stands as one of the most important, yet perhaps less well-known coding theorems in quantum information theory. Not only does it make an illuminative statement about measurement in quantum theory, but it also underlies several other general protocols used for entanglement distillation or local purity distillation.
We propose a framework to describe and simulate a class of many-body quantum states. We do so by considering joint eigenspaces of sets of monomial unitary matrices, called "M-spaces"; a unitary matrix is monomial if precisely one entry per row and column is nonzero. We show that M-spaces encompass various important state families, such as all Pauli stabilizer states and codes, the AKLT model, Kitaev's anyon models, W states and several others.
Based on the joint work with Sergey Bravyi, IBM Watson. We show that any topologically ordered local stabilizer model of spins in three dimensional lattices that lacks string logical operators can be used as a reliable quantum memory against thermal noise. It is shown that any local process creating a topologically charged particle separated from other particles by distance $R$, must cross an energy barrier of height $c \log R$. This property makes the model glassy.
In this talk, I will briefly review the recent progress on quantum computation and simulation in the trapped ion system, with particular emphasis on the idea of scaling (how to scale up the number of qubits). I will discuss ideas towards large-scale quantum computation/simulation based on the network approach or the use of transverse phonon modes in anharmonic traps and then review the recent experimental progress along this direction.
Quantum field theory provides the framework for the Standard Model of particle physics and plays a key role in many areas of physics. However, calculations are generally computationally complex and limited to weak interaction strengths. I shall describe a polynomial-time algorithm for computing, on a quantum computer, relativistic scattering amplitudes in massive scalar quantum field theories. The quantum algorithm applies at both weak and strong coupling, achieving exponential speedup over known classical methods at high precision or strong coupling.