Talks

In the past few years there have been a number of major advances for quantum simulation.  I will be reviewing a number of them in this talk including the interaction picture simulation method, the QDRIFT algorithm, well conditioned multi-product formulas and new commutator bounds for high-order Trotter Suzuki methods which show that those algorithms are much more efficient than previously thought.  Finally I will discuss applications of these algorithms to problems in chemistry and simulation of the Schwinger model in 1+1D.

This talk aims at providing an overview of some of the major ideas and techniques that were developed for Hamiltonian simulation, including Trotterization, linear combination of unitaries, oblivious amplitude amplification and quantum signal processing. The adaptation and clever combination of these techniques led to a flurry of new results in different variants of Hamiltonian simulation problems, as well as in other important quantum algorithmic tasks.

Noisy quantum computers can outperform classical computers on certain sampling tasks, but it's unclear whether NISQ machines can outperform classical computers on a commercially relevant task. If NISQ machines can't do this, then it will be necessary to build fault tolerant quantum computers before a "quantum information age" could truly begin. The goal of this talk is to contextualize the expected overhead of fault tolerant quantum computation using superconducting qubits and the surface code. We will cover the cost of performing the simplest possible classically intractable task (random circuit sampling) in a fault tolerant fashion.

The subject of this talk will be quantum distributed computing, i.e., distributed computing when the processors of the network can exchange quantum information. After describing the basics of distributed computing, I will explain a result obtained with Frédéric Magniez (arXiv:1804.02917) on quantum algorithms computing the diameter of the network. I will then present others results (arXiv:1810.10838 and arXiv:1908.11488) that show separations between the computational powers of quantum and classical distributed algorithms in several fundamental models of distributed computing. I will conclude my talk by mentioning interesting and important open questions in quantum distributed computing.

"st-connectivity" is the problem of deciding whether two points in a graph are connected or not (i.e. whether there is a path between them). I will show that a range of common problems can be reduced to st-connectivity, and furthermore, this reduction leads to an optimal quantum algorithm in many cases of interest. The analysis of the quantum algorithm is fairly simple, and uses standard graph theoretic quantities. These properties suggest that st-connectivity would make a good building block, or primitive, for designing and analyzing quantum algorithms.

As the search continues for useful applications of noisy intermediate scale quantum devices, variational simulations of fermionic systems remain one of the most promising directions. Here, we demonstrate an experimental quantum simulation of chemistry with more than ten times times the number of entangling gates as the largest prior implementation. We variationally model the isomerization of diazene and correctly distinguish between competing reaction mechanisms to within the model chemistry. The parameterized circuits explored in our work realize the Givens rotation approach to free fermion evolution. This ubiquitous algorithmic primitive performs an arbitrary change of orbital basis and is required by many proposals for correlated simulations of molecules and Hubbard models. Because free fermion evolutions are classically tractable to simulate yet still generate highly entangled states over the computational basis, we are able to use these experiments to benchmark the performance of our quantum processor while establishing a foundation for scaling up intermediate scale correlated electron simulations.

I will survey some recent results that illustrate the current state-of-the-art in classical simulations of chemical and materials systems and discuss some areas of near-term interest for quantum computers.