Benchmarking Adiabatic Quantum Optimization for Complex Network Analysis

Abstract

We lay the foundation for a benchmarking methodology for assessing current and future quantum computers. We pose and begin addressing fundamental questions about how to fairly compare computational devices at vastly different stages of technological maturity. We critically evaluate and offer our own contributions to current quantum benchmarking efforts, in particular those involving adiabatic quantum computation and the Adiabatic Quantum Optimizers produced by D-Wave Systems, Inc. We find that the performance of D-Wave's Adiabatic Quantum Optimizers scales roughly on par with classical approaches for some hard combinatorial optimization problems; however, architectural limitations of D-Wave devices present a significant hurdle in evaluating real-world applications. In addition to identifying and isolating such limitations, we develop algorithmic tools for circumventing these limitations on future D-Wave devices, assuming they continue to grow and mature at an exponential rate for the next several years.

The potential of quantum annealing for rapid solution structure identification

“…These challenges include: persistent coefficient biases, which are an artifact of hardware slowly drifting out of calibration between re-calibration cycles; programming biases, which introduce some minor errors in the J , h values that were requested; and environmental noise, which disrupts the quantum behavior of the hardware and results in a reduction of solution quality. Overall, these hardware constraints have made the identification of QA-based performance gains notoriously challenging [16,42,54,58,65].…”

“…This extract and optimize process is repeated until a specified time limit is reached. This approach has demonstrated remarkable results in a variety of benchmarking studies [16,44,48,49,65]. The notable success of this solver can be attributed to three key factors.…”

Recall Performance for Content-Addressable Memory Using Adiabatic Quantum Optimization

“…Because CAM recall using orthogonal memories is expected to be well behaved, we use that case to test the fundamental performance of the D-Wave processor to recall stored memories. The remaining parameters are chosen from the following sets respectively, n ∈ {8, 12,16,20,24,28 For each parameter combination (n, m, θ), 100 problem instances are randomly generated as specified in Section 3.1 and utilizing one of the learning rules to encode the memories into a weight matrix. Each selected problem instance is then programmed and executed N = 1000 times on the D-Wave QPU to calculate the average recall accuracy c.…”

“…This finite-temperature, open system model is expected to more accurately describe the dynamics underlying the QPU [8]. Nevertheless, several experimental tests of the D-Wave QPU have been carried out including applications of machine learning, binary classification, protein folding, graph analysis, and network analysis [9][10][11][12][13][14][15][16][17][18]. Demonstrations of enhanced performance using the D-Wave QPU have been found only for a few selected and highly contrived problem instances [19][20][21].…”

A Quantum Computational Approach to Correspondence Problems on Point Sets

“…A fully connected graph of layers with N qubits would require N 2 qubits for processing. Some QUBOP cannot be mapped to the chimera graph, and some problems can be mapped in multiple ways [55].…”