Variational Quantum Factoring

Anschuetz, Eric R.; Olson, Jonathan P.; Aspuru‐Guzik, Alán; Cao, Yudong

doi:10.48550/arxiv.1808.08927

Cited by 26 publications

(29 citation statements)

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“…The number of qubits needed depends on the number of bits in the clauses. As discussed in [9], some number of classical preprocessing heuristics can be used to simplify the clauses (that is, assign values to some of the bits {p i } and {q i }). As classical preprocessing removes variables from the optimization problem (by explicitly assigning bit values), the number of qubits needed to complete the solution to the problem is reduced.…”

Section: Variational Quantum Factoringmentioning

confidence: 99%

“…In order to optimize the QAOA circuit to find γ opt and β opt we employ a layer-by-layer approach [19]. Although there are alternative strategies for training QAOA circuits [20,21], this approach has been shown to require a grid resolution that scales polynomially with respect to the number of qubits required [9]. This approach has two phases.…”

Section: Experimental Analysismentioning

confidence: 99%

“…1. In this work, we implement the variational quantum factoring (VQF) algorithm [9] on a superconducting quantum processor. VQF is an algorithm for tackling an NP problem with a tunable trade off between classical and quantum computing resources, and is feasible for near-term devices.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Analyzing the Performance of Variational Quantum Factoring on a Superconducting Quantum Processor

Karamlou,

Simon,

Katabarwa

et al. 2020

Preprint

Self Cite

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Quantum computers hold promise as accelerators onto which some classically-intractable problems may be offloaded, necessitating hybrid quantum-classical workflows. Understanding how these two computing paradigms can work in tandem is critical for identifying where such workflows could provide an advantage over strictly classical ones. In this work, we study such workflows in the context of quantum optimization, using an implementation of the Variational Quantum Factoring (VQF) algorithm as a prototypical example of QAOA-based quantum optimization algorithms. We execute experimental demonstrations using a superconducting quantum processor, and investigate the trade off between quantum resources (number of qubits and circuit depth) and the probability that a given integer is successfully factored. In our experiments, the integers 1,099,551,473,989 and 6,557 are factored with 3 and 5 qubits, respectively, using a QAOA ansatz with up to 8 layers. Our results empirically demonstrate the impact of different noise sources, and reveal a residual ZZcoupling between qubits as a dominant source of error. Additionally, we are able to identify the optimal number of circuit layers for a given instance to maximize success probability.

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Section: Variational Quantum Factoringmentioning

confidence: 99%

Section: Experimental Analysismentioning

confidence: 99%

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Analyzing the Performance of Variational Quantum Factoring on a Superconducting Quantum Processor

Karamlou,

Simon,

Katabarwa

et al. 2020

Preprint

Self Cite

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“…VQA is advantageous given the fact that preparing a tunable circuit ansatz is found to be difficult on a classical computer. It has already been widely applied in quantum chemistry [3][4][5][6][7][8], condensed matter physics [9][10][11][12], solving linear system of equations [13], combinatorial optimization problems [14,15], and several others [16,17]. Remarkably, one of the early implementations of the VQA was performed using photonic quantum processors [18], which prompted further theoretical progress [19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Digitized-counterdiabatic quantum approximate optimization algorithm

Chandarana,

Hegade,

Paul

et al. 2021

Preprint

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The quantum approximate optimization algorithm (QAOA) has proved to be an effective classical-quantum algorithm serving multiple purposes, from solving combinatorial optimization problems to finding the ground state of many-body quantum systems. Since QAOA is an ansatz-dependent algorithm, there is always a need to design ansatz for better optimization. To this end, we propose a digitized version of QAOA enhanced via the use of shortcuts to adiabaticity. Specifically, we use a counterdiabatic (CD) driving term to design a better ansatz, along with the Hamiltonian and mixing terms, enhancing the global performance. We apply our digitizedcounterdiabatic QAOA to Ising models, classical optimization problems, and the P-spin model, demonstrating that it outperforms standard QAOA in all cases we study.

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“…QAOA can be used to solve combinatorial optimization problems such as MaxCut [10], Max E3LIN2 [11] and generative machine learning tasks such as sampling from Gibbs states [12]. Interestingly there also exist QAOA versions of Shor's number factoring algorithm [13], and Grover's problem of searching an unstructured database [14] that substantially reduce the number of gates with respect to their counterparts for fully error-corrected quantum computers. Moreover it has been shown that there is no efficient classical algorithm that can simulate sampling from the output of a QAOA circuit [15].…”

Section: Introduction -mentioning

confidence: 99%

Comparison of QAOA with Quantum and Simulated Annealing

Streif,

Leib

2019

Preprint

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We present a comparison between the Quantum Approximate Optimization Algorithm (QAOA) and two widely studied competing methods, Quantum Annealing (QA) and Simulated Annealing (SA). To achieve this, we define a class of optimization problems with respect to their spectral properties which are exactly solvable with QAOA. In this class, we identify instances for which QA and SA have an exponentially small probability to find the solution. Consequently, our results define a first demarcation line between QAOA, Simulated Annealing and Quantum Annealing, and highlight the fundamental differences between an interference-based search heuristic such as QAOA and heuristics that are based on thermal and quantum fluctuations like SA and QA respectively.

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Variational Quantum Factoring

Cited by 26 publications

References 0 publications

Analyzing the Performance of Variational Quantum Factoring on a Superconducting Quantum Processor

Analyzing the Performance of Variational Quantum Factoring on a Superconducting Quantum Processor

Digitized-counterdiabatic quantum approximate optimization algorithm

Comparison of QAOA with Quantum and Simulated Annealing

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