Parallel quantum chemistry on noisy intermediate-scale quantum computers

Schade, Robert; Bauer, Carsten; Tamoev, Konstantin; Mazur, Lukas; Plessl, Christian; Kühne, Thomas D.

doi:10.1103/physrevresearch.4.033160

Cited by 7 publications

(4 citation statements)

References 39 publications

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“…The main goal of this work is to elaborate on the vrepresentability problem and its relation to other fundamental features and concepts in 1RDMFT. Accordingly, we complement all the recent theoretical investigations of 1RDMFT and hope that our insights could guide the intense development of novel functionals and their implementations [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50] . To achieve this, we first discuss by concise means the so-called scope of a functional theory and explain how it identifies a functional variable in a natural way.…”

Section: Introductionmentioning

confidence: 78%

Refining and relating fundamentals of functional theory

Liebert¹,

Chaou²,

Schilling³

2023

Preprint

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To advance the foundation of one-particle reduced density matrix functional theory (1RDMFT) we refine and relate some of its fundamental features and underlying concepts. We define by concise means the scope of a 1RDMFT, identify its possible natural variables and explain how symmetries could be exploited. In particular, for systems with time-reversal symmetry, we explain why there exist six equivalent universal functionals, prove concise relations among them and conclude that the important notion of v-representability is relative to the scope and choice of variable. All these fundamental concepts are then comprehensively discussed and illustrated for the Hubbard dimer and its generalization to arbitrary pair interactions W . For this, we derive by analytical means the pure and ensemble functionals with respect to both the real-and complex-valued Hilbert space. The comparison of various functionals allows us to solve the underlying v-representability problems analytically and the dependence of its solution on the pair interaction is demonstrated. Intriguingly, the gradient of each universal functional is found to always diverge repulsively on the boundary of the domain. In that sense, this key finding emphasizes the universal character of the fermionic exchange force, recently discovered and proven in the context of translationally-invariant one-band lattice models.

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Section: Introductionmentioning

confidence: 78%

Refining and relating fundamentals of functional theory

Liebert¹,

Chaou²,

Schilling³

2023

Preprint

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“…Using parallel computations in QC is not a new idea [32]. It is already used to speedup computations by either splitting the computation into smaller problems, which can be computed in parallel [33][34][35], or computing multiple problems in parallel [36,37].…”

Section: Vertical Layers In Qvcmentioning

confidence: 99%

A Case Study for Cyber-Attack Detection using Quantum Variational Circuits

Moll

Kunczik

2023

Preprint

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Identification of malicious attacks in network traffic is one of many important Big Data problems that have been approached from different directions, including machine learning. In this paper, it is used as an example for investigating the applicability of quantum machine learning to such problems. Particular focus is kept on the NISQ era, in which available computer sizes are typically fairly small. A new approach is introduced that allows quantum variational circuits to be split between different computers without the typical overhead cost of cutting and knitting techniques. It is compared to classical and established quantum approaches on a real-world data set.

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“…[ 19 ] In quantum computing, ALM has been used in ref. [20] for solving the quantum‐chemical ground‐state energy problem on a gate‐based quantum computers. Yonaga et al.…”

Section: Previous Workmentioning

confidence: 99%

“…[19] In quantum computing, ALM has been used in ref. [20] for solving the quantum-chemical ground-state energy problem on a gate-based quantum computers. Yonaga et al [21] use the alternating direction method of multipliers, a variant of ALM, to solve the quadratic knapsack problem.…”

Section: Previous Workmentioning

confidence: 99%

Quantum Annealing with Inequality Constraints: The Set Cover Problem

Djidjev

2023

Adv Quantum Tech

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Quantum annealing is a promising method for solving hard optimization problems by transforming them into quadratic unconstrained binary optimization (QUBO) problems. However, when constraints are involved, particularly multiple inequality constraints, incorporating them into the objective function poses challenges. In this paper, the authors present two novel approaches for solving problems with multiple inequality constraints on a quantum annealer and apply them to the set cover problem (SCP). The first approach uses the augmented Lagrangian method to represent the constraints, while the second approach employs a higher‐order binary optimization (HUBO) formulation. The experiments show that both approaches outperform the standard approach for solving the SCP on the D‐Wave Advantage quantum annealer. The HUBO formulation performs slightly better than the augmented Lagrangian method in solving the SCP, but its scalability in terms of embeddability in the quantum chip is worse. The results demonstrate that the proposed augmented Lagrangian and HUBO methods can successfully implement a large number of inequality constraints, making them applicable to a broad range of constrained problems beyond the SCP.

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Parallel quantum chemistry on noisy intermediate-scale quantum computers

Cited by 7 publications

References 39 publications

Refining and relating fundamentals of functional theory

Refining and relating fundamentals of functional theory

A Case Study for Cyber-Attack Detection using Quantum Variational Circuits

Quantum Annealing with Inequality Constraints: The Set Cover Problem

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