Globally Optimizing QAOA Circuit Depth for Constrained Optimization Problems

Herrman, Rebekah; Treffert, Lorna; Ostrowski, James; Lotshaw, Phillip C.; Humble, Travis S.; Siopsis, George

doi:10.3390/a14100294

Cited by 13 publications

(5 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We also assumed 3-regular problem graphs, which have been studied with great interest in the QAOA literature. However, many practically relevant problems use denser problem graphs, for example in constrained optimization problems 18 , 45 , 46 . For denser graphs the average degree can scale as n and changes in degree can significantly affect M .…”

Section: Discussionmentioning

confidence: 99%

“…First we consider problem features such as the average degree of the graph defining the problem instance, where is related to the number of non-zero terms in the quadratic unconstrained binary optimization problem. While much of the QAOA literature has focused on problems with small , larger arises naturally in constrained combinatorial optimization problems 45 , 46 . In addition to , the problem size n and the number of QAOA layers p also contribute to the gate counts and hence the resources required to implement the algorithm.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Scaling quantum approximate optimization on near-term hardware

Lotshaw

Nguyen

Santana

et al. 2022

Sci Rep

Self Cite

View full text Add to dashboard Cite

The quantum approximate optimization algorithm (QAOA) is an approach for near-term quantum computers to potentially demonstrate computational advantage in solving combinatorial optimization problems. However, the viability of the QAOA depends on how its performance and resource requirements scale with problem size and complexity for realistic hardware implementations. Here, we quantify scaling of the expected resource requirements by synthesizing optimized circuits for hardware architectures with varying levels of connectivity. Assuming noisy gate operations, we estimate the number of measurements needed to sample the output of the idealized QAOA circuit with high probability. We show the number of measurements, and hence total time to solution, grows exponentially in problem size and problem graph degree as well as depth of the QAOA ansatz, gate infidelities, and inverse hardware graph degree. These problems may be alleviated by increasing hardware connectivity or by recently proposed modifications to the QAOA that achieve higher performance with fewer circuit layers.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Scaling quantum approximate optimization on near-term hardware

Lotshaw

Nguyen

Santana

et al. 2022

Sci Rep

Self Cite

View full text Add to dashboard Cite

show abstract

“…For applying QAOA to MAX-3SAT, the cost function in equation ( 2) is encoded in a cost Hamiltonian H ϕ . There are various formulations of this Hamiltonian [33,[36][37][38][39], with some focusing on reducing the number of operations required when implementing this cost function in the phase-separation operator. The formulations generally describe the cost Hamiltonian as a sum of clause operators…”

Section: Motivation and Research Questionsmentioning

confidence: 99%

Amplitude amplification-inspired QAOA: improving the success probability for solving 3SAT

Mandl,

Barzen,

Bechtold

et al. 2024

Quantum Sci. Technol.

View full text Add to dashboard Cite

The Boolean satisfiability problem (SAT), in particular 3SAT with its bounded clause size, is a well-studied problem since a wide range of decision problems can be reduced to it. The Quantum Approximate Optimization Algorithm (QAOA) is a promising candidate for solving 3SAT for Noisy Intermediate-Scale Quantum devices in the near future due to its simple quantum ansatz. However, although QAOA generally exhibits a high approximation ratio, there are 3SAT problem instances where the algorithm's success probability when obtaining a satisfying variable assignment from the approximated solution drops sharply compared to the approximation ratio. To address this problem, in this paper, we present variants of the algorithm that are inspired by the amplitude amplification algorithm to improve the success probability for 3SAT. For this, (i) three amplitude amplification-inspired QAOA variants are introduced and implemented, (ii) the variants are experimentally compared with a standard QAOA implementation, and (iii) the impact on the success probability and ansatz complexity is analyzed. The experiment results show that an improvement in the success probability can be achieved with only a moderate increase in circuit complexity.

show abstract

“…One of the most commonly used hybrid algorithms is the Quantum Approximate Optimization Algorithm (QAOA) [8,[21][22][23][24]. One of the main drawbacks of the QAOA is that it scales linearly with problem size [25].…”

Section: Introductionmentioning

confidence: 99%

Solving various NP-Hard problems using exponentially fewer qubits on a Quantum Computer

Chatterjee¹,

Bourreau²,

Rančić³

2023

Preprint

View full text Add to dashboard Cite

NP-hard problems are not believed to be exactly solvable through general polynomial time algorithms. Hybrid quantum-classical algorithms to address such combinatorial problems have been of great interest in the past few years. Such algorithms are heuristic in nature and aim to obtain an approximate solution. Significant improvements in computational time and/or the ability to treat large problems are some of the principal promises of quantum computing in this regard. The hardware, however, is still in its infancy and the current Noisy Intermediate Scale Quantum (NISQ) computers are not able to optimize industrially relevant problems. Moreover, the storage of qubits and introduction of entanglement require extreme physical conditions. An issue with quantum optimization algorithms such as QAOA is that they scale linearly with problem size. In this paper, we build upon a proprietary methodology which scales logarithmically with problem size -opening an avenue for treating optimization problems of unprecedented scale on gate-based quantum computers. In order to test the performance of the algorithm, we first find a way to apply it to a handful of NPhard problems: Maximum Cut, Minimum Partition, Maximum Clique, Maximum Weighted Independent Set. Subsequently, these algorithms are tested on a quantum simulator with graph sizes of over a hundred nodes and on a real quantum computer up to graph sizes of 256. To our knowledge, these constitute the largest realistic combinatorial optimization problems ever run on a NISQ device, overcoming previous problem sizes by almost tenfold.

show abstract

Globally Optimizing QAOA Circuit Depth for Constrained Optimization Problems

Cited by 13 publications

References 19 publications

Scaling quantum approximate optimization on near-term hardware

Scaling quantum approximate optimization on near-term hardware

Amplitude amplification-inspired QAOA: improving the success probability for solving 3SAT

Solving various NP-Hard problems using exponentially fewer qubits on a Quantum Computer

Contact Info

Product

Resources

About