Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer

Rosenberg, Gili; Haghnegahdar, Poya; Goddard, Phil; Carr, Peter; Wu, Kesheng; Prado, Marcos López de

doi:10.2139/ssrn.2649376

Cited by 12 publications

(13 citation statements)

References 35 publications

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“…Optimization problems comprise a large class of hard to solve financial problems, not to mention the fact that many supervised and reinforcement learning tools used in finance are trained via solving optimization problems (minimization of a cost function, maximization of reward). Several proposed applications of the D-Wave machine to portfolio optimization [7,8], dealt with portfolios that were too small to evaluate the scaling of the chosen approach with the problem size. In this paper we go beyond these early approaches and provide an analysis on sufficient data points to infer a scaling and measure a limited speedup with respect a state-of-the-art numerical method based on genetic algorithms.…”

Section: Introductionmentioning

confidence: 99%

Reverse quantum annealing approach to portfolio optimization problems

Venturelli

Kondratyev²

2019

Quantum Mach. Intell.

183

129

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We investigate a hybrid quantum-classical solution method to the mean-variance portfolio optimization problems. Starting from real financial data statistics and following the principles of the Modern Portfolio Theory, we generate parametrized samples of portfolio optimization problems that can be related to quadratic binary optimization forms programmable in the analog D-Wave Quantum Annealer 2000Q TM . The instances are also solvable by an industry-established Genetic Algorithm approach, which we use as a classical benchmark. We investigate several options to run the quantum computation optimally, ultimately discovering that the best results in terms of expected time-to-solution as a function of number of variables for the hardest instances set are obtained by seeding the quantum annealer with a solution candidate found by a greedy local search and then performing a reverse annealing protocol. The optimized reverse annealing protocol is found to be more than 100 times faster than the corresponding forward quantum annealing on average.

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Section: Introductionmentioning

confidence: 99%

Reverse quantum annealing approach to portfolio optimization problems

Venturelli

Kondratyev²

2019

Quantum Mach. Intell.

183

129

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“…The potential applications of the Ising annealer can be classified into two groups, as summarized in a recent white paper by the D-Wave team [29]. First, a variety of optimization problems, such as the traveling salesman problem and generalizations thereof [30][31][32], financial portfolio optimization [33], protein folding [34], as well as constraint satisfaction problems, e.g. factorization [35] and satisfiability [36,37], can be reduced to the Ising optimization.…”

Section: Discussionmentioning

confidence: 99%

Annealing by simulating the coherent Ising machine

Tiunov¹,

Ulanov²,

Lvovsky³

2019

Opt. Express

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The coherent Ising machine (CIM) enables efficient sampling of low-lying energy states of the Ising Hamiltonian with all-to-all connectivity by encoding the spins in the amplitudes of pulsed modes in an optical parametric oscillator (OPO). The interaction between the pulses is realized by means of measurement-based optoelectronic feedforward which enhances the gain for lower-energy spin configurations. We present an efficient method of simulating the CIM on a classical computer that outperforms the CIM itself as well as the noisy mean-field annealer in terms of both the quality of the samples and the computational speed. It is furthermore advantageous with respect to the CIM in that it can handle Ising Hamiltonians with arbitrary real-valued node coupling strengths. These results illuminate the nature of the faster performance exhibited by the CIM and may give rise to a new class of quantum-inspired algorithms of classical annealing that can successfully compete with existing methods.Introduction. The Ising model, originally developed for the description of phase transitions in magnetic materials [1], is a pillar of many branches in science. Its applications range from quantum field theory [2] and quantum gravity [3] to economics [4] and machine learning [5]. The model is defined by the Hamiltonianwhere J i j = J ji , J ii = 0. The spin variable σ i can be a quantum operator or a number, continuous or discrete. In this paper we are interested in the classical discrete case, σ i = ±1. The goal is to find the configurations of spins which realize or approach the global minimum of the Ising Hamiltonian (1). This is an NP-hard problem, meaning that the number of operations needed to find the exact solution grows exponentially with the size of the spin system [6]. However, there exists a variety of classical algorithms to find an approximate solution [7][8][9][10].Recently, the Ising problem has been approached using noisy intermediate-scale quantum (NISQ) devices. One example is the D-Wave quantum annealer based on superconducting qubits. However, it has a shortcoming associated with low connectivity: each physical qubit in the D-Wave chimera graph architecture is connected to only eight others. Therefore each logical spin must be embedded in multiple physical qubits to model the fully connected Hamiltonian (1), resulting in a significant overhead [11].

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“…Rather, they employ a nonadiabatic counterpart [18][19][20][21] and the thermal effect 22 . The quantum annealer has been tested for numerous applications, such as portfolio optimization 23 , protein folding 24 , the molecular similarity problem 25 , computational biology 26 , job-shop scheduling 27 , traffic optimization 28 , election forecasting 29 , machine learning [30][31][32][33][34][35] , and automated guided vehicles in plants 36 .…”

Section: Introductionmentioning

confidence: 99%

Breaking limitation of quantum annealer in solving optimization problems under constraints

Ohzeki

2020

Sci Rep

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Quantum annealing is a generic solver for optimization problems that uses fictitious quantum fluctuation. The most groundbreaking progress in the research field of quantum annealing is its hardware implementation, i.e., the so-called quantum annealer, using artificial spins. However, the connectivity between the artificial spins is sparse and limited on a special network known as the chimera graph. Several embedding techniques have been proposed, but the number of logical spins, which represents the optimization problems to be solved, is drastically reduced. In particular, an optimization problem including fully or even partly connected spins suffers from low embeddable size on the chimera graph. In the present study, we propose an alternative approach to solve a large-scale optimization problem on the chimera graph via a well-known method in statistical mechanics called the Hubbard-Stratonovich transformation or its variants. The proposed method can be used to deal with a fully connected Ising model without embedding on the chimera graph and leads to nontrivial results of the optimization problem. We tested the proposed method with a number of partition problems involving solving linear equations and the traffic flow optimization problem in Sendai and Kyoto cities in Japan. Fig. 10, we test our method to find the ground state of the original cost function (28). As in

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Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer

Cited by 12 publications

References 35 publications

Reverse quantum annealing approach to portfolio optimization problems

Reverse quantum annealing approach to portfolio optimization problems

Annealing by simulating the coherent Ising machine

Breaking limitation of quantum annealer in solving optimization problems under constraints

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