Parity Quantum Optimization: Compiler

Ender, Kilian; Roeland, ter Hoeven,; Niehoff, Benjamin E.; Maike, Drieb-Schön,; Lechner, Wolfgang

doi:10.48550/arxiv.2105.06233

Cited by 10 publications

(38 citation statements)

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“…3 and Ref. [24]). In the simplest case, requiring only fourbody constraints, we can construct a driver Hamiltonian which preserves all constraints from only straight horizontal and vertical lines (cf.…”

Section: B Arbitrary (Hyper-)graphsmentioning

confidence: 91%

“…( 1) can be challenging to implement directly. Instead, we utilize the parity architecture [23,24] that allows one to encode arbitrary k-body terms on a square lattice requiring only nearest-neighbor interactions. This involves mapping the product of k problem spins s i onto a single, physical parity qubit (denoted by σz ), e.g.…”

Section: Parity Qaoamentioning

confidence: 99%

“…The recently introduced parity architecture [23,24] addresses this mismatch between the connectivity of the problem and hardware graphs by mapping problemdefining interactions onto single-body terms, while restricting the enlarged Hilbert space via quasilocal constraint terms. In particular, the parity architecture allows one to tackle generic optimization problems, i.e.…”

Section: Introductionmentioning

confidence: 99%

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Modular Parity Quantum Approximate Optimization

Ender¹,

Messinger²,

Fellner³

et al. 2022

Preprint

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The parity transformation encodes spin models in the low-energy subspace of a larger Hilbertspace with constraints on a planar lattice. Applying the Quantum Approximate Optimization Algorithm (QAOA), the constraints can either be enforced explicitly, by energy penalties, or implicitly, by restricting the dynamics to the low-energy subspace via the driver Hamiltonian. While the explicit approach allows for parallelization with a system-size-independent circuit depth, the implicit approach shows better QAOA performance. Here we combine the two approaches in order to improve the QAOA performance while keeping the circuit parallelizable. In particular, we introduce a modular parallelization method that partitions the circuit into clusters of subcircuits with fixed maximal circuit depth, relevant for scaling up to large system sizes.

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Section: B Arbitrary (Hyper-)graphsmentioning

confidence: 91%

Section: Parity Qaoamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modular Parity Quantum Approximate Optimization

Ender¹,

Messinger²,

Fellner³

et al. 2022

Preprint

Self Cite

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show abstract

“…Assuming the hardware topology is fixed, however, an embedding can potentially be efficiently found for QUBOs with certain structure [329]. 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].…”

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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“…Therefore, a future direction is to go beyond current architectures with only nearestneighbor interactions, in a co-design spirit, which can efficiently encode the problem Hamiltonian and the CD terms. In this context, recent works show an efficient alternative to implement k-local interactions [40][41][42], which could improve a variety of DAdQC protocols. Finally, this work shows how to build efficient quantum algorithms for NISQ devices, with the potential to approach us to quantum advantage.…”

mentioning

confidence: 99%

Digitized Adiabatic Quantum Factorization

Hegade,

Paul,

Albarrán-Arriagada

et al. 2021

Preprint

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Quantum integer factorization is a potential quantum computing solution that may revolutionize cryptography. Nevertheless, a scalable and efficient quantum algorithm for noisy intermediate-scale quantum computers looks far-fetched. We propose an alternative factorization method, within the digitized-adiabatic quantum computing paradigm, by digitizing an adiabatic quantum factorization algorithm enhanced by shortcuts to adiabaticity techniques. We find that this fast factorization algorithm is suitable for available gate-based quantum computers. We test our quantum algorithm in an IBM quantum computer with up to six qubits, surpassing the performance of the more commonly used factorization algorithms on the long way towards quantum advantage.

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Parity Quantum Optimization: Compiler

Cited by 10 publications

References 0 publications

Modular Parity Quantum Approximate Optimization

Modular Parity Quantum Approximate Optimization

A Survey of Quantum Computing for Finance

Digitized Adiabatic Quantum Factorization

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