• Corpus ID: 249642678

An entanglement perspective on the quantum approximate optimization algorithm

@inproceedings{Dupont2022AnEP,
  title={An entanglement perspective on the quantum approximate optimization algorithm},
  author={Maxime Dupont and Nicolas Didier and Mark Hodson and Joel E. Moore and Matthew Reagor},
  year={2022}
}
Many quantum algorithms seek to output a specific bitstring solving the problem of interest—or a few if the solution is degenerate. It is the case for the quantum approximate optimization algorithm (QAOA) in the limit of large circuit depth, which aims to solve quadratic unconstrained binary optimization problems. Hence, the expected final state for these algorithms is either a product state or a low-entangled superposition involving a few bitstrings. What happens in between the initial N-qubit… 
View PDF on arXiv
1 Citations

Figures from this paper

One Citation

Bang-bang algorithms for quantum many-body ground states: a tensor network exploration
We use matrix product techniques to investigate the performance of two algorithms for obtaining the ground state of a quantum many-body Hamiltonian H = H A + H B in infinite systems. The first…

References

SHOWING 1-10 OF 105 REFERENCES
Performance of the Quantum Approximate Optimization Algorithm on the Maximum Cut Problem
TLDR
It is found that QAOA can amortize the training cost by optimizing on batches of problems instances, and can exceed the performance of the classical polynomial time Goemans-Williamson algorithm with modest circuit depth, and that performance with fixed circuit depth is insensitive to problem size.
Practical optimization for hybrid quantum-classical algorithms
A novel class of hybrid quantum-classical algorithms based on the variational approach have recently emerged from separate proposals addressing, for example, quantum chemistry and combinatorial…
Calibrating the classical hardness of the quantum approximate optimization algorithm
TLDR
The fidelity for the quantum approximate optimization algorithm is characterized by the expectation value of the cost function it seeks to minimize and it is found that it follows a scaling law F (ln χ/N ) with N the number of qubits.
Scaling of the quantum approximate optimization algorithm on superconducting qubit based hardware
TLDR
This work investigates swap strategies to map dense problems into linear, grid and heavy-hex coupling maps and finds that the required gate fidelity for dense problems lies deep below the fault-tolerant threshold.
Quantum approximate optimization of the long-range Ising model with a trapped-ion quantum simulator
TLDR
This work applies a variational quantum algorithm (QAOA) to approximate the ground-state energy of a long-range Ising model, both quantum and classical, and investigates the algorithm performance on a trapped-ion quantum simulator, observing that the QAOA performance does not degrade significantly as the authors scale up the system size and that the runtime is approximately independent from the number of qubits.
Quantum Supremacy through the Quantum Approximate Optimization Algorithm
TLDR
It is argued that beyond its possible computational value the QAOA can exhibit a form of Quantum Supremacy in that, based on reasonable complexity theoretic assumptions, the output distribution of even the lowest depth version cannot be efficiently simulated on any classical device.
Exploring entanglement and optimization within the Hamiltonian Variational Ansatz
TLDR
This paper focuses on a special family of quantum circuits called the Hamiltonian Variational Ansatz (HVA), which takes inspiration from the quantum approximation optimization algorithm and adiabatic quantum computation and exhibits favorable structural properties and numerically observes that the optimization landscape of HVA becomes almost trap free when the ansatz is over-parameterized.
Quantum Approximate Optimization With Parallelizable Gates
  • W. Lechner
  • Computer Science, Physics
    IEEE Transactions on Quantum Engineering
  • 2020
TLDR
A scheme to parallelize the quantum approximate optimization algorithm for arbitrary all-to-all connected problem graphs in a layout of quantum bits (qubits) with nearest-neighbor interactions in a lattice gauge model.
A Quantum Approximate Optimization Algorithm
TLDR
A quantum algorithm that produces approximate solutions for combinatorial optimization problems that depends on a positive integer p and the quality of the approximation improves as p is increased, and is studied as applied to MaxCut on regular graphs.
From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
TLDR
The essence of this extension, the quantum alternating operator ansatz, is the consideration of general parameterized families of unitaries rather than only those corresponding to the time evolution under a fixed local Hamiltonian for a time specified by the parameter.
...
...