Quantum Optimization for Maximum Independent Set Using Rydberg Atom Arrays

Pichler, Hannes; Wang, Shengtao; Zhou, Leo; Choi, Soonwon; Lukin, Mikhail D.

doi:10.48550/arxiv.1808.10816

Cited by 51 publications

(80 citation statements)

References 38 publications

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“…Moreover, Rydberg simulators allow for detailed studies of dynamics across quantum phase transitions (QPTs) and other quantum critical phenomena. Finally, they provide a natural many-body platform for exploring quantum advantage in solving combinatorial optimization problems [19,20]. These advances motivate detailed quantitative understanding of the QPTs between complex phases in such systems, with realistic interactions and geometries.…”

Section: Introductionmentioning

confidence: 99%

“…Crucially, the nature of these phase transitions dictates the efficacy of experimentally preparing the corresponding states via quasi-adiabatic dynamics in large systems. Therefore, in order to utilize Rydberg atom arrays to probe different phases of matter or prepare the ground states of Hamiltonians encoding combinatorial optimization problems [19], it is essential to establish a quantitative understanding of the quantum critical points.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Bulk and Boundary Quantum Phase Transitions in a Square Rydberg Atom Array

Kalinowski,

Samajdar,

Melko

et al. 2021

Preprint

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Motivated by recent experimental realizations of exotic phases of matter on programmable quantum simulators, we carry out a comprehensive theoretical study of quantum phase transitions in a Rydberg atom array on a square lattice, with both open and periodic boundary conditions. In the bulk, we identify several first-order and continuous phase transitions by performing large-scale quantum Monte Carlo simulations and develop an analytical understanding of the nature of these transitions using the framework of Landau-Ginzburg-Wilson theory. Remarkably, we find that under open boundary conditions, the boundary itself undergoes a second-order quantum phase transition, independent of the bulk. These results explain recent experimental observations and provide important new insights into both the adiabatic state preparation of novel quantum phases and quantum optimization using Rydberg atom array platforms.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bulk and Boundary Quantum Phase Transitions in a Square Rydberg Atom Array

Kalinowski,

Samajdar,

Melko

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In addition, there are methods to overcome the measurement count limitations. One approach is to significantly increase hardware connectivity or modify the gate set, for example, using ion-trap quantum computers with globally-entangling Mølmer-Sørensen gates [60] or Rydberg atoms that naturally enforce constraints in some instances of QAOA [61]. Another approach is to modify the QAOA ansatz.…”

Section: Discussionmentioning

confidence: 99%

Scaling Quantum Approximate Optimization on Near-term Hardware

Lotshaw,

Nguyen,

Santana

et al. 2022

Preprint

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The quantum approximate optimization algorithm (QAOA) is an approach for near-term quantum computers to potentially demonstrate computational advantage in solving combinatorial optimization problems. However, the viability of the QAOA depends on how its performance and resource requirements scale with problem size and complexity for realistic hardware implementations. Here, we quantify scaling of the expected resource requirements by synthesizing optimized circuits for hardware architectures with varying levels of connectivity. Assuming noisy gate operations, we estimate the number of measurements needed to sample the output of the idealized QAOA circuit with high probability. We show the number of measurements, and hence total time to solution, grows exponentially in problem size and problem graph degree as well as depth of the QAOA ansatz, gate infidelities, and inverse hardware graph degree. These problems may be alleviated by increasing hardware connectivity or by recently proposed modifications to the QAOA that achieve higher performance with fewer circuit layers.

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“…Among several quantum algorithms implemented on noisy intermediate-scale quantum (NISQ) devices [1][2][3][4][5][6][7][8][9][10][11][12], the quantum approximate optimization algorithm (QAOA) offers an opportunity to approximately solve combinatorial optimization problems such as MaxCut, Max Independent Set, and Max k-cover [13][14][15][16][17][18][19][20][21][22]. 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.…”

Section: Introductionmentioning

confidence: 99%

Multi-angle Quantum Approximate Optimization Algorithm

Herrman¹,

Lotshaw²,

Ostrowski³

et al. 2021

Preprint

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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 introduce 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. 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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Quantum Optimization for Maximum Independent Set Using Rydberg Atom Arrays

Cited by 51 publications

References 38 publications

Bulk and Boundary Quantum Phase Transitions in a Square Rydberg Atom Array

Bulk and Boundary Quantum Phase Transitions in a Square Rydberg Atom Array

Scaling Quantum Approximate Optimization on Near-term Hardware

Multi-angle Quantum Approximate Optimization Algorithm

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