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:10.1145/2830556.2830563

Cited by 54 publications

(54 citation statements)

References 30 publications

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“…Databases [66], Fault Diagnostics [55], Machine Learning [54], Finance [59], Data Analysis [47], Chemistry [31], and Space Sciences/-Aeronautics [3]. A Similar problem to ML detection, CDMA multiuser demodulation, was solved using quantum fluctuations controlled by the transverse field (similar as QA) in [53].…”

Section: Related Workmentioning

confidence: 99%

Leveraging quantum annealing for large MIMO processing in centralized radio access networks

Kim

Venturelli

Jamieson

2019

Proceedings of the ACM Special Interest Group on Data Communication

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User demand for increasing amounts of wireless capacity continues to outpace supply, and so to meet this demand, significant progress has been made in new MIMO wireless physical layer techniques. Higher-performance systems now remain impractical largely only because their algorithms are extremely computationally demanding. For optimal performance, an amount of computation that increases at an exponential rate both with the number of users and with the data rate of each user is often required. The base station's computational capacity is thus becoming one of the key limiting factors on wireless capacity. QuAMax is the first large MIMO centralized radio access network design to address this issue by leveraging quantum annealing on the problem. We have implemented QuAMax on the 2,031 qubit D-Wave 2000Q quantum annealer, the state-of-the-art in the field. Our experimental results evaluate that implementation on real and synthetic MIMO channel traces, showing that 10 µs of compute time on the 2000Q can enable 48 user, 48 AP antenna BPSK communication at 20 dB SNR with a bit error rate of 10 −6 and a 1,500 byte frame error rate of 10 −4 .

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Section: Related Workmentioning

confidence: 99%

Leveraging quantum annealing for large MIMO processing in centralized radio access networks

Kim

Venturelli

Jamieson

2019

Proceedings of the ACM Special Interest Group on Data Communication

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“…Substituting eqs. (19) and (22) into (21) gives (16). The guiding principle of ME design to achieve a high performance in Ising machines is that the intra-ring-coupling strength must be tuned according to eq.…”

Section: Types Of Minor-embeddingmentioning

confidence: 99%

“…The appendix provides a detailed derivation of the correlation length in a one-dimensional Ising model [see eq. (19) in the main text]. The correlation length is determined by the correlation function, which is given by…”

Section: Appendix a Correlation Length In A One-dimensional Ising Modelmentioning

confidence: 99%

Guiding Principle for Minor-Embedding in Simulated-Annealing-Based Ising Machines

2020

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We propose a novel type of minor-embedding (ME) in simulated-annealing-based Ising machines. The Ising machines can solve combinatorial optimization problems. Many combinatorial optimization problems are mapped to find the ground (lowest-energy) state of the logical Ising model. When connectivity is restricted on Ising machines, ME is required for mapping from the logical Ising model to a physical Ising model, which corresponds to a specific Ising machine. Herein we discuss the guiding principle of ME design to achieve a high performance in Ising machines. We derive the proposed ME based on a theoretical argument of statistical mechanics. The performance of the proposed ME is compared with two existing types of MEs for different benchmarking problems. Simulated annealing shows that the proposed ME outperforms existing MEs for all benchmarking problems, especially when the distribution of the degree in a logical Ising model has a large standard deviation. This study validates the guiding principle of using statistical mechanics for ME to realize fast and high-precision solvers for combinatorial optimization problems.

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“…Permanent price impact refers to the shift in the equilibrium price due to our trading strategy which lasts at least up to the end of a round. 6 As we consider the liquidation problem, our formulation is given in terms of the bid price. 7 A policy is risk-averse if the trader would like to select actions such that the variance of the cost does not change much.…”

Section: Actionsmentioning

confidence: 99%

Online Learning in Limit Order Book Trade Execution

Akbarzadeh

Tekin

Schaar³

2018

IEEE Trans. Signal Process.

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In this paper, we propose an online learning algorithm for optimal execution in the limit order book of a financial asset. Given a certain number of shares to sell and an allocated time window to complete the transaction, the proposed algorithm dynamically learns the optimal number of shares to sell via market orders at prespecified time slots within the allocated time interval. We model this problem as a Markov Decision Process (MDP), which is then solved by dynamic programming. First, we prove that the optimal policy has a specific form, which requires either selling no shares or the maximum allowed amount of shares at each time slot. Then, we consider the learning problem, in which the state transition probabilities are unknown and need to be learned on the fly. We propose a learning algorithm that exploits the form of the optimal policy when choosing the amount to trade. Interestingly, this algorithm achieves bounded regret with respect to the optimal policy computed based on the complete knowledge of the market dynamics. Our numerical results on several finance datasets show that the proposed algorithm performs significantly better than the traditional Q-learning algorithm by exploiting the structure of the problem.Index Terms-Limit order book, Markov decision process, online learning, dynamic programming, bounded regret.

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Solving the optimal trading trajectory problem using a quantum annealer

Cited by 54 publications

References 30 publications

Leveraging quantum annealing for large MIMO processing in centralized radio access networks

Leveraging quantum annealing for large MIMO processing in centralized radio access networks

Guiding Principle for Minor-Embedding in Simulated-Annealing-Based Ising Machines

Online Learning in Limit Order Book Trade Execution

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