Daniel Ranard

Postdoctoral Fellow in Theoretical Physics

California Institute of Technology

I am a theoretical physicist studying many-body physics and quantum information theory. Currently, I am a postdoctoral fellow at Caltech, advised by Alexei Kitaev. I received my PhD at Stanford under Xiaoliang Qi, and I was previously a postdoc at MIT.

Some of my recent interests include topological phases, open systems, and the emergence of classicality. My work often involves information-theoretic perspectives on many-body physics, or physics-inspired quantum algorithms. I am also interested in connections to high-energy theory.

Some of my work is mathematical physics. A style of question I enjoy is: what physical structures can be recovered from other structures? For instance, can we uniquely recover a local Hamiltonian from the ground state? Or recover topological invariants from the state alone? Can we recover a notion of locality from an abstract Hamiltonian operator, or a notion of classicality from a generic multipartite channel?

See Google Scholar for a complete list of my publications.

Selected papers

Classifying 2D topological phases: mapping ground states to string-nets

Isaac H. Kim, Daniel Ranard

2024

We prove the conjectured classification of topological phases for 2D systems with gappable boundary, subject to some simplifying assumptions, e.g., assuming that correlations between disjoint regions are precisely zero. While such a classification is sometimes taken for granted, it is not obvious. For instance, if two gapped ground states of two different Hamiltonians have the same anyon content, how do you actually find a constant-depth quantum circuit connecting the states?

String-net diagram

Learning State Preparation Circuits for Quantum Phases of Matter

Hyun-Soo Kim, Isaac H. Kim, Daniel Ranard

2024

Many-body ground state preparation is an important subroutine for quantum simulation. We show how to build a state preparation circuit for a large class of many-body ground states. We introduce polynomial-time classical algorithms that take reduced density matrices over O(1)-sized balls as inputs, and output a circuit that prepares the global state. This works for both short-range entangled states and a large class of long-range entangled ground states.

State preparation circuit diagram

Ehrenfest's theorem beyond the Ehrenfest time

Felipe Hernández, Daniel Ranard, C. Jess Riedel

2023

In closed quantum systems, wavepackets can spread exponentially in time due to chaos, forming long-range superpositions in just seconds for ordinary macroscopic systems. A weakly coupled environment is conjectured to decohere the system and restore the quantum-classical correspondence. We prove this in some generality for Hamiltonians H(x,p) of continuous variables coupled to a Markovian bath, and we identify a threshold strength of the bath coupling beyond which classicality is guaranteed. Also see our more mathematical companion paper.

Ehrenfest time diagram

Lower bounding the MaxCut of high girth 3-regular graphs using the QAOA

Edward Farhi, Sam Gutmann, Daniel Ranard, Benjamin Villalonga

2025

We give a performance guarantee for the Quantum Approximate Optimization Algorithm (QAOA) on a certain class of MaxCut optimization problems. In fact, we show the QAOA yields an exponential speedup over currently known classical algorithms with comparable performance guarantees. However, that may be subject to change with further development of classical algorithms. On the purely mathematical side, as a consequence, we obtain new lower bounds on the MaxCut of high-girth 3-regular graphs.

QAOA performance diagram

A converse to Lieb-Robinson bounds in one dimension using index theory

Daniel Ranard, Michael Walter, Freek Witteveen

Annales Henri Poincaré (2022)

The Lieb-Robinson bounds show that local Hamiltonian evolution on the lattice has an approximate lightcone. But can all unitary evolutions with an approximate lightcone be expressed as a local Hamiltonian evolution? We answer questions like this in one spatial dimension, by showing the index theory for quantum cellular automata is robust.

Lieb-Robinson bounds diagram

Fluctuations of subsystem entropies at late times

Jordan Cotler, Nicholas Hunter-Jones, Daniel Ranard

Physical Review A (2022)

After a quantum many-body system thermalizes, how do the entanglement entropies of local subsystems fluctuate in time? How do these compare to classical entropy fluctuations? We find the former are much smaller at late times, revealing a stark difference between quantum and classical thermalization, or perhaps a disanalogy in notions of entropy. For fun, we comment on consequences for the "Boltzmann brain" paradox.

Entropy fluctuations diagram

Determining a local Hamiltonian from a single eigenstate

Xiao-Liang Qi, Daniel Ranard

Quantum (2019)

Given the ground state of a local lattice Hamiltonian, we demonstrate how to recover the Hamiltonian from the state. Under some conditions that appear to hold generically, the recovery is unique and numerically tractable.

Hamiltonian determination diagram

Locality from the Spectrum

Jordan S. Cotler, Geoffrey R. Penington, Daniel H. Ranard

Communications in Mathematical Physics (2019)

Given an abstract Hamiltonian operator, without a privileged basis, what can we say about the quantum system? Does it allow a decomposition into locally interacting subsystems? We demonstrate a sense in which this decomposition is generically unique when it exists. As a consequence, exact dualities between quantum systems are non-generic.

Locality from spectrum diagram

Contact

Email

dranard@caltech.edu

Address

Caltech
Norman Bridge Laboratory (West Bridge), Office 158

Links

Google Scholar