CoChat
Sign Up
Cited by 123Quantum Computing Algorithms and ArchitectureMetaheuristic Optimization Algorithms ResearchQuantum many-body systems

Grover Mixers for QAOA: Shifting Complexity from Mixer Design to State Preparation

Open access
Bartschi, Andreas, Eidenbenz, Stephan·2020·2020 IEEE International Conference on Quantum Computing and Engineering (QCE)
DOI 10.1109/qce49297.2020.00020
Open this paper in CoChat — free accountOpen PDF

Abstract

We propose GM-QAOA, a variation of the Quantum Alternating Operator Ansatz (QAOA) that uses Grover-like selective phase shift mixing operators. GM-QAOA works on any NP optimization problem for which it is possible to efficiently prepare an equal superposition of all feasible solutions; it is designed to perform particularly well for constraint optimization problems, where not all possible variable assignments are feasible solutions. GM-QAOA has the following features: (i) It is not susceptible to Hamiltonian Simulation error (such as Trotterization errors) as its operators can be implemented exactly using standard gate sets and (ii) Solutions with the same objective value are always sampled with the same amplitude. We illustrate the potential of GM-QAOA on several optimization problem classes: for permutation-based optimization problems such as the Traveling Salesperson Problem, we present an efficient algorithm to prepare a superposition of all possible permutations of$n$numbers, defined on O (n2) qubits; for the hard constraint k-Vertex-Cover problem, and for an application to Discrete Portfolio Rebalancing, we show that GM-QAOA outperforms existing QAOA approaches.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1109/qce49297.2020.00020

Cites

21 of 21 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Ansatz adaptations can occur as a byproduct, as in the Quantum Alternating Operator Ansatz where the primary goal is to find a mixing Hamiltonian that ensures staying in the feasible subspace.

    “Besides the mentioned ansatz search, as the driving force behind ansatz adaptation, there is also the possibility of having these adaptations as a byproduct, like it happens, e.g., within the Quantum Alternating Operator Ansatz where the primary goal is to find a mixing Hamiltonian that ensures to stay in the feasible subspace [11, 58, 95, 112, 116, 117, 120, 127].”

    From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [11]

  • Another possibility is to shift the complexity to the generation of the initial state, utilizing the state preparation circuit for the design of the mixing Hamiltonian.

    “Another possibility is to shift the complexity to the generation of the initial state [11], where the idea is to further utilize the state preparation circuit, which creates an equal superposition of all feasible states, for the design of the mixing Hamiltonian.”

    From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [11]

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Cites

Flagged first, then by citations

Research works printed but not linked: 7

  1. [3][3] E. Farhi, J. Goldstone, and S. Gutmann, 'A Quantum Approximate Optimization Algorithm,' arXiv e-prints , 2014, arXiv:1411.4028. - · arXiv
  2. [5][5] J. Cook, S. Eidenbenz, and A. Bärtschi, 'The Quantum Alternating Operator Ansatz on Max-k Vertex Cover,' in IEEE International Conference on Quantum Computing & Engineering, QCE'20 , 2020, arXiv:1910.13483. - · arXiv
  3. [6][6] E. Farhi, J. Goldstone, and S. Gutmann, 'A Quantum Approximate Optimization Algorithm Applied to a Bounded Occurrence Constraint Problem,' arXiv e-prints , 2014, arXiv:1412.6062. - · arXiv
  4. [15][15] G. Brassard, P. Hoyer, M. Mosca, and A. Tapp, 'Quantum Amplitude Amplification and Estimation,' arXiv e-prints , 2000, arXiv:quant-ph/0005055. - · arXiv
  5. [18][18] B. Sundar, R. Paredes, D. T. Damanik, L. Dueñas-Osorio, and K. R. A. Hazzard, 'A quantum algorithm to count weighted ground states of classical spin Hamiltonians,' 2019, arXiv:1908.01745. - · arXiv
  6. [20][20] B. O'Gorman, W. J. Huggins, E. G. Rieffel, and K. B. Whaley, 'Generalized swap networks for near-term quantum computing,' arXiv e-prints , 2019, arXiv:1905.05118. - · arXiv
  7. [30][30] M. Hodson, B. Ruck, H. Ong, D. Garvin, and S. Dulman, 'Portfolio rebalancing experiments using the Quantum Alternating Operator Ansatz,' arXiv e-prints , 2019, arXiv:1911.05296. · arXiv

Cited by

Sorted by citations

Related

Authors
Bartschi, A., & Eidenbenz, S.
Affiliations
Los Alamos National Laboratory (US)
ORCID
Eidenbenz, Stephan
Venue
2020 IEEE International Conference on Quantum Computing and Engineering (QCE)
Publisher
IEEE
Published
2020-10
Pages
72-82
DOI
10.1109/qce49297.2020.00020
OpenAlex
W3029819693
Cited by
122
References
21
Citations by year
2026: 11 · 2025: 27 · 2024: 25 · 2023: 29 · 2022: 17 · 2021: 10 · 2020: 3
FWCI
5.55
Type
conference paper
Language
en
Open access
Licence
Locations
  • IEEE International Conference on Quantum Computing and Engineering (QCE) (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Computer Science › Artificial Intelligence › Metaheuristic Optimization Algorithms Research
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
Keywords
Quantum Alternating Operator Ansatz, mixer design, quantum state preparation, constraint optimization, traveling salesman problem

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review