Faster quantum and classical SDP approximations for quadratic binary optimization

Brandão, Fernando G. S. L.; Kueng, Richard; França, Daniel Stilck

doi:10.22331/q-2022-01-20-625

Cited by 15 publications

(3 citation statements)

References 58 publications

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“…Different possibilities are suggested by quantum algorithms for semidefinite programming [36], which can offer significant speedup over the current classical solution but require fault-tolerant quantum hardware. Authors in [37] have shown how to formulate semidefinite relaxations of QUBO problems.…”

Section: Combinatorial Optimization Techniques On Quantum Computersmentioning

confidence: 99%

Diversifying Investments and Maximizing Sharpe Ratio: A Novel Quadratic Unconstrained Binary Optimization Formulation

Mattesi,

Asproni,

Mattia

et al. 2024

Quantum Reports

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The optimization of investment portfolios represents a pivotal task within the field of financial economics. Its objective is to identify asset combinations that meet specified criteria for return and risk. Traditionally, the maximization of the Sharpe Ratio, often achieved through quadratic programming, has constituted a popular approach for this purpose. However, real-world scenarios frequently necessitate more complex considerations, particularly in relation to portfolio diversification with a view to mitigating sector-specific risks and enhancing stability. The incorporation of diversification alongside the Sharpe Ratio into the optimization model creates a joint optimization task, which can be formulated as Quadratic Unconstrained Binary Optimization (QUBO) and addressed using quantum annealing or hybrid computing techniques. These techniques offer promising solutions. We present a novel QUBO formulation for this optimization, detailing its mathematical formulation and demonstrating its advantages over classical methods, particularly in handling diversification objectives. By leveraging available QUBO solvers and hybrid approaches, we explore the feasibility of handling large-scale problems while highlighting the importance of diversification in achieving robust portfolio performance. We finally elaborate on the results showing the trade-off between the observed values of the portfolio’s Sharpe Ratio and diversification, as a natural consequence of solving a multi-objective optimization problem.

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Section: Combinatorial Optimization Techniques On Quantum Computersmentioning

confidence: 99%

Diversifying Investments and Maximizing Sharpe Ratio: A Novel Quadratic Unconstrained Binary Optimization Formulation

Mattesi,

Asproni,

Mattia

et al. 2024

Quantum Reports

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“…Both algorithms demand a number of qubits linearly proportional to the problem's dimension, which poses challenges for solving large-scale QCQPs. Besides variational quantum algorithms, there is also a quantum algorithm based on a classical approximation algorithm called semi-definite relaxation [10]. This approach involves solving a semi-definite program as an approximation of the original QUBO problem, employing the quantum Gibbs sampling algorithm [11].…”

Section: Introductionmentioning

confidence: 99%

A hybrid algorithm for quadratically constrained quadratic optimization problems

Zhou,

Peng,

et al. 2024

Phys. Scr.

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Quadratically Constrained Quadratic Programs (QCQPs) are an important class of optimization problems with diverse real-world applications. In this work, we propose a variational quantum algorithm for general QCQPs. By encoding the variables on the amplitude of a quantum state, the requirement of the qubit number scales logarithmically with the dimension of the variables, which makes our algorithm suitable for current quantum devices. Using the primal-dual interior-point method in classical optimization, we can deal with general quadratic constraints.Our numerical experiments on typical QCQP problems, including Max-Cut and optimal power flow problems, demonstrate a better performance of our hybrid algorithm over the classical counterparts.

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“…The ubiquity of optimization problems across disciplines and the incredible computational resources they consume continues to motivate researchers to explore new and more efficient approaches to tackle them. Though quantum computing has so far offered limited provable computational advantages for combinatorial optimization problems [1][2][3][4][5][6][7][8][9][10][11][12][13][14], we expect that the library of quantum approaches for tackling different classes of optimization problems will expand as quantum information processors mature and become more readily available.…”

Section: Introductionmentioning

confidence: 99%

Diabatic quantum annealing for the frustrated ring model

Côté,

Sauvage,

Larocca

et al. 2023

Quantum Sci. Technol.

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Quantum annealing is a continuous-time heuristic quantum algorithm for solving or approximately solving classical optimization problems. The algorithm uses a schedule to interpolate between a driver Hamiltonian with an easy-to-prepare ground state and a problem Hamiltonian whose ground state encodes solutions to an optimization problem. The standard implementation relies on the evolution being adiabatic: keeping the system in the instantaneous ground state with high probability and requiring a time scale inversely related to the minimum energy gap between the instantaneous ground and excited states. However, adiabatic evolution can lead to evolution times that scale exponentially with the system size, even for computationally simple problems. Here, we study whether non-adiabatic evolutions with optimized annealing schedules can bypass this exponential slowdown for one such class of problems called the frustrated ring model. For suﬃciently optimized annealing schedules and system sizes of up to 39 qubits, we provide numerical evidence that we can avoid the exponential slowdown. Our work highlights the potential of highly-controllable quantum annealing to circumvent bottlenecks associated with the standard implementation of quantum annealing.

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Faster quantum and classical SDP approximations for quadratic binary optimization

Cited by 15 publications

References 58 publications

Diversifying Investments and Maximizing Sharpe Ratio: A Novel Quadratic Unconstrained Binary Optimization Formulation

Diversifying Investments and Maximizing Sharpe Ratio: A Novel Quadratic Unconstrained Binary Optimization Formulation

A hybrid algorithm for quadratically constrained quadratic optimization problems

Diabatic quantum annealing for the frustrated ring model

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