Toward Digital Quantum Simulation of Standard Model Physics - a look from my path
Quantum simulations are expected to be able to provide predictions of the dynamics of quantum many-body systems of importance to Standard Model physics research from dense non-equilibrium matter to systems of neutrinos that lie beyond the capabilities of classical computation. After an introduction, I will discuss recent work we have performed in simulating 1+1D quantum field theories, including the evolution of two-flavor QCD and beta-decay of a single baryon using quantum computers, then move to flavor oscillations in dense neutrino systems, then to recent results within the Lipkin model as a demonstrator for potentially interesting directions in nuclear many-body systems. Finally, we then discuss challenges and make some observations about possible paths forward.
Martin Savage(Institute for Nuclear Theory)
Exponential quantum speedup in simulating coupled classical oscillators
We present a quantum algorithm for simulating the classical dynamics of 2n coupled oscillators (e.g., 2n masses coupled by springs). Our approach leverages a mapping between the Schrödinger equation and Newton's equation for harmonic potentials such that the amplitudes of the evolved quantum state encode the momenta and displacements of the classical oscillators. When individual masses and spring constants can be efficiently queried, and when the initial state can be efficiently prepared, the complexity of our quantum algorithm is polynomial in n, almost linear in the evolution time, and sublinear in the sparsity. As an example application, we apply our quantum algorithm to efficiently estimate the kinetic energy of an oscillator at any time. We show that any classical algorithm solving this same problem is inefficient and must make 2Ω(n) queries to the oracle and, when the oracles are instantiated by efficient quantum circuits, the problem is BQP-complete. Thus, our approach solves a potentially practical application with an exponential speedup over classical computers. Finally, we show that under similar conditions our approach can efficiently simulate more general classical harmonic systems with 2n modes.
Nathan Wiebe(University of Toronto)
Search for Non-Abelian Majorana modes as a route to topological quantum computation
Majorana zero modes are fermion-like excitations that were originally proposed in particle physics by Ettore Majorana and are characterized as being their own anti-particle. In condensed matter systems Majorana zero modes occur as fractionalized excitations with topologically protected degeneracy associated with such excitations. For over a decade the only candidate systems for observing Majorana zero modes were the non-Abelian fractional quantum Hall state and chiral p-wave superconductors. In this colloquium, I will start by explaining the basic ideas of topological quantum computation using Majorana zero modes and the potential advantages over existing systems. I will then discuss the current experimental progress, challenges in the field and our theoretical analysis of current devices. I will then provide a more detailed explanation of braiding, Majorana operators and the associated topological degeneracy.