Sam Gutmann
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View article: Strategies for running the QAOA at hundreds of qubits
Strategies for running the QAOA at hundreds of qubits Open
We explore strategies aimed at reducing the amount of computation, both quantum and classical, required to run the Quantum Approximate Optimization Algorithm (QAOA). First, following Wurtz et al. [Phys.Rev A 104:052419], we consider the st…
View article: Conditional probability of derangements and fixed points
Conditional probability of derangements and fixed points Open
The probability that a random permutation in $S_n$ is a derangement is well known to be $\displaystyle\sum\limits_{j=0}^n (-1)^j \frac{1}{j!}$. In this paper, we consider the conditional probability that the $(k+1)^{st}$ point is fixed, gi…
View article: The QAOA gets stuck starting from a good classical string
The QAOA gets stuck starting from a good classical string Open
The Quantum Approximate Optimization Algorithm (QAOA) is designed to maximize a cost function over bit strings. While the initial state is traditionally a uniform superposition over all strings, it is natural to try expediting the QAOA: fi…
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: Conditional Probability of Derangements and Fixed Points
Conditional Probability of Derangements and Fixed Points Open
The probability that a random permutation in $S_n$ is a derangement is well known to be $\displaystyle\sum\limits_{j=0}^n (-1)^j \frac{1}{j!}$. In this paper, we consider the conditional probability that the $(k+1)^{st}$ point is fixed, gi…
View article: The Quantum Approximate Optimization Algorithm Needs to See the Whole Graph: Worst Case Examples
The Quantum Approximate Optimization Algorithm Needs to See the Whole Graph: Worst Case Examples Open
The Quantum Approximate Optimization Algorithm can be applied to search problems on graphs with a cost function that is a sum of terms corresponding to the edges. When conjugating an edge term, the QAOA unitary at depth p produces an opera…
View article: The Quantum Approximate Optimization Algorithm Needs to See the Whole Graph: A Typical Case
The Quantum Approximate Optimization Algorithm Needs to See the Whole Graph: A Typical Case Open
The Quantum Approximate Optimization Algorithm can naturally be applied to combinatorial search problems on graphs. The quantum circuit has p applications of a unitary operator that respects the locality of the graph. On a graph with bound…
View article: For Fixed Control Parameters the Quantum Approximate Optimization Algorithm's Objective Function Value Concentrates for Typical Instances
For Fixed Control Parameters the Quantum Approximate Optimization Algorithm's Objective Function Value Concentrates for Typical Instances Open
The Quantum Approximate Optimization Algorithm, QAOA, uses a shallow depth quantum circuit to produce a parameter dependent state. For a given combinatorial optimization problem instance, the quantum expectation of the associated cost func…
View article: For Fixed Control Parameters the Quantum Approximate Optimization\n Algorithm's Objective Function Value Concentrates for Typical Instances
For Fixed Control Parameters the Quantum Approximate Optimization\n Algorithm's Objective Function Value Concentrates for Typical Instances Open
The Quantum Approximate Optimization Algorithm, QAOA, uses a shallow depth\nquantum circuit to produce a parameter dependent state. For a given\ncombinatorial optimization problem instance, the quantum expectation of the\nassociated cost f…
View article: Quantum Algorithms for Fixed Qubit Architectures
Quantum Algorithms for Fixed Qubit Architectures Open
Gate model quantum computers with too many qubits to be simulated by available classical computers are about to arrive. We present a strategy for programming these devices without error correction or compilation. This means that the number…