Parity Quantum Optimization: Encoding Constraints

Maike, Drieb-Schön,; Ender, Kilian; Javanmard, Younes; Lechner, Wolfgang

doi:10.48550/arxiv.2105.06235

Cited by 7 publications

(10 citation statements)

References 33 publications

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“…[12] and Ref. [14] of this series is the generalization of the LHZarchitecture [13]. For completeness we summarize the main steps.…”

Section: Parity Quantum Computingmentioning

confidence: 99%

“…We compare the number of gates required in three scenarios: a standard compiler using CNOT gates on a square lattice, the parity compiler on the same hardware with the same gates, and the parity compiler using parity gates (i.e., 4-body gates). The parity architecture [12], which generalizes the LHZ-architecture [13], allows one to implement problems with highly nonlocal higher-order terms, using only local interactions, and to encode constraints [14]. The mapping is thus an alternative to expressing problems as quadratic unconstrained binary optimization (QUBO) problems and allows for a direct implementation of higher-order constrained optimization (HCBO) problems.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Parity Quantum Optimization: Benchmarks

Fellner

Ender

Roeland

et al. 2023

Quantum

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We present benchmarks of the parity transformation for the Quantum Approximate Optimization Algorithm (QAOA). We analyse the gate resources required to implement a single QAOA cycle for real-world scenarios. In particular, we consider random spin models with higher order terms, as well as the problems of predicting financial crashes and finding the ground states of electronic structure Hamiltonians. For the spin models studied our findings imply a significant advantage of the parity mapping compared to the standard gate model. In combination with full parallelizability of gates this has the potential to boost the race for demonstrating quantum advantage.

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“…[12] and Ref. [14] of this series is the generalization of the LHZarchitecture [13]. For completeness we summarize the main steps.…”

Section: Parity Quantum Computingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Parity Quantum Optimization: Benchmarks

Fellner

Ender

Roeland

et al. 2023

Quantum

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show abstract

“…Alternatively, the embedding problem associated with restricted connectivity can be avoided if the hardware supports three-and four-qubit interactions, by using the LHZ encoding [210] or its extension by Ender et al [123]. The extension by Ender et al even supports higher-order binary optimization problems [118,130]. Moreover, the current devices for QA provide no guarantees on the adiabaticity of the trajectory that the system follows.…”

Section: Quantum Annealingmentioning

confidence: 99%

A Survey of Quantum Computing for Finance

Herman¹,

Googin²,

Liu³

et al. 2022

Preprint

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Quantum computers are expected to surpass the computational capabilities of classical computers during this decade and have transformative impact on numerous industry sectors, particularly finance. In fact, finance is estimated to be the first industry sector to benefit from quantum computing, not only in the medium and long terms, but even in the short term. This survey paper presents a comprehensive summary of the state of the art of quantum computing for financial applications, with particular emphasis on Monte Carlo integration, optimization, and machine learning, showing how these solutions, adapted to work on a quantum computer, can help solve more efficiently and accurately problems such as derivative pricing, risk analysis, portfolio optimization, natural language processing, and fraud detection. We also discuss the feasibility of these algorithms on near-term quantum computers with various hardware implementations and demonstrate how they relate to a wide range of use cases in finance. We hope this article will not only serve as a reference for academic researchers and industry practitioners but also inspire new ideas for future research.

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“…are consistent with the existence of solutions). This covers the cases of product constraints and sum constraints, as well as more general constraints [27].…”

Section: Introductionmentioning

confidence: 99%

Parity Quantum Optimization: Compiler

Ender

Roeland

Niehoff³

et al. 2023

Quantum

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We introduce parity quantum optimization with the aim of solving optimization problems consisting of arbitrary k-body interactions and side conditions using planar quantum chip architectures. The method introduces a decomposition of the problem graph with arbitrary k-body terms using generalized closed cycles of a hypergraph. Side conditions of the optimization problem in form of hard constraints can be included as open cycles containing the terms involved in the side conditions. The generalized parity mapping thus circumvents the need to translate optimization problems to a quadratic unconstrained binary optimization problem (QUBO) and allows for the direct encoding of higher-order constrained binary optimization problems (HCBO) on a square lattice and full parallelizability of gates.

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Parity Quantum Optimization: Encoding Constraints

Cited by 7 publications

References 33 publications

Parity Quantum Optimization: Benchmarks

Parity Quantum Optimization: Benchmarks

A Survey of Quantum Computing for Finance

Parity Quantum Optimization: Compiler

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