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1. Zero and Finite Temperature Quantum Simulations Powered by Quantum Magic

   https://doi.org/10.22331/q-2024-07-23-1422  

   Gu, Andi; Hu, Hong-Ye; Luo, Di; Patti, Taylor L; Rubin, Nicholas C; Yelin, Susanne F (July 2024, Quantum)

   We introduce a quantum information theory-inspired method to improve the characterization of many-body Hamiltonians on near-term quantum devices. We design a new class of similarity transformations that, when applied as a preprocessing step, can substantially simplify a Hamiltonian for subsequent analysis on quantum hardware. By design, these transformations can be identified and applied efficiently using purely classical resources. In practice, these transformations allow us to shorten requisite physical circuit-depths, overcoming constraints imposed by imperfect near-term hardware. Importantly, the quality of our transformations is $tunable$: we define a 'ladder' of transformations that yields increasingly simple Hamiltonians at the cost of more classical computation. Using quantum chemistry as a benchmark application, we demonstrate that our protocol leads to significant performance improvements for zero and finite temperature free energy calculations on both digital and analog quantum hardware. Specifically, our energy estimates not only outperform traditional Hartree-Fock solutions, but this performance gap also consistently widens as we tune up the quality of our transformations. In short, our quantum information-based approach opens promising new pathways to realizing useful and feasible quantum chemistry algorithms on near-term hardware. 

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2. Differentiable Analog Quantum Computing for Optimization and Control

   Leng, Jiaqi; Peng, Yuxiang; Qiao, Yi-Ling; Lin, Ming; Wu, Xiaodi (January 2022, Advances in neural information processing systems)

   We formulate the first differentiable analog quantum computing framework with specific parameterization design at the analog signal (pulse) level to better exploit near-term quantum devices via variational methods. We further propose a scalable approach to estimate the gradients of quantum dynamics using a forward pass with Monte Carlo sampling, which leads to a quantum stochastic gradient descent algorithm for scalable gradient-based training in our framework. Applying our framework to quantum optimization and control, we observe a significant advantage of differentiable analog quantum computing against SOTAs based on parameterized digital quantum circuits by {\em orders of magnitude}. 

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3. Expressive quantum perceptrons for quantum neuromorphic computing

   https://doi.org/10.1088/2058-9565/ad9fa4  

   Bravo, Rodrigo Araiza; Patti, Taylor L; Najafi, Khadijeh; Gao, Xun; Yelin, Susanne F (January 2025, Quantum Science and Technology)

   Abstract Quantum neuromorphic computing (QNC) is a sub-field of quantum machine learning (QML) that capitalizes on inherent system dynamics. As a result, QNC can run on contemporary, noisy quantum hardware and is poised to realize challenging algorithms in the near term. One key issue in QNC is the characterization of the requisite dynamics for ensuring expressive quantum neuromorphic computation. We address this issue by adapting previous proposals of quantum perceptrons (QPs), a quantum version of a simplistic model for neural computation, to the QNC setting. Our QPs compute based on the analog dynamics of interacting qubits with tunable coupling constants. We show that QPs are, with restricted resources, a quantum equivalent to the classical perceptron, a simple mathematical model for a neuron that is the building block of various machine learning architectures. Moreover, we show that QPs are theoretically capable of producing any unitary operation. Thus, QPs are computationally more expressive than their classical counterparts. As a result, QNC architectures built using our QPs are, theoretically, universal. We introduce a technique for mitigating barren plateaus in QPs called entanglement thinning. We demonstrate QPs’ effectiveness by applying them to numerous QML problems, including calculating the inner products between quantum states, energy measurements, and time reversal. Finally, we discuss potential implementations of QPs and how they can be used to build more complex QNC architectures such as quantum reservoir computers. 

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4. Practical verification protocols for analog quantum simulators

   https://doi.org/10.1038/s41534-021-00380-8  

   Shaffer, Ryan; Megidish, Eli; Broz, Joseph; Chen, Wei-Ting; Häffner, Hartmut (December 2021, npj Quantum Information)

   Abstract Analog quantum simulation is expected to be a significant application of near-term quantum devices. Verification of these devices without comparison to known simulation results will be an important task as the system size grows beyond the regime that can be simulated classically. We introduce a set of experimentally-motivated verification protocols for analog quantum simulators, discussing their sensitivity to a variety of error sources and their scalability to larger system sizes. We demonstrate these protocols experimentally using a two-qubit trapped-ion analog quantum simulator and numerically using models of up to five qubits. 

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5. Benchmarking highly entangled states on a 60-atom analogue quantum simulator

   https://doi.org/10.1038/s41586-024-07173-x  

   Shaw, Adam L.; Chen, Zhuo; Choi, Joonhee; Mark, Daniel K.; Scholl, Pascal; Finkelstein, Ran; Elben, Andreas; Choi, Soonwon; Endres, Manuel (April 2024, Nature)

   Abstract Quantum systems have entered a competitive regime in which classical computers must make approximations to represent highly entangled quantum states^1,2. However, in this beyond-classically-exact regime, fidelity comparisons between quantum and classical systems have so far been limited to digital quantum devices^2–5, and it remains unsolved how to estimate the actual entanglement content of experiments⁶. Here, we perform fidelity benchmarking and mixed-state entanglement estimation with a 60-atom analogue Rydberg quantum simulator, reaching a high-entanglement entropy regime in which exact classical simulation becomes impractical. Our benchmarking protocol involves extrapolation from comparisons against an approximate classical algorithm, introduced here, with varying entanglement limits. We then develop and demonstrate an estimator of the experimental mixed-state entanglement⁶, finding our experiment is competitive with state-of-the-art digital quantum devices performing random circuit evolution^2–5. Finally, we compare the experimental fidelity against that achieved by various approximate classical algorithms, and find that only the algorithm we introduce is able to keep pace with the experiment on the classical hardware we use. Our results enable a new model for evaluating the ability of both analogue and digital quantum devices to generate entanglement in the beyond-classically-exact regime, and highlight the evolving divide between quantum and classical systems. 

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