Hamiltonian Complexity Initiative

What is the computational complexity of simulating a given Hamiltonian? What is the computational complexity of finding its ground state?

These questions are fundamental to condensed matter physics, to computational complexity but also have deep practical merit. Ground state quantum computation (e.g. adiabatic quantum computation) utilize properties of the ground states of Hamiltonians to compute.

Adiabatic quantum computing generally relies on the idea of embedding a problem instance into a physical system, such that the systems lowest energy configuration stores the problem instance solution. […]

Quantum Walks

Chiral quantum walks offer a means to control quantum evolutions on graphs by controlling time-reversal symmetry breaking and the interplay of this effect with the global topological structure of the underlying network.  The theory is part of a larger idea to merge time-symmetry theory with quantum information science and to address the quantum challenges of control on complex networks. […]

Experimental Collaborations

Experimental quantum physics is where the rubber meets the road. There’s been incredible progress in demonstrating various quantum algorithms and other building blocks for a future device to surpass the best conceivable classical computer.  The most interesting aspect of quantum information science is the fact that […]

Quantum Software

We developed quantum computer algorithms which utilize quantum effects to

  1. Accelerate machine learning – particularly, deep learning
  2. Perform tensor operations on a quantum computer
  3. Simulate quantum chemistry and materials science

In our work, we have taken part in several experimental collaborations which have realized prototypes of our algorithms.

In his famous 1981 talk, Feynman proposed that unlike classical computers, which would presumably experience an exponential slowdown when simulating quantum phenomena, a universal quantum simulator would not. An ideal quantum simulator would be controllable, and built using existing technology. […]

Tensor Networks Initiative

Tensor networks gave rise to efficiently compact representations for certain classes of quantum states, and provide a graphical language to reason about quantum processes.

The methods reach outside of physics to large areas of computer science and even more recently have found applications in complex networks. […]