Leo Zhou
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View article: A Quantum Approximate Optimization Algorithm for Local Hamiltonian Problems
A Quantum Approximate Optimization Algorithm for Local Hamiltonian Problems Open
Local Hamiltonian Problems (LHPs) are important problems that are computationally QMA-complete and physically relevant for many-body quantum systems. Quantum MaxCut (QMC), which equates to finding ground states of the quantum Heisenberg mo…
View article: Quantum speedups in solving near-symmetric optimization problems by low-depth QAOA
Quantum speedups in solving near-symmetric optimization problems by low-depth QAOA Open
We present new advances towards achieving exponential quantum speedups for solving optimization problems by low-depth quantum algorithms. Specifically, we focus on families of combinatorial optimization problems that exhibit symmetry and c…
View article: Local Minima in Quantum Systems
Local Minima in Quantum Systems Open
Finding ground states of quantum many-body systems is known to be hard for both classical and quantum computers. As a result, when Nature cools a quantum system in a low-temperature thermal bath, the ground state cannot always be found eff…
View article: Statistical Estimation in the Spiked Tensor Model via the Quantum Approximate Optimization Algorithm
Statistical Estimation in the Spiked Tensor Model via the Quantum Approximate Optimization Algorithm Open
The quantum approximate optimization algorithm (QAOA) is a general-purpose algorithm for combinatorial optimization. In this paper, we analyze the performance of the QAOA on a statistical estimation problem, namely, the spiked tensor model…
View article: Local minima in quantum systems
Local minima in quantum systems Open
Finding ground states of quantum many-body systems is known to be hard for both classical and quantum computers. As a result, when Nature cools a quantum system in a low-temperature thermal bath, the ground state cannot always be found eff…
View article: The Quantum Approximate Optimization Algorithm and the Sherrington-Kirkpatrick Model at Infinite Size
The Quantum Approximate Optimization Algorithm and the Sherrington-Kirkpatrick Model at Infinite Size Open
The Quantum Approximate Optimization Algorithm (QAOA) is a general-purpose algorithm for combinatorial optimization problems whose performance can only improve with the number of layers . While QAOA holds promise as an algorithm that can b…
View article: Quantum optimization of maximum independent set using Rydberg atom arrays
Quantum optimization of maximum independent set using Rydberg atom arrays Open
Realizing quantum speedup for practically relevant, computationally hard problems is a central challenge in quantum information science. Using Rydberg atom arrays with up to 289 qubits in two spatial dimensions, we experimentally investiga…
View article: Performance and limitations of the QAOA at constant levels on large sparse hypergraphs and spin glass models
Performance and limitations of the QAOA at constant levels on large sparse hypergraphs and spin glass models Open
The Quantum Approximate Optimization Algorithm (QAOA) is a general purpose quantum algorithm designed for combinatorial optimization. We analyze its expected performance and prove concentration properties at any constant level (number of l…
View article: Quantum Optimization of Maximum Independent Set using Rydberg Atom Arrays
Quantum Optimization of Maximum Independent Set using Rydberg Atom Arrays Open
Data and code for the publication Quantum Optimization of Maximum Independent Set using Rydberg Atom Arrays.
View article: The Quantum Approximate Optimization Algorithm at High Depth for MaxCut on Large-Girth Regular Graphs and the Sherrington-Kirkpatrick Model
The Quantum Approximate Optimization Algorithm at High Depth for MaxCut on Large-Girth Regular Graphs and the Sherrington-Kirkpatrick Model Open
The Quantum Approximate Optimization Algorithm (QAOA) finds approximate solutions to combinatorial optimization problems. Its performance monotonically improves with its depth $p$. We apply the QAOA to MaxCut on large-girth $D$-regular gra…
View article: Symmetry-protected dissipative preparation of matrix product states
Symmetry-protected dissipative preparation of matrix product states Open
We propose and analyze a method for efficient dissipative preparation of\nmatrix product states that exploits their symmetry properties. Specifically, we\nconstruct an explicit protocol that makes use of driven-dissipative dynamics to\npre…
View article: Strongly Universal Hamiltonian Simulators
Strongly Universal Hamiltonian Simulators Open
A universal family of Hamiltonians can be used to simulate any local Hamiltonian by encoding its full spectrum as the low-energy subspace of a Hamiltonian from the family. Many spin-lattice model Hamiltonians -- such as Heisenberg or XY in…
View article: Quantum Approximate Optimization Algorithm: Performance, Mechanism, and Implementation on Near-Term Devices
Quantum Approximate Optimization Algorithm: Performance, Mechanism, and Implementation on Near-Term Devices Open
The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid quantum-classical variational algorithm designed to tackle combinatorial optimization problems. Despite its promise for near-term quantum applications, not much is currently…
View article: Computational complexity of the Rydberg blockade in two dimensions
Computational complexity of the Rydberg blockade in two dimensions Open
We discuss the computational complexity of finding the ground state of the two-dimensional array of quantum bits that interact via strong van der Waals interactions. Specifically, we focus on systems where the interaction strength between …
View article: Quantum Optimization for Maximum Independent Set Using Rydberg Atom Arrays
Quantum Optimization for Maximum Independent Set Using Rydberg Atom Arrays Open
We describe and analyze an architecture for quantum optimization to solve maximum independent set (MIS) problems using neutral atom arrays trapped in optical tweezers. Optimizing independent sets is one of the paradigmatic, NP-hard problem…
View article: On Gap-Simulation of Hamiltonians and the Impossibility of Quantum Degree-Reduction
On Gap-Simulation of Hamiltonians and the Impossibility of Quantum Degree-Reduction Open
It is often the case in quantum Hamiltonian complexity (e.g. in the context of quantum simulations, adiabatic algorithms, perturbative gadgets and quantum NP theory) that one is mainly interested in the properties of the groundstate(s) of …
View article: Hamiltonian sparsification and gap-simulations
Hamiltonian sparsification and gap-simulations Open
Analog quantum simulations---simulations of one Hamiltonian by another---is one of the major goals in the noisy intermediate-scale quantum computation (NISQ) era, and has many applications in quantum complexity. We initiate the rigorous st…
View article: Error suppression in Hamiltonian-based quantum computation using energy penalties
Error suppression in Hamiltonian-based quantum computation using energy penalties Open
We consider the use of quantum error detecting codes, together with energy penalties against leaving the codespace, as a method for suppressing environmentally induced errors in Hamiltonian based quantum computation. This method was introd…