Sublinear Classical and Quantum Algorithms for General Matrix Games

Li, Tongyang; Wang, Chunhao; Chakrabarti, Shouvanik; Wu, Xiaodi

doi:10.1609/aaai.v35i10.17028

Cited by 8 publications

(9 citation statements)

References 27 publications

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“…Substituting inequality (15) into inequality (13) and summing inequality (13) from t = 1 to T, we have…”

Section: Can Achieve the Regret Bound O(g 2 Log T) With Probability G...mentioning

confidence: 99%

“…On the one hand, combinatorial optimization was shown to be acceleratable by using quantum techniques such as Grover's algorithm or quantum walks [4,[7][8][9][10][11][12][13]. On the other hand, in the last few years, some significant quantum improvements were achieved for convex optimization in linear programming [14][15][16], second-order cone programming [17][18][19], quadratic programming [20], polynomial optimization [21], and semi-definite optimization [14,[22][23][24][25]. Note that they are all special cases of convex optimization.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quantum algorithm for online convex optimization

He¹,

Yang²,

Zhang³

et al. 2022

Quantum Sci. Technol.

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We explore whether quantum advantages can be found for the zeroth-order online convex optimization problem, which is also known as bandit convex optimization with multi-point feedback. In this setting, given access to zeroth-order oracles (that is, the loss function is accessed as a black box that returns the function value for any queried input), a player attempts to minimize a sequence of adversarially generated convex loss functions. This procedure can be described as a $T$ round iterative game between the player and the adversary. In this paper, we present quantum algorithms for the problem and show for the first time that potential quantum advantages are possible for problems of online convex optimization. Specifically, our contributions are as follows. (i) When the player is allowed to query zeroth-order oracles $O(1)$ times in each round as feedback, we give a quantum algorithm that achieves $O(\sqrt{T})$ regret without additional dependence of the dimension $n$, which outperforms the already known optimal classical algorithm only achieving $O(\sqrt{nT})$ regret. Note that the regret of our quantum algorithm has achieved the lower bound of classical first-order methods. (ii) We show that for strongly convex loss functions, the quantum algorithm can achieve $O(\log T)$ regret with $O(1)$ queries as well, which means that the quantum algorithm can achieve the same regret bound as the classical algorithms in the full information setting.

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“…Substituting inequality (15) into inequality (13) and summing inequality (13) from t = 1 to T, we have…”

Section: Can Achieve the Regret Bound O(g 2 Log T) With Probability G...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum algorithm for online convex optimization

He¹,

Yang²,

Zhang³

et al. 2022

Quantum Sci. Technol.

View full text Add to dashboard Cite

show abstract

“…Finally, we will get the desired result (10) by applying the inverse of the oracle to cancel the query of a ij in the above state. The above simple idea has been used in [44,45].…”

Section: Block Encodingmentioning

confidence: 99%

“…In a classical computer, calculating each s j costs O(N) operations. In equation (44), there are d terms, thus the total cost of the classical method to accomplish naïve Bayes's classifier is O(Nd). However, the following result shows that quantum computer can do exponentially better.…”

Section: Quantum Speedup Of Naïve Bayes' Classifiermentioning

confidence: 99%

Quantum speedup of Bayes’ classifiers

Shao¹

2020

J. Phys. A: Math. Theor.

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Data classification is a fundamental problem in machine learning. We study quantum speedup of the supervised data classification algorithms (quadratic, linear and naïve Bayes classifiers) based on Bayes' theory. The main technique we use to achieve quantum speedup is block-encoding. However, to apply this technique effectively, we propose a general method to construct the block-encoding. As an application, we show that all the three classifiers achieve exponential speedup at the number of samples over their classical counterparts. As for the dimension of the space, quantum quadratic and linear classifiers achieve varying degrees of polynomial speedup, while quantum naïve Bayes' classifier achieves an exponential speedup. The only assumption we make is the qRAM to prepare quantum states of the input data.

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“…Specific areas within classical learning, such as Deep Learning and Support Vector Machines, could potentially benefit from quantum computing [7], [8]. Quantum speed-ups have been achieved for several algorithms, including expectation maximization solving [9] (where the algorithm's speed has been increased to sublinear time [10]), Support Vector Machines [11], and natural language processing [12].…”

Section: Introductionmentioning

confidence: 99%

A Quantum-Classical Collaborative Training Architecture Based on Quantum State Fidelity

L'Abbate,

D'Onofrio,

Stein

et al. 2024

IEEE Trans. Quantum Eng.

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Recent advancements have highlighted the limitations of current quantum systems, particularly the restricted number of qubits available on near-term quantum devices. This constraint greatly inhibits the range of applications that can leverage quantum computers. Moreover, as the available qubits increase, the computational complexity grows exponentially, posing additional challenges. Consequently, there is an urgent need to use qubits efficiently and mitigate both present limitations and future complexities. To address this, existing quantum applications attempt to integrate classical and quantum systems in a hybrid framework. In this study, we concentrate on quantum deep learning and introduce a collaborative classical-quantum architecture called co-TenQu. The classical component employs a tensor network for compression and feature extraction, enabling higher-dimensional data to be encoded onto logical quantum circuits with limited qubits. On the quantum side, we propose a quantum-state-fidelity-based evaluation function to iteratively train the network through a feedback loop between the two sides. co-TenQu has been implemented and evaluated with both simulators and the IBM-Q platform. Compared to state-ofthe-art approaches, co-TenQu enhances a classical deep neural network by up to 41.72% in a fair setting. Additionally, it outperforms other quantum-based methods by up to 1.9 times and achieves similar accuracy while utilizing 70.59% fewer qubits.

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Sublinear Classical and Quantum Algorithms for General Matrix Games

Cited by 8 publications

References 27 publications

Quantum algorithm for online convex optimization

Quantum algorithm for online convex optimization

Quantum speedup of Bayes’ classifiers

A Quantum-Classical Collaborative Training Architecture Based on Quantum State Fidelity

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