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1. Quantum approximate optimization of the long-range Ising model with a trapped-ion quantum simulator

   https://doi.org/10.1073/pnas.2006373117  

   Pagano, Guido; Bapat, Aniruddha; Becker, Patrick; Collins, Katherine S.; De, Arinjoy; Hess, Paul W.; Kaplan, Harvey B.; Kyprianidis, Antonis; Tan, Wen Lin; Baldwin, Christopher; et al (October 2020, Proceedings of the National Academy of Sciences)

   null (Ed.)

   Quantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly improving performance for solving exponentially hard problems, such as optimization and satisfiability. Here, we report the implementation of a low-depth Quantum Approximate Optimization Algorithm (QAOA) using an analog quantum simulator. We estimate the ground-state energy of the Transverse Field Ising Model with long-range interactions with tunable range, and we optimize the corresponding combinatorial classical problem by sampling the QAOA output with high-fidelity, single-shot, individual qubit measurements. We execute the algorithm with both an exhaustive search and closed-loop optimization of the variational parameters, approximating the ground-state energy with up to 40 trapped-ion qubits. We benchmark the experiment with bootstrapping heuristic methods scaling polynomially with the system size. We observe, in agreement with numerics, that the QAOA performance does not degrade significantly as we scale up the system size and that the runtime is approximately independent from the number of qubits. We finally give a comprehensive analysis of the errors occurring in our system, a crucial step in the path forward toward the application of the QAOA to more general problem instances. 

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2. Massively parallel probabilistic computing with sparse Ising machines

   Aadit Navid Anjum; Grimaldi Andrea; Carpentieri Mario; Theogarajan Luke; Martinis John; Finocchio Giovanni; Camsari Kerem (June 2022, Nature electronics)

   Solving computationally hard problems using conventional computing architectures is often slow and energetically inefficient. Quantum computing may help with these challenges, but it is still in the early stages of development. A quantum-inspired alternative is to build domain-specific architectures with classical hardware. Here we report a sparse Ising machine that achieves massive parallelism where the flips per second—the key figure of merit—scales linearly with the number of probabilistic bits. Our sparse Ising machine architecture, prototyped on a field-programmable gate array, is up to six orders of magnitude faster than standard Gibbs sampling on a central processing unit, and offers 5–18 times improvements in sampling speed compared with approaches based on tensor processing units and graphics processing units. Our sparse Ising machine can reliably factor semi-primes up to 32 bits and it outperforms competition-winning Boolean satisfiability solvers in approximate optimization. Moreover, our architecture can find the correct ground state, even when inexact sampling is made with faster clocks. Our problem encoding and sparsification techniques could be applied to other classical and quantum Ising machines, and our architecture could potentially be scaled to 1,000,000 or more p-bits using analogue silicon or nanodevice technologies. 

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3. Sampling Approximately Low-Rank Ising Models: MCMC meets Variational Methods

   Koehler, Frederic; Lee, Holden; Risteski, Andrej (January 2022, Proceedings of Thirty Fifth Conference on Learning Theory, PMLR)

   We consider Ising models on the hypercube with a general interaction matrix 𝐽, and give a polynomial time sampling algorithm when all but 𝑂(1) eigenvalues of 𝐽 lie in an interval of length one, a situation which occurs in many models of interest. This was previously known for the Glauber dynamics when \emph{all} eigenvalues fit in an interval of length one; however, a single outlier can force the Glauber dynamics to mix torpidly. Our general result implies the first polynomial time sampling algorithms for low-rank Ising models such as Hopfield networks with a fixed number of patterns and Bayesian clustering models with low-dimensional contexts, and greatly improves the polynomial time sampling regime for the antiferromagnetic/ferromagnetic Ising model with inconsistent field on expander graphs. It also improves on previous approximation algorithm results based on the naive mean-field approximation in variational methods and statistical physics. Our approach is based on a new fusion of ideas from the MCMC and variational inference worlds. As part of our algorithm, we define a new nonconvex variational problem which allows us to sample from an exponential reweighting of a distribution by a negative definite quadratic form, and show how to make this procedure provably efficient using stochastic gradient descent. On top of this, we construct a new simulated tempering chain (on an extended state space arising from the Hubbard-Stratonovich transform) which overcomes the obstacle posed by large positive eigenvalues, and combine it with the SGD-based sampler to solve the full problem. 

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4. Robust Effective Ground State in a Nonintegrable Floquet Quantum Circuit

   https://doi.org/10.1103/PhysRevLett.133.030401  

   Ikeda, Tatsuhiko N; Sugiura, Sho; Polkovnikov, Anatoli (July 2024, Physical Review Letters)

   An external periodic (Floquet) drive is believed to bring any initial state to the featureless infinite temperature state in generic nonintegrable isolated quantum many-body systems in the thermodynamic limit, irrespective of the driving frequency $\mathrm{\Omega }$. However, numerical or analytical evidence either proving or disproving this hypothesis is very limited and the issue has remained unsettled. Here, we study the initial state dependence of Floquet heating in a nonintegrable kicked Ising chain of length up to $L=30$with an efficient quantum circuit simulator, showing a possible counterexample: the ground state of the effective Floquet Hamiltonian is exceptionally robust against heating, and could stay at finite energy density even after infinitely many Floquet cycles, if the driving period is shorter than a threshold value. This sharp energy localization transition or crossover does not happen for generic excited states. The exceptional robustness of the ground state is interpreted by (i) its isolation in the energy spectrum and (ii) the fact that those states with $L$-independent $\hslash \mathrm{\Omega }$energy above the ground state energy of any generic local Hamiltonian, like the approximate Floquet Hamiltonian, are atypical and viewed as a collection of noninteracting quasiparticles. Our finding paves the way for engineering Floquet protocols with finite driving periods realizing long-lived, or possibly even perpetual, Floquet phases by initial state design. Published by the American Physical Society2024 

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5. Momentum-exchange interactions in a Bragg atom interferometer suppress Doppler dephasing

   https://doi.org/10.1126/science.adi1393  

   Luo, Chengyi; Zhang, Haoqing; Koh, Vanessa_P W; Wilson, John D; Chu, Anjun; Holland, Murray J; Rey, Ana Maria; Thompson, James K (May 2024, Science)

   Large ensembles of laser-cooled atoms interacting through infinite-range photon-mediated interactions are powerful platforms for quantum simulation and sensing. Here we realize momentum-exchange interactions in which pairs of atoms exchange their momentum states by collective emission and absorption of photons from a common cavity mode, a process equivalent to a spin-exchange or XX collective Heisenberg interaction. The momentum-exchange interaction leads to an observed all-to-all Ising-like interaction in a matter-wave interferometer. A many-body energy gap also emerges, effectively binding interferometer matter-wave packets together to suppress Doppler dephasing in analogy to Mössbauer spectroscopy. The tunable momentum-exchange interaction expands the capabilities of quantum interaction–enhanced matter-wave interferometry and may enable the realization of exotic behaviors, including simulations of superconductors and dynamical gauge fields. 

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