Engineering topics

Djidjev, Hristo N.

Publications and source records attributed to Djidjev, Hristo N..

5 records

DOE OSTI2023

Posiform planting: generating QUBO instances for benchmarking

We are interested in benchmarking both quantum annealing and classical algorithms for minimizing quadratic unconstrained binary optimization (QUBO) problems. Such problems are NP-hard in general, implying that the exact minima of randomly generated instances are hard to find and thus typically unknown. While brute forcing smaller instances is possible, such instances are typically not interesting due to being too easy for both quantum and classical algorithms. In this contribution, we propose a novel method, called posiform planting , for generating random QUBO instances of arbitrary size with known optimal solutions, and use those instances to benchmark the sampling quality of four D-Wave quantum annealers utilizing different interconnection structures (Chimera, Pegasus, and Zephyr hardware graphs) and the simulated annealing algorithm. Posiform planting differs from many existing methods in two key ways. It ensures the uniqueness of the planted optimal solution, thus avoiding groundstate degeneracy, and it enables the generation of QUBOs that are tailored to a given hardware connectivity structure, provided that the connectivity is not too sparse. Posiform planted QUBOs are a type of 2-SAT boolean satisfiability combinatorial optimization problems. Our experiments demonstrate the capability of the D-Wave quantum annealers to sample the optimal planted solution of combinatorial optimization problems with up to 5, 627 qubits.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Quantum Annealing with Inequality Constraints: The Set Cover Problem

Abstract 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.

Djidjev, Hristo N.↗

DOE OSTI2023

Noise dynamics of quantum annealers: estimating the effective noise using idle qubits

Quantum annealing is a type of analog computation that aims to use quantum mechanical fluctuations in search of optimal solutions of QUBO (quadratic unconstrained binary optimization) or, equivalently, Ising problems. Since NP-hard problems can in general be mapped to Ising and QUBO formulations, the quantum annealing paradigm has the potential to help solve various NP-hard problems. Current quantum annealers, such as those manufactured by D-Wave Systems, Inc. have various practical limitations including the size (number of qubits) of the problem that can be solved, the qubit connectivity, and error due to the environment or system calibration, which can reduce the quality of the solutions. Typically, for an arbitrary problem instance, the corresponding QUBO (or Ising) structure will not natively embed onto the available qubit architecture on the quantum chip. Thus, in these cases, a minor embedding of the problem structure onto the device is necessary. However, minor embeddings on these devices do not always make use of the full sparse chip hardware graph, and a large portion of the available qubits stay unused during quantum annealing. In this work, we embed a disjoint random QUBO on the unused parts of the chip alongside the QUBO to be solved, which acts as an indicator of the solution quality of the device over time. Using experiments on three different D-Wave quantum annealers, we demonstrate that (i) long term trends in solution quality exist on the D-Wave device, and (ii) the unused qubits can be used to measure the current level of noise of the quantum system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Quantum annealing algorithms for Boolean tensor networks

Abstract Quantum annealers manufactured by D-Wave Systems, Inc., are computational devices capable of finding high-quality heuristic solutions of NP-hard problems. In this contribution, we explore the potential and effectiveness of such quantum annealers for computing Boolean tensor networks. Tensors offer a natural way to model high-dimensional data commonplace in many scientific fields, and representing a binary tensor as a Boolean tensor network is the task of expressing a tensor containing categorical (i.e., $$\{0, 1\}$$ { 0 , 1 } ) values as a product of low dimensional binary tensors. A Boolean tensor network is computed by Boolean tensor decomposition, and it is usually not exact. The aim of such decomposition is to minimize the given distance measure between the high-dimensional input tensor and the product of lower-dimensional (usually three-dimensional) tensors and matrices representing the tensor network. In this paper, we introduce and analyze three general algorithms for Boolean tensor networks: Tucker, Tensor Train, and Hierarchical Tucker networks. The computation of a Boolean tensor network is reduced to a sequence of Boolean matrix factorizations, which we show can be expressed as a quadratic unconstrained binary optimization problem suitable for solving on a quantum annealer. By using a novel method we introduce called parallel quantum annealing, we demonstrate that Boolean tensor’s with up to millions of elements can be decomposed efficiently using a DWave 2000Q quantum annealer.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Parallel quantum annealing

Quantum annealers of D-Wave Systems, Inc., offer an efficient way to compute high quality solutions of NP-hard problems. This is done by mapping a problem onto the physical qubits of the quantum chip, from which a solution is obtained after quantum annealing. However, since the connectivity of the physical qubits on the chip is limited, a minor embedding of the problem structure onto the chip is required. In this process, and especially for smaller problems, many qubits will stay unused. We propose a novel method, called parallel quantum annealing, to make better use of available qubits, wherein either the same or several independent problems are solved in the same annealing cycle of a quantum annealer, assuming enough physical qubits are available to embed more than one problem. Although the individual solution quality may be slightly decreased when solving several problems in parallel (as opposed to solving each problem separately), we demonstrate that our method may give dramatic speed-ups in terms of the Time-To-Solution (TTS) metric for solving instances of the Maximum Clique problem when compared to solving each problem sequentially on the quantum annealer. Additionally, we show that solving a single Maximum Clique problem using parallel quantum annealing reduces the TTS significantly.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗