Warm-starting quantum optimization

Egger, Daniel J.; Marecek, Jakub; Woerner, Stefan

doi:10.48550/arxiv.2009.10095

Cited by 13 publications

(15 citation statements)

References 76 publications

(138 reference statements)

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“…[62]. By experimentally comparing different optimization methods we observed that for local methods, a gradient-free Nelder-Mead [63] is the best choice for our purposes: its performance is comparable to the one of the quasi-Newton BFGS [64] (and both methods outperform the COBYLA routine [65] which is often used in works on applied QAOA [58]) while it requires less evaluations of the objective function (see Fig. 11).…”

Section: C2 Local Vs Global Methodsmentioning

confidence: 98%

“…An experimental protocol for QAOA should specify the method to use in the parameter optimization step as well as its additional parameters. Local optimization routines are often used in works on applied QAOA [58][59][60], however the reasons why a certain method is chosen for a particular application are usually omitted. For (SC1) we compared different methods in terms of their performances (evaluated by the approximation ratio of the QAOA with returned parameters) and costs (measured in number of calls of the function to optimize, i.e.…”

Section: C2 Local Vs Global Methodsmentioning

confidence: 99%

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Qualifying quantum approaches for hard industrial optimization problems. A case study in the field of smart-charging of electric vehicles

Dalyac,

Henriet,

Jeandel

et al. 2020

Preprint

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In order to qualify quantum algorithms for industrial NP-Hard problems, comparing them to available polynomial approximate classical algorithms and not only to exact ones -exponential by nature -, is necessary. This is a great challenge as, in many cases, bounds on the reachable approximation ratios exist according to some highly-trusted conjectures of Complexity Theory. An interesting setup for such qualification is thus to focus on particular instances of these problems known to be "less difficult" than the worst-case ones and for which the above bounds can be outperformed: quantum algorithms should perform at least as well as the conventional approximate ones on these instances, up to very large sizes. We present a case study of such a protocol for two industrial problems drawn from the strongly developing field of smart-charging of electric vehicles. Tailored implementations of the Quantum Approximate Optimization Algorithm (QAOA) have been developed for both problems, and tested numerically with classical resources either by emulation of Pasqal's Rydberg atom based quantum device or using Atos Quantum Learning Machine. In both cases, quantum algorithms exhibit the same approximation ratios than conventional approximation algorithms, or improve them. These are very encouraging results, although still for instances of limited size as allowed by studies on classical computing resources. The next step will be to confirm them on larger instances, on actual devices, and for more complex versions of the problems addressed.

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Section: C2 Local Vs Global Methodsmentioning

confidence: 98%

Section: C2 Local Vs Global Methodsmentioning

confidence: 99%

Qualifying quantum approaches for hard industrial optimization problems. A case study in the field of smart-charging of electric vehicles

Dalyac,

Henriet,

Jeandel

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…Further variations of RQAOA have been proposed and studied in [5,20]. There, the authors consider "warm-starting" the algorithm by beginning with a solution returned by an efficient classical algorithm (for the case of MAX-CUT, the Goemans-Williamson algorithm) instead of the standard product state.…”

Section: Adapting Rqaoa To Max-k-cutmentioning

confidence: 99%

Hybrid quantum-classical algorithms for approximate graph coloring

Bravyi,

Kliesch,

Koenig

et al. 2020

Preprint

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We show how to apply the recursive quantum approximate optimization algorithm (RQAOA) to MAX-k-CUT, the problem of finding an approximate k-vertex coloring of a graph. We compare this proposal to the best known classical and hybrid classical-quantum algorithms. First, we show that the standard (non-recursive) QAOA fails to solve this optimization problem for most regular bipartite graphs at any constant level p: the approximation ratio achieved by QAOA is hardly better than assigning colors to vertices at random. Second, we construct an efficient classical simulation algorithm which simulates level-1 QAOA and level-1 RQAOA for arbitrary graphs. In particular, these hybrid algorithms give rise to efficient classical algorithms, and no benefit arising from the use of quantum mechanics is to be expected. Nevertheless, they provide a suitable testbed for assessing the potential benefit of hybrid algorithm: We use the simulation algorithm to perform large-scale simulation of level-1 QAOA and RQAOA with up to 300 qutrits applied to ensembles of randomly generated 3-colorable constant-degree graphs. We find that level-1 RQAOA is surprisingly competitive: for the ensembles considered, its approximation ratios are often higher than those achieved by the best known generic classical algorithm based on rounding an SDP relaxation. This suggests the intriguing possibility that higher-level RQAOA may be a potentially useful algorithm for NISQ devices.

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“…Quantum computers have the potential to impact a broad range of disciplines such as quantum chemistry [1], finance [2,3], optimization [4,5], and machine learning [6,7]. The performance of noisy quantum computers has been improving as measured by metrics such as the Quantum Volume [8,9] or the coherence of superconducting transmon-based devices [10][11][12] which has exceeded 100 µs [13,14].…”

Section: Introductionmentioning

confidence: 99%

Pulse-efficient circuit transpilation for quantum applications on cross-resonance-based hardware

Earnest,

Tornow,

Egger

2021

Preprint

Self Cite

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We show a pulse-efficient circuit transpilation framework for noisy quantum hardware. This is achieved by scaling cross-resonance pulses and exposing each pulse as a gate to remove redundant single-qubit operations with the transpiler. Crucially, no additional calibration is needed to yield better results than a CNOT-based transpilation. This pulse-efficient circuit transpilation therefore enables a better usage of the finite coherence time without requiring knowledge of pulse-level details from the user. As demonstration, we realize a continuous family of cross-resonance-based gates for SU (4) by leveraging Cartan's decomposition. We measure the benefits of a pulse-efficient circuit transpilation with process tomography and observe up to a 50% error reduction in the fidelity of RZZ (θ) and arbitrary SU (4) gates on IBM Quantum devices. We apply this framework for quantum applications by running circuits of the Quantum Approximate Optimization Algorithm applied to MAXCUT. For an 11 qubit non-hardware native graph, our methodology reduces the overall schedule duration by up to 52% and errors by up to 38%. II. SCALING HARDWARE-NATIVE CROSS-RESONANCE GATESWe consider an all-microwave fixed-frequency transmon architecture that implements the echoed crossresonance gate [32]. A two-qubit system in which a control qubit is driven at the frequency of a target qubit

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Warm-starting quantum optimization

Cited by 13 publications

References 76 publications

Qualifying quantum approaches for hard industrial optimization problems. A case study in the field of smart-charging of electric vehicles

Qualifying quantum approaches for hard industrial optimization problems. A case study in the field of smart-charging of electric vehicles

Hybrid quantum-classical algorithms for approximate graph coloring

Pulse-efficient circuit transpilation for quantum applications on cross-resonance-based hardware

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