Publications

Let H be a frustration-free Hamiltonian describing a 2D grid of qudits with local interactions, a unique ground state, and local spectral gap lower bounded by a positive constant. For any bipartition defined by a vertical cut of length L running from top...

We prove that the entanglement entropy of the ground state of a locally gapped frustration-free 2D lattice spin system satisfies an area law with respect to a vertical bipartition of the lattice into left and right regions. We first establish that the...

The No Low-energy Trivial States (NLTS) conjecture of Freedman and Hastings, 2014 -- which posits the existence of a local Hamiltonian with a super-constant quantum circuit lower bound on the complexity of all low-energy states -- identifies a fundamental...

Ground-state entanglement governs various properties of quantum many-body systems at low temperatures and is the key to understanding gapped quantum phases of matter. Here we identify a structural property of entanglement in the ground state of gapped...

We address the question of efficient implementation of quantum protocols, with small communication and entanglement, and short depth circuit for encoding or decoding. We introduce two methods for this; the first constructs a resource-efficient convex...

As small quantum computers are becoming available on different physical platforms, a benchmarking task known as cross-platform verification has been proposed that aims to estimate the fidelity of states prepared on two quantum computers. This task is...

The NLTS (No Low-Energy Trivial State) conjecture of Freedman and Hastings [2014] posits that there exist families of Hamiltonians with all low energy states of high complexity (with complexity measured by the quantum circuit depth preparing the state)...

The NLTS (No Low-Energy Trivial State) conjecture of Freedman and Hastings [2014] posits that there exist families of Hamiltonians with all low energy states of non-trivial complexity (with complexity measured by the quantum circuit depth preparing the...

Learning the Hamiltonian that describes interactions in a quantum system is an important task in both condensed-matter physics and the verification of quantum technologies. Its classical analogue arises as a central problem in machine learning known as...

One of the most fundamental problems in quantum many-body physics is the characterization of correlations among thermal states. Of particular relevance is the thermal area law, which justifies the tensor network approximations to thermal states with a...

We consider the task of approximating the ground state energy of two-local quantum Hamiltonians on bounded-degree graphs. Most existing algorithms optimize the energy over the set of product states. Here we describe a family of shallow quantum circuits...