Fixed-angle conjectures for the quantum approximate optimization algorithm on regular MaxCut graphs

Wurtz, Jonathan; Lykov, Danylo

doi:10.1103/physreva.104.052419

Cited by 34 publications

(20 citation statements)

References 18 publications

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“…While the present work focuses on improving the quantum implementation part of the parity QAOA, there are additional opportunities to improve its performance via the classical part, for example different decoding strategies that result in smarter cost functions. More generally, further improvements of the parity QAOA might also involve exploiting recently investigated phenomena regarding QAOA parameters [35][36][37] and utilizing other types of mixing Hamiltonians [38]. The case where a physical qubit is involved in multiple driver lines has to be treated with care.…”

Section: Discussionmentioning

confidence: 99%

Modular Parity Quantum Approximate Optimization

Ender¹,

Messinger²,

Fellner³

et al. 2022

Preprint

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The parity transformation encodes spin models in the low-energy subspace of a larger Hilbertspace with constraints on a planar lattice. Applying the Quantum Approximate Optimization Algorithm (QAOA), the constraints can either be enforced explicitly, by energy penalties, or implicitly, by restricting the dynamics to the low-energy subspace via the driver Hamiltonian. While the explicit approach allows for parallelization with a system-size-independent circuit depth, the implicit approach shows better QAOA performance. Here we combine the two approaches in order to improve the QAOA performance while keeping the circuit parallelizable. In particular, we introduce a modular parallelization method that partitions the circuit into clusters of subcircuits with fixed maximal circuit depth, relevant for scaling up to large system sizes.

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Section: Discussionmentioning

confidence: 99%

Modular Parity Quantum Approximate Optimization

Ender¹,

Messinger²,

Fellner³

et al. 2022

Preprint

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show abstract

“…This is, indeed, a crucial task for QAOA and VQAs in general, where the classical optimization outerloop is often the main computational bottleneck and several strategies have been proposed that go beyond a local search from a random start. These strategies range from problem-specific methods to general iterative techniques, based on observed patterns in the optimal schedules [5,[65][66][67].…”

Section: B Heuristic Local Optimization: Two-step Qaoamentioning

confidence: 99%

Two-dimensional $\mathbb{Z}_2$ lattice gauge theory on a near-term quantum simulator: variational quantum optimization, confinement, and topological order

Lumia,

Torta,

Mbeng

et al. 2021

Preprint

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We propose an implementation of a two-dimensional Z2 lattice gauge theory model on a shallow quantum circuit, involving a number of single and two-qubits gates comparable to what can be achieved with present-day and near-future technologies. The ground state preparation is numerically analyzed on a small lattice with a variational quantum algorithm, which requires a small number of parameters to reach high fidelities and can be efficiently scaled up on larger systems. Despite the reduced size of the lattice we consider, a transition between confined and deconfined regimes can be detected by measuring expectation values of Wilson loop operators or the topological entropy. Moreover, if periodic boundary conditions are implemented, the same optimal solution is transferable among all four different topological sectors, without any need for further optimization on the variational parameters. Our work shows that variational quantum algorithms provide a useful technique to be added in the growing toolbox for digital simulations of lattice gauge theories.

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“…QAOA tunes a set of classical parameters to optimize the cost function expectation value for a quantum state prepared by well-defined sequence of operators acting on a known initial state. Variations to the original algorithm include alternative operators and initial states 23 – 30 while purely classical aspects such as the parameter optimization and problem structure have been tested as well 31 – 36 . However, an outstanding concern is that practical implementations of QAOA require large numbers of qubits and deep circuits 37 .…”

Section: Introductionmentioning

confidence: 99%

Multi-angle quantum approximate optimization algorithm

Herrman

Lotshaw

Ostrowski

et al. 2022

Sci Rep

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The quantum approximate optimization algorithm (QAOA) generates an approximate solution to combinatorial optimization problems using a variational ansatz circuit defined by parameterized layers of quantum evolution. In theory, the approximation improves with increasing ansatz depth but gate noise and circuit complexity undermine performance in practice. Here, we investigate a multi-angle ansatz for QAOA that reduces circuit depth and improves the approximation ratio by increasing the number of classical parameters. Even though the number of parameters increases, our results indicate that good parameters can be found in polynomial time for a test dataset we consider. This new ansatz gives a 33% increase in the approximation ratio for an infinite family of MaxCut instances over QAOA. The optimal performance is lower bounded by the conventional ansatz, and we present empirical results for graphs on eight vertices that one layer of the multi-angle anstaz is comparable to three layers of the traditional ansatz on MaxCut problems. Similarly, multi-angle QAOA yields a higher approximation ratio than QAOA at the same depth on a collection of MaxCut instances on fifty and one-hundred vertex graphs. Many of the optimized parameters are found to be zero, so their associated gates can be removed from the circuit, further decreasing the circuit depth. These results indicate that multi-angle QAOA requires shallower circuits to solve problems than QAOA, making it more viable for near-term intermediate-scale quantum devices.

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Fixed-angle conjectures for the quantum approximate optimization algorithm on regular MaxCut graphs

Cited by 34 publications

References 18 publications

Modular Parity Quantum Approximate Optimization

Modular Parity Quantum Approximate Optimization

Two-dimensional $\mathbb{Z}_2$ lattice gauge theory on a near-term quantum simulator: variational quantum optimization, confinement, and topological order

Multi-angle quantum approximate optimization algorithm

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