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1. Noise-tolerant quantum speedups in quantum annealing without fine tuning

   https://doi.org/10.1088/2058-9565/abd59a  

   Kapit, Eliot ; Oganesyan, Vadim ( February 2021 , Quantum Science and Technology)

   Quantum annealing is a powerful alternative model of quantum computing, which can succeed in the presence of environmental noise even without error correction. However, despite great effort, no conclusive demonstration of a quantum speedup (relative to state of the art classical algorithms) has been shown for these systems, and rigorous theoretical proofs of a quantum advantage (such as the adiabatic formulation of Grover’s search problem) generally rely on exponential precision in at least some aspects of the system, an unphysical resource guaranteed to be scrambled by experimental uncertainties and random noise. In this work, we propose a new variant of quantum annealing, called RFQA, which can maintain a scalable quantum speedup in the face of noise and modest control precision. Specifically, we consider a modification of flux qubit-based quantum annealing which includes low-frequency oscillations in the directions of the transverse field terms as the system evolves. We show that this method produces a quantum speedup for finding ground states in the Grover problem and quantum random energy model, and thus should be widely applicable to other hard optimization problems which can be formulated as quantum spin glasses. Further, we explore three realistic noise channels and show that the speedupmore »from RFQA is resilient to 1/f-like local potential fluctuations and local heating from interaction with a sufficiently low temperature bath. Another noise channel, bath-assisted quantum cooling transitions, actually accelerates the algorithm and may outweigh the negative effects of the others. We also detail how RFQA may be implemented experimentally with current technology.

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2. Faster quantum and classical SDP approximations for quadratic binary optimization

   https://doi.org/10.22331/q-2022-01-20-625  

   G.S L. Brandão, Fernando ; Kueng, Richard ; Stilck França, Daniel ( January 2022 , Quantum)

   We give a quantum speedup for solving the canonical semidefinite programming relaxation for binary quadratic optimization. This class of relaxations for combinatorial optimization has so far eluded quantum speedups. Our methods combine ideas from quantum Gibbs sampling and matrix exponent updates. A de-quantization of the algorithm also leads to a faster classical solver. For generic instances, our quantum solver gives a nearly quadratic speedup over state-of-the-art algorithms. Such instances include approximating the ground state of spin glasses and MaxCut on Erdös-Rényi graphs. We also provide an efficient randomized rounding procedure that converts approximately optimal SDP solutions into approximations of the original quadratic optimization problem.
3. A Scalable Randomized Algorithm for Triangle Enumeration on Graphs Based on SQL Queries

   https://doi.org/10.1007/978-3-030-59065-9_12  

   Farouzi, Abir ; Bellatreche, Ladjel ; Ordonez, Carlos ; Pandurangan, Gopal ; Malki, Mimoun ( January 2020 , International Conference on Big Data Analytics and Knowledge Discovery (DaWaK))

   Triangle enumeration is a fundamental problem in large-scale graph analysis. For instance, triangles are used to solve practical problems like community detection and spam filtering. On the other hand, there is a large amount of data stored on database management systems (DBMSs), which can be modeled and analyzed as graphs. Alternatively, graph data can be quickly loaded into a DBMS. Our paper shows how to adapt and optimize a randomized distributed triangle enumeration algorithm with SQL queries, which is a significantly different approach from programming graph algorithms in traditional languages such as Python or C++. We choose a parallel columnar DBMS given its fast query processing, but our solution should work for a row DBMS as well. Our randomized solution provides a balanced workload for parallel query processing, being robust to the existence of skewed degree vertices. We experimentally prove our solution ensures a balanced data distribution, and hence workload, among machines. The key idea behind the algorithm is to evenly partition all possible triplets of vertices among machines, sending edges that may form a triangle to a proxy machine; this edge redistribution eliminates shuffling edges during join computation and therefore triangle enumeration becomes local and fully parallel. In summary,more »our algorithm exhibits linear speedup with large graphs, including graphs that have high skewness in vertex degree distributions.« less
4. Classically verifiable quantum advantage from a computational Bell test

   https://doi.org/10.1038/s41567-022-01643-7  

   Kahanamoku-Meyer, Gregory D. ; Choi, Soonwon ; Vazirani, Umesh V. ; Yao, Norman Y. ( August 2022 , Nature Physics)

   Existing experimental demonstrations of quantum computational advantage have had the limitation that verifying the correctness of the quantum device requires exponentially costly classical computations. Here we propose and analyse an interactive protocol for demonstrating quantum computational advantage, which is efficiently classically verifiable. Our protocol relies on a class of cryptographic tools called trapdoor claw-free functions. Although this type of function has been applied to quantum advantage protocols before, our protocol employs a surprising connection to Bell’s inequality to avoid the need for a demanding cryptographic property called the adaptive hardcore bit, while maintaining essentially no increase in the quantum circuit complexity and no extra assumptions. Leveraging the relaxed cryptographic requirements of the protocol, we present two trapdoor claw-free function constructions, based on Rabin’s function and the Diffie–Hellman problem, which have not been used in this context before. We also present two independent innovations that improve the efficiency of our implementation and can be applied to other quantum cryptographic protocols. First, we give a scheme to discard so-called garbage bits, removing the need for reversibility in the quantum circuits. Second, we show a natural way of performing postselection that reduces the fidelity needed to demonstrate quantum advantage. Combining these results,more »we describe a blueprint for implementing our protocol on Rydberg atom-based quantum devices, using hardware-native operations that have already been demonstrated experimentally.

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5. Parallel Five-cycle Counting Algorithms

   https://doi.org/10.1145/3556541  

   Shi, Jessica ; Huang, Louisa Ruixue ; Shun, Julian ( December 2022 , ACM Journal of Experimental Algorithmics)

   Counting the frequency of subgraphs in large networks is a classic research question that reveals the underlying substructures of these networks for important applications. However, subgraph counting is a challenging problem, even for subgraph sizes as small as five, due to the combinatorial explosion in the number of possible occurrences. This article focuses on the five-cycle, which is an important special case of five-vertex subgraph counting and one of the most difficult to count efficiently. We design two new parallel five-cycle counting algorithms and prove that they are work efficient and achieve polylogarithmic span. Both algorithms are based on computing low out-degree orientations, which enables the efficient computation of directed two-paths and three-paths, and the algorithms differ in the ways in which they use this orientation to eliminate double-counting. Additionally, we present new parallel algorithms for obtaining unbiased estimates of five-cycle counts using graph sparsification. We develop fast multicore implementations of the algorithms and propose a work scheduling optimization to improve their performance. Our experiments on a variety of real-world graphs using a 36-core machine with two-way hyper-threading show that our best exact parallel algorithm achieves 10–46× self-relative speedup, outperforms our serial benchmarks by 10–32×, and outperforms the previous state-of-the-artmore »serial algorithm by up to 818×. Our best approximate algorithm, for a reasonable probability parameter, achieves up to 20× self-relative speedup and is able to approximate five-cycle counts 9–189× faster than our best exact algorithm, with between 0.52% and 11.77% error.« less