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1. A Haskell Adiabatic DSL: Solving Classical Optimization Problems on Quantum Hardware

   https://doi.org/10.1145/3747521  

   Li, Liyi; Young, David; Graves, James Bryan; Dissanayake, Chandeepa; Sabry, Amr (August 2025, Proceedings of the ACM on Programming Languages)

   In physics and chemistry, quantum systems are typically modeled using energy constraints formulated as Hamiltonians. Investigations into such systems often focus on the evolution of the Hamiltonians under various initial conditions, an approach summarized as Adiabatic Quantum Computing (AQC). Although this perspective may initially seem foreign to functional programmers, we demonstrate that conventional functional programming abstractions—specifically, the Traversable and Monad type classes—naturally capture the essence of AQC. To illustrate this connection, we introduce EnQ, a functional programming library designed to express diverse optimization problems as energy constraint computations (ECC). The library comprises three core components: generating the solution space, associating energy costs with potential solutions, and searching for optimal or near-optimal solutions. Because EnQ is implemented using standard Haskell, it can be executed directly through conventional classical Haskell compilers. More interestingly, we develop and implement a process to compile EnQ programs into circuits executable on quantum hardware. We validate EnQ’s effectiveness through a number of case studies, demonstrating its capacity to express and solve classical optimization problems on quantum hardware, including search problems, type inference, number partitioning, clique finding, and graph coloring. 

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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 few 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. 

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3. Boosting quantum amplitude exponentially in variational quantum algorithms

   https://doi.org/10.1088/2058-9565/acf4ba  

   Kyaw, Thi Ha; Soley, Micheline B; Allen, Brandon; Bergold, Paul; Sun, Chong; Batista, Victor S; Aspuru-Guzik, Alán (October 2023, Quantum Science and Technology)

   Abstract We introduce a family of variational quantum algorithms, which we coin as quantum iterative power algorithms (QIPAs), and demonstrate their capabilities as applied to global-optimization numerical experiments. Specifically, we demonstrate the QIPA based on a double exponential oracle as applied to ground state optimization of theH₂molecule, search for the transmon qubit ground-state, and biprime factorization. Our results indicate that QIPA outperforms quantum imaginary time evolution (QITE) and requires a polynomial number of queries to reach convergence even with exponentially small overlap between an initial quantum state and the final desired quantum state, under some circumstances. We analytically show that there exists an exponential amplitude amplification at every step of the variational quantum algorithm, provided the initial wavefunction has non-vanishing probability with the desired state and that the unique maximum of the oracle is given by ${\lambda }_1>0$, while all other values are given by the same value $0<{\lambda }_2<{\lambda }_1$(hereλcan be taken as eigenvalues of the problem Hamiltonian). The generality of the global-optimization method presented here invites further application to other problems that currently have not been explored with QITE-based near-term quantum computing algorithms. Such approaches could facilitate identification of reaction pathways and transition states in chemical physics, as well as optimization in a broad range of machine learning applications. The method also provides a general framework for adaptation of a class of classical optimization algorithms to quantum computers to further broaden the range of algorithms amenable to implementation on current noisy intermediate-scale quantum computers. 

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4. Scalable neural quantum states architecture for quantum chemistry

   https://doi.org/10.1088/2632-2153/acdb2f  

   Zhao, Tianchen; Stokes, James; Veerapaneni, Shravan (June 2023, Machine Learning: Science and Technology)

   Abstract Variational optimization of neural-network representations of quantum states has been successfully applied to solve interacting fermionic problems. Despite rapid developments, significant scalability challenges arise when considering molecules of large scale, which correspond to non-locally interacting quantum spin Hamiltonians consisting of sums of thousands or even millions of Pauli operators. In this work, we introduce scalable parallelization strategies to improve neural-network-based variational quantum Monte Carlo calculations forab-initioquantum chemistry applications. We establish GPU-supported local energy parallelism to compute the optimization objective for Hamiltonians of potentially complex molecules. Using autoregressive sampling techniques, we demonstrate systematic improvement in wall-clock timings required to achieve coupled cluster with up to double excitations baseline target energies. The performance is further enhanced by accommodating the structure of resultant spin Hamiltonians into the autoregressive sampling ordering. The algorithm achieves promising performance in comparison with the classical approximate methods and exhibits both running time and scalability advantages over existing neural-network based methods. 

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5. Learning quantum symmetries with interactive quantum-classical variational algorithms

   https://doi.org/10.1088/1751-8121/ad5ee0  

   Lu, Jonathan Z; Araiza_Bravo, Rodrigo; Hou, Kaiying; Dagnew, Gebremedhin A; Yelin, Susanne F; Najafi, Khadijeh (July 2024, Journal of Physics A: Mathematical and Theoretical)

   Abstract A symmetry of a state $|\psi ⟩$is a unitary operator of which $|\psi ⟩$is an eigenvector. When $|\psi ⟩$is an unknown state supplied by a black-box oracle, the state’s symmetries provide key physical insight into the quantum system; symmetries also boost many crucial quantum learning techniques. In this paper, we develop a variational hybrid quantum–classical learning scheme to systematically probe for symmetries of $|\psi ⟩$with noa prioriassumptions about the state. This procedure can be used to learn various symmetries at the same time. In order to avoid re-learning already known symmetries, we introduce an interactive protocol with a classical deep neural net. The classical net thereby regularizes against repetitive findings and allows our algorithm to terminate empirically with all possible symmetries found. An iteration of the learning algorithm can be implemented efficiently with non-local SWAP gates; we also give a less efficient algorithm with only local operations, which may be more appropriate for current noisy quantum devices. We simulate our algorithm on representative families of states, including cluster states and ground states of Rydberg and Ising Hamiltonians. We also find that the numerical query complexity scales well for up to moderate system sizes. 

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