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1. Noise resilience of variational quantum compiling

   https://doi.org/10.1088/1367-2630/ab784c  

   Sharma, Kunal ; Khatri, Sumeet ; Cerezo, M. ; Coles, Patrick J. ( April 2020 , New Journal of Physics)

   Variational hybrid quantum-classical algorithms (VHQCAs) are near-term algorithms that leverage classical optimization to minimize a cost function, which is efficiently evaluated on a quantum computer. Recently VHQCAs have been proposed for quantum compiling, where a target unitaryUis compiled into a short-depth gate sequenceV. In this work, we report on a surprising form of noise resilience for these algorithms. Namely, we find one often learns the correct gate sequenceV(i.e. the correct variational parameters) despite various sources of incoherent noise acting during the cost-evaluation circuit. Our main results are rigorous theorems stating that the optimal variational parameters are unaffected by amore »broad class of noise models, such as measurement noise, gate noise, and Pauli channel noise. Furthermore, our numerical implementations on IBM’s noisy simulator demonstrate resilience when compiling the quantum Fourier transform, Toffoli gate, and W-state preparation. Hence, variational quantum compiling, due to its robustness, could be practically useful for noisy intermediate-scale quantum devices. Finally, we speculate that this noise resilience may be a general phenomenon that applies to other VHQCAs such as the variational quantum eigensolver.

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2. Quantum Wasserstein Generative Adversarial Networks

   Chakrabarti, Shouvanik ; Huang, Yiming ; Li, Tongyang ; Feizi, Soheil ; Wu, Xiaodi ( December 2019 , Advances in neural information processing systems)

   The study of quantum generative models is well-motivated, not only because of its importance in quantum machine learning and quantum chemistry but also because of the perspective of its implementation on near-term quantum machines. Inspired by previous studies on the adversarial training of classical and quantum generative models, we propose the first design of quantum Wasserstein Generative Adversarial Networks (WGANs), which has been shown to improve the robustness and the scalability of the adversarial training of quantum generative models even on noisy quantum hardware. Specifically, we propose a definition of the Wasserstein semimetric between quantum data, which inherits a fewmore »key theoretical merits of its classical counterpart. We also demonstrate how to turn the quantum Wasserstein semimetric into a concrete design of quantum WGANs that can be efficiently implemented on quantum machines. Our numerical study, via classical simulation of quantum systems, shows the more robust and scalable numerical performance of our quantum WGANs over other quantum GAN proposals. As a surprising application, our quantum WGAN has been used to generate a 3-qubit quantum circuit of ~50 gates that well approximates a 3-qubit 1-d Hamiltonian simulation circuit that requires over 10k gates using standard techniques.« less
3. Analyzing the performance of variational quantum factoring on a superconducting quantum processor

   https://doi.org/10.1038/s41534-021-00478-z  

   Karamlou, Amir H. ; Simon, William A. ; Katabarwa, Amara ; Scholten, Travis L. ; Peropadre, Borja ; Cao, Yudong ( October 2021 , npj Quantum Information)

   In the near-term, hybrid quantum-classical algorithms hold great potential for outperforming classical approaches. Understanding how these two computing paradigms work in tandem is critical for identifying areas where such hybrid algorithms could provide a quantum advantage. In this work, we study a QAOA-based quantum optimization approach by implementing the Variational Quantum Factoring (VQF) algorithm. We execute experimental demonstrations using a superconducting quantum processor, and investigate the trade off between quantum resources (number of qubits and circuit depth) and the probability that a given biprime is successfully factored. In our experiments, the integers 1099551473989, 3127, and 6557 are factored withmore »3, 4, and 5 qubits, respectively, using a QAOA ansatz with up to 8 layers and we are able to identify the optimal number of circuit layers for a given instance to maximize success probability. Furthermore, we demonstrate the impact of different noise sources on the performance of QAOA, and reveal the coherent error caused by the residualZZ-coupling between qubits as a dominant source of error in a near-term superconducting quantum processor.

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4. Coreset Clustering on Small Quantum Computers

   https://doi.org/10.3390/electronics10141690  

   Tomesh, Teague ; Gokhale, Pranav ; Anschuetz, Eric R. ; Chong, Frederic T. ( July 2021 , Electronics)

   null (Ed.)

   Many quantum algorithms for machine learning require access to classical data in superposition. However, for many natural data sets and algorithms, the overhead required to load the data set in superposition can erase any potential quantum speedup over classical algorithms. Recent work by Harrow introduces a new paradigm in hybrid quantum-classical computing to address this issue, relying on coresets to minimize the data loading overhead of quantum algorithms. We investigated using this paradigm to perform k-means clustering on near-term quantum computers, by casting it as a QAOA optimization instance over a small coreset. We used numerical simulations to compare themore »performance of this approach to classical k-means clustering. We were able to find data sets with which coresets work well relative to random sampling and where QAOA could potentially outperform standard k-means on a coreset. However, finding data sets where both coresets and QAOA work well—which is necessary for a quantum advantage over k-means on the entire data set—appears to be challenging.« less
5. Machine Learning Framework for Quantum Sampling of Highly-Constrained, Continuous Optimization Problems

   B. Wilson, Z. Kudyshev ( May 2021 , ArXivorg)

   In the recent years, there is a growing interest in using quantum computers for solving combinatorial optimization problems. In this work, we developed a generic, machine learning-based framework for mapping continuous-space inverse design problems into surrogate quadratic unconstrained binary optimization (QUBO) problems by employing a binary variational autoencoder and a factorization machine. The factorization machine is trained as a low-dimensional, binary surrogate model for the continuous design space and sampled using various QUBO samplers. Using the D-Wave Advantage hybrid sampler and simulated annealing, we demonstrate that by repeated resampling and retraining of the factorization machine, our framework finds designs thatmore »exhibit figures of merit exceeding those of its training set. We showcase the framework’s performance on two inverse design problems by optimizing (i) thermal emitter topologies for thermophotovoltaic applications and (ii) diffractive meta-gratings for highly efficient beam steering. This technique can be further scaled to leverage future developments in quantum optimization to solve advanced inverse design problems for science and engineering applications.« less