Benchmarking the performance of portfolio optimization with QAOA

Brandhofer, Sebastian; Braun, Daniel; Dehn, Vanessa; Hellstern, Gerhard; Hüls, Matthias; Ji, Yanjun; Polian, Ilia; Bhatia, Amandeep Singh; Wellens, Thomas

doi:10.1007/s11128-022-03766-5

Cited by 32 publications

(21 citation statements)

References 30 publications

(65 reference statements)

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“…The five-asset PortOpt instance that runs on five qubits (5Q) is taken from [43], and its first three and four assets are used for the three-(3Q) and four-qubit (4Q) instances, respectively. The values of the variables q, B, A, and λ vary across the three cases considered.…”

Section: Resultsmentioning

confidence: 99%

“…PortOpt aims to select the best portfolio from all portfolios in order to maximize expected returns and minimize financial risk. The QAOA holds promise for solving this problem [42][43][44][45].…”

Section: Qaoa For Portoptmentioning

confidence: 99%

“…Given n available assets and B assets to be selected, the cost function C can be represented in terms of quantum operators [43]:…”

Section: Qaoa For Portoptmentioning

confidence: 99%

See 2 more Smart Citations

Optimizing QAOA on Bipotent Architectures

Ji¹,

Koenig²,

Polian³

2023

Preprint

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Vigorous optimization of quantum gates has led to bipotent quantum architectures, where the optimized gates are available for some qubits but not for others. However, such gate-level improvements limit the application of user-side pulse-level optimizations, which have proven effective for quantum circuits with a high level of regularity, such as the ansatz circuit of the Quantum Approximate Optimization Algorithm (QAOA). In this paper, we investigate the trade-off between hardware-level and algorithm-level improvements on bipotent quantum architectures. Our results for various QAOA instances on two quantum computers offered by IBM indicate that the benefits of pulse-level optimizations currently outweigh the improvements due to vigorously optimized monolithic gates. Furthermore, our data indicate that the fidelity of circuit primitives is not always the best indicator for the overall algorithm performance; also their gate type and schedule duration should be taken into account. This effect is particularly pronounced for QAOA on dense portfolio optimization problems, since their transpilation requires many SWAP gates, for which efficient pulse-level optimization exists. Our findings provide practical guidance on optimal qubit selection on bipotent quantum architectures and suggest the need for improvements of those architectures, ultimately making pulse-level optimization available for all gate types.

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Section: Resultsmentioning

confidence: 99%

Section: Qaoa For Portoptmentioning

confidence: 99%

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Optimizing QAOA on Bipotent Architectures

Ji¹,

Koenig²,

Polian³

2023

Preprint

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“…Our work opens up new avenues for further research into improving quantum optimisation algorithms as well as their impact on various applications. For example, QAOA and its variants have already found numerous potential uses in solving various optimisation problems beyond MaxCut, including problems in graph theory [109][110][111], finance [112], chemistry [113,114], and others [15,115]. Future work could extend these results by adopting and exploiting the advantages of XQAOA in various applications.…”

Section: Discussionmentioning

confidence: 99%

An Expressive Ansatz for Low-Depth Quantum Optimisation

Vijendran¹,

Das²,

Koh³

et al. 2023

Preprint

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The Quantum Approximate Optimisation Algorithm (QAOA) is a hybrid quantum-classical algorithm used to approximately solve combinatorial optimisation problems. It involves multiple iterations of a parameterised ansatz that consists of a problem and mixer Hamiltonian, with the parameters being classically optimised. While QAOA can be implemented on near-term quantum hardware, physical limitations such as gate noise, restricted qubit connectivity, and statepreparation-and-measurement (SPAM) errors can limit circuit depth and decrease performance. To address these limitations, this work introduces the eXpressive QAOA (XQAOA), a modified version of QAOA that assigns more classical parameters to the ansatz to improve the performance of low-depth quantum circuits. XQAOA includes an additional Pauli-Y component in the mixer Hamiltonian, thereby allowing the mixer to effectively implement arbitrary unitary transformations on each qubit. To benchmark the performance of the XQAOA ansatz at low depth, we derive its closed-form expression for the MaxCut problem and compare it to QAOA, MA-QAOA [Sci Rep 12, 6781 (2022)], a Classical-Relaxed algorithm, and the state-of-the-art Goemans-Williamson algorithm on a set of unweighted regular graphs with 128 and 256 nodes and degrees ranging from 3 to 10. Our results show that XQAOA performs better than QAOA, MA-QAOA, and the Classical-Relaxed algorithm on all graph instances and outperforms the Goemans-Williamson algorithm on unweighted regular graphs with degrees greater than 4. Additionally, we find an infinite family of graphs for which XQAOA solves MaxCut exactly and show analytically that for some graphs in this family, special cases of XQAOA are capable of achieving a much larger approximation ratio than QAOA. Overall, XQAOA is a more viable choice for implementing quantum combinatorial optimisation on near-term quantum devices, as it can achieve better results with a single iteration, despite requiring additional classical resources.

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“…We apply AlgAw to the QAOA on dense portfolio optimization problems [23] where the qubits are required to have the maximum connectivity. An exact approach [9] is used to search solutions for qubit mapping of a subcircuit containing all two-qubit gates in a small-scale QAOA circuit on linear and T-shaped subtopologies.…”

Section: Introductionmentioning

confidence: 99%

Algorithm-Aware Qubit Mapping

Ji¹,

Polian²

2023

Preprint

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<p>Algorithm-Aware (AlgAw) qubit mapping aims at directly providing the solutions to qubit mapping of algorithms with regular structures based on the algorithm's features. Although the exact method provides a high-quality solution, its compilation time grows exponentially with the circuit size. To improve its scalability, we propose the AlgAw qubit mapping. The main idea is to first determine the subcircuits in an algorithm to be mapped, then analyze the optimal solutions of small-scale subcircuits found by exact methods to obtain solutions of large-scale subcircuits, and finally reconstruct the entire circuit and assign parameters. Applying AlgAw to the Quantum Approximate Optimization Algorithm (QAOA) on linear and T-shaped subtopologies produces optimal and scalable solutions for arbitrary numbers of qubits and depths, which is critical to the algorithm's performance on Noisy Intermediate-Scale Quantum (NISQ) computers. Compared to Qiskit, Tket, and SWAP-Network, AlgAw produces the least number of CNOT gates and the lowest circuit depth. Furthermore, AlgAw takes only a few seconds to obtain a circuit with a hundred qubits that satisfies the connectivity constraints. The benchmarking results on Quantum Processing Units (QPUs) show that AlgAw qubit mapping yields higher values of approximation ratio than others. AlgAw can also be applied to other algorithms such as the Variational Quantum Eigensolver (VQE).</p>

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Benchmarking the performance of portfolio optimization with QAOA

Cited by 32 publications

References 30 publications

Optimizing QAOA on Bipotent Architectures

Optimizing QAOA on Bipotent Architectures

An Expressive Ansatz for Low-Depth Quantum Optimisation

Algorithm-Aware Qubit Mapping

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