37 citations · 101 across the 12 of their papers we have counts for
14 papers
Products of unitaries as continuous evolutions at finite precision
Michael Jarret
I present a short approach to discretizing continuous unitary evolution. It gives a correspondence in both directions between continuous unitary evolutions and products of unitarie…
Quantum Query Complexity and Span Programs from Pre-Geometry
Justin Roy Cox, Neil Epstein, Zhirui Hu +2
Span programs provide a general method for designing quantum query algorithms, and for Boolean coordinate queries their optimum cost agrees with the general adversary bound. We dev…
On the stability of solutions to Schrödinger's equation short of the adiabatic limit
Jacob Bringewatt, Michael Jarret, T. C. Mooney
We prove an adiabatic theorem that applies at timescales short of the typical adiabatic limit. Our proof analyzes the stability of solutions to Schrodinger's equation under perturb…
Effective gaps are not effective: quasipolynomial classical simulation of obstructed stoquastic Hamiltonians
Jacob Bringewatt, Michael Jarret
All known examples confirming the possibility of an exponential separation between classical simulation algorithms and stoquastic adiabatic quantum computing (AQC) exploit symmetri…
Quantum adiabatic optimization without heuristics
Michael Jarret, Brad Lackey, Aike Liu +1
Quantum adiabatic optimization (QAO) is performed using a time-dependent Hamiltonian with spectral gap . Assuming the existence of an oracle such that $γ_\min = Θ\…
Quantum Algorithms for Connectivity and Related Problems
Michael Jarret, Stacey Jeffery, Shelby Kimmel +1
An important family of span programs, st-connectivity span programs, have been used to design quantum algorithms in various contexts, including a number of graph problems and formu…
Hamiltonian surgery: Cheeger-type gap inequalities for nonpositive (stoquastic), real, and Hermitian matrices
Michael Jarret
Cheeger inequalities bound the spectral gap of a space by isoperimetric properties of that space and vice versa. In this paper, I derive Cheeger-type inequalities for nonpositi…
Improved quantum backtracking algorithms using effective resistance estimates
Michael Jarret, Kianna Wan
We investigate quantum backtracking algorithms of a type previously introduced by Montanaro (arXiv:1509.02374). These algorithms explore trees of unknown structure, and in certain…
Substochastic Monte Carlo Algorithms
Michael Jarret, Brad Lackey
In this paper we introduce and formalize Substochastic Monte Carlo (SSMC) algorithms. These algorithms, originally intended to be a better classical foil to quantum annealing than…
Adiabatic optimization versus diffusion Monte Carlo
Michael Jarret, Stephen P. Jordan, Brad Lackey
Most experimental and theoretical studies of adiabatic optimization use stoquastic Hamiltonians, whose ground states are expressible using only real nonnegative amplitudes. This ra…
Yang-Baxter operators need quantum entanglement to distinguish knots
Gorjan Alagic, Michael Jarret, Stephen P. Jordan
Any solution to the Yang-Baxter equation yields a family of representations of braid groups. Under certain conditions, identified by Turaev, the appropriately normalized trace of t…
Modulus of continuity eigenvalue bounds for homogeneous graphs and convex subgraphs with applications to quantum Hamiltonians
Michael Jarret, Stephen P. Jordan
We adapt modulus of continuity estimates to the study of spectra of combinatorial graph Laplacians, as well as the Dirichlet spectra of certain weighted Laplacians. The latter case…
Adiabatic optimization without local minima
Michael Jarret, Stephen P. Jordan
Several previous works have investigated the circumstances under which quantum adiabatic optimization algorithms can tunnel out of local energy minima that trap simulated annealing…
The Fundamental Gap for a Class of Schrödinger Operators on Path and Hypercube Graphs
Michael Jarret, Stephen P. Jordan
We consider the difference between the two lowest eigenvalues (the fundamental gap) of a Schrödinger operator acting on a class of graphs. In particular, we derive tight bounds for…