An integrated programming and development environment for adiabatic quantum optimization

Humble, Travis S.; McCaskey, Alexander; Bennink, Ryan S.; Billings, Jay Jay; D’Azevedo, E.; Sullivan, Blair D.; Klymko, Christine; Seddiqi, Hadayat

doi:10.1088/1749-4680/7/1/015006

Cited by 27 publications

(29 citation statements)

References 55 publications

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“…While the latest 2000Q system contains up to 2048 qubits arranged in a connectivity pattern expressed as a 16-by-16 Chimera graph, this sparse connectivity pattern requires additional resources to ensure the required interactions between the logical variables defining the problem Hamiltonian. This is accomplished by embedding the problem Hamiltonian into the hardware graph while maintaining the logical form of the cost function 27 – 29 . From the coupling matrix J , we define a graph G that represents the variables as vertices and non-zero coupling as edges.…”

Section: Methodsmentioning

confidence: 99%

Quantum Annealing for Prime Factorization

Jiang

Britt

McCaskey

et al. 2018

Sci Rep

150

117

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We have developed a framework to convert an arbitrary integer factorization problem to an executable Ising model by first writing it as an optimization function then transforming the k-bit coupling (k ≥ 3) terms to quadratic terms using ancillary variables. Our resource-efficient method uses binary variables (qubits) for finding the factors of an integer N. We present how to factorize 15, 143, 59989, and 376289 using 4, 12, 59, and 94 logical qubits, respectively. This method was tested using the D-Wave 2000Q for finding an embedding and determining the prime factors for a given composite number. The method is general and could be used to factor larger integers as the number of available qubits increases, or combined with other ad hoc methods to achieve better performances for specific numbers.

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Section: Methodsmentioning

confidence: 99%

Quantum Annealing for Prime Factorization

Jiang

Britt

McCaskey

et al. 2018

Sci Rep

150

117

View full text Add to dashboard Cite

show abstract

“…While the problem of finding an optimal graph-minor is itself NP-hard, an efficient embedding for many graphs can be found systematically with heuristic techniques [34]. Mapping the objective function onto the physical quantum processing unit is followed by the realization of quantum annealing process [35] which searches for low-energy solutions of the corresponding problem Hamiltonian [36]. The probability of recovering the global optimal solution is highly dependent on the embedding and annealing schedule [37,38].…”

Section: Figure 1 A) Entangled Qubits In Superposition States B) Gamentioning

confidence: 99%

Quantum computing based hybrid solution strategies for large-scale discrete-continuous optimization problems

Ajagekar

Humble

You

2020

Computers & Chemical Engineering

137

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Quantum computing (QC) has gained popularity due to its unique capabilities that are quite different from that of classical computers in terms of speed and methods of operations. This paper proposes hybrid models and methods that effectively leverage the complementary strengths of deterministic algorithms and QC techniques to overcome combinatorial complexity for solving large-scale mixed-integer programming problems. Four applications, namely the molecular conformation problem, job-shop scheduling problem, manufacturing cell formation problem, and the vehicle routing problem, are specifically addressed. Large-scale instances of these application problems across multiple scales ranging from molecular design to logistics optimization are computationally challenging for deterministic optimization algorithms on classical computers. To address the computational challenges, hybrid QC-based algorithms are proposed and extensive computational experimental results are presented to demonstrate their applicability and efficiency.The proposed QC-based solution strategies enjoy high computational efficiency in terms of solution quality and computation time, by utilizing the unique features of both classical and quantum computers.Quantum computing (QC) is the next frontier in computation and has attracted a lot of attention from the scientific community in recent years. QC provides a novel approach to help solve some of the most complex optimization problems while offering an essential speed advantage over classical methods [10]. This is evident from QC techniques like Shor's algorithm for integer factorization [11], Grover's search algorithm for unstructured databases [12], quantum algorithm for linear system of equations [13], and many more [14]. Quantum adiabatic algorithms too are efficient optimization strategies that quickly search over the solution space [15]. Quantum computers perform computation by inducing quantum speedups whose scaling far exceeds the capability of the most powerful classical computers. QC's major applications can be perceived in areas of optimization, machine learning, cryptography, and quantum chemistry [16]. Despite the contrasting views on QC's viability and performance, there is no doubt that QC holds great promise to open up a new era of computing.QC-based solution approaches are in their earliest stages of development compared to their much more matured classical counterparts. Current quantum machines have very limited functionality in the context of optimization, such that QC hardware and algorithms are inadequate for large-scale optimization problems. Although it has been shown that some optimization problems relevant to energy systems can be solved using quantum computers, their performance deteriorates with increasing size and complexity [17]. A number of technological limitations face commercially available quantum computers, such as relatively small number of qubits with limited connectivity, and lack of quantum memory. Therefore, harnessing the complementary strengths of classical and...

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“…where q ai represents the measured value of physical qubit a i in the computational basis. In addition to its being used routinely in decoding minor embedded quantum annealing [58][59][60][61][62], MVD has been successfully used in the context of quantum annealing correction (QAC) [30,31,63] and hybrid minor-embedded implementations of QAC [16,64]. MVD relies on the assumption that the decoded values {q i } are the most likely to recover the logical ground state.…”

Section: Majority Vote Decoding Of the Me Schemementioning

confidence: 99%

Simulated-quantum-annealing comparison between all-to-all connectivity schemes

2016

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Quantum annealing aims to exploit quantum mechanics to speed up the search for the solution to optimization problems. Most problems exhibit complete connectivity between the logical spin variables after they are mapped to the Ising spin Hamiltonian of quantum annealing. To account for hardware constraints of current and future physical quantum annealers, methods enabling the embedding of fully connected graphs of logical spins into a constant-degree graph of physical spins are therefore essential. Here, we compare the recently proposed embedding scheme for quantum annealing with all-to-all connectivity due to Lechner, Hauke and Zoller (LHZ) [Science Advances 1 (2015)] to the commonly used minor embedding (ME) scheme. Using both simulated quantum annealing and parallel tempering simulations, we find that for a set of instances randomly chosen from a class of fully connected, random Ising problems, the ME scheme outperforms the LHZ scheme when using identical simulation parameters, despite the fault tolerance of the latter to weakly correlated spin-flip noise. This result persists even after we introduce several decoding strategies for the LHZ scheme, including a minimumweight decoding algorithm that results in substantially improved performance over the original LHZ scheme. We explain the better performance of the ME scheme in terms of more efficient spin updates, which allows it to better tolerate the correlated spin-flip errors that arise in our model of quantum annealing. Our results leave open the question of whether the performance of the two embedding schemes can be improved using scheme-specific parameters and new error correction approaches.

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An integrated programming and development environment for adiabatic quantum optimization

Cited by 27 publications

References 55 publications

Quantum Annealing for Prime Factorization

Quantum Annealing for Prime Factorization

Quantum computing based hybrid solution strategies for large-scale discrete-continuous optimization problems

Simulated-quantum-annealing comparison between all-to-all connectivity schemes

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