Daan Camps

Quantum algorithms exploiting real-time evolution under a target Hamiltonian have demonstrated remarkable efficiency in extracting key spectral information. However, the broader potential of these methods, particularly beyond ground-state calculations, is underexplored. In this work, we introduce the framework of multiobservable dynamic mode decomposition (MODMD), which combines the observable dynamic mode decomposition (DMD), a measurement-driven eigensolver tailored for near-term implementation, with classical shadow tomography. MODMD leverages random scrambling in the classical shadow technique to construct, with exponentially reduced resource requirements, a signal subspace that encodes rich spectral information. Notably, we replace typical Hadamard-test circuits with a protocol designed to predict low-rank observables, thereby broadening the use of classical shadow tomography for predicting many low-rank observables. We establish theoretical guarantees on the spectral approximation from MODMD, taking into account distinct sources of error. In the ideal case, we prove that the spectral error scales as exp  ( − Δ E t max ) , where Δ E is the Hamiltonian spectral gap and t max is the maximal simulation time. This analysis provides a rigorous justification of the rapid convergence observed across simulations. To demonstrate the utility of our framework, we consider its application to fundamental tasks, such as determining the low-lying, i.e., ground or excited, energies of representative many-body systems. Our work paves the path for efficient designs of measurement-driven algorithms on near-term and early fault-tolerant quantum devices.

Unitary designs are widely used in quantum computation, but in many practical settings it suffices to construct a diagonal state design generated with unitary gates diagonal in the computational basis. In this work, we introduce a simple and efficient diagonal state 3-design based on real-time evolutions under 2-local Hamiltonians. Our construction is inspired by the classical Girard-Hutchinson trace estimator in that it involves the stochastic preparation of many random-phase states. Though the exact Girard-Hutchinson states are not tractably implementable on a quantum computer, we can construct states that match the statistical moments of the Girard-Hutchinson states with real-time evolution. Importantly, our random states are all generated using the same Hamiltonians for real-time evolution, with the randomness arising solely from stochastic variations in the durations of the evolutions. In this sense, the circuit is fully reconfigurable and thus suited for near-term realizations on both digital and analog platforms. Moreover, we show how to extend our construction to achieve diagonal state designs of arbitrarily high order.

The Kibble-Zurek mechanism quantifies defect formation during adiabatic passage across a continuous phase transition, providing key insights into universality in quantum many-body systems. We explore counting statistics of defects in adiabatic passage experiments on long 1D Rydberg atom chains. The experiments reveal an anomaly in the defect number distribution at long ramp times, challenging the hypothesis of defect formation through independent domain mergers. Numerical simulations confirm the anomaly and suggest its link to non-critical coarsening dynamics, which we suppress in prepare-and-hold experiments. Our results highlight the ability of quantum simulators to uncover unexpected correlated quantum phenomena.

Randomized quantum algorithms have been proposed in the context of quantum simulation and quantum linear algebra with the goal of constructing shallower circuits than methods based on block encodings. While the algorithmic complexities of such randomized schemes have been shown to be suboptimal, it has been speculated that they may offer benefits in the early fault-tolerant era where circuit depth comes at a premium. In this work, we investigate the end-to-end resource requirements for a randomized quantum linear systems solver to estimate scalar properties of the matrix inverse by combining sampling from a Fourier series with Hamiltonian simulation. We derive explicit bounds on all relevant algorithmic parameters that control the total error. We analyze two algorithmic kernels for Hamiltonian simulation: a second order product formula approximation and a method called random Taylor expansion (RTE). Finally, we provide numerical demonstrations that confirm the validity of our analytical results and question the actual practicality of the randomized Fourier series-based approach for linear systems problems as we show that the sampling complexity can grow exponentially. By providing explicit bounds, our work serves as a bridge between theoretical algorithmic proposals and efficient hardware implementations while also enabling fair comparisons to alternative algorithms that exhibit optimal asymptotic complexities at the cost of large resource overheads.

The dynamics of isolated quantum systems following a sudden quench plays a central role in many areas of material science, high-energy physics, and quantum chemistry. Featuring complex phenomena with implications for thermalization, non-equilibrium phase transitions, and Floquet phase engineering, such far-from-equilibrium quantum dynamics is challenging to study numerically, in particular, in high-dimensional systems. Here, we use a programmable neutral atom quantum simulator to systematically explore quench dynamics in spin models with up to 180 qubits. By initializing the system in a product state and performing quenches across a broad parameter space, we discover several stable, qualitatively distinct dynamical regimes. We trace their robustness to Floquet-like prethermal steady states that are stabilized over long emergent timescales by strong dynamical constraints. In addition, we observe sharp peaks in the dynamical response that are quantitatively explained by the structured melting of prethermalization through resonances. In two dimensions, we uncover a sharp dynamical response change that converges with increased system size, that is linked to the proliferation of Néel-order defects and indicative of a dynamical phase transition with no equilibrium analogs. Uncovering an intricate interplay between quantum prethermalization and emergent dynamical phases, our results demonstrate the use of quantum simulators for revealing complex non-equilibrium quantum many-body phenomena.

The 2024 Quantum Computing, Math and Physics Camp (QCaMP) for Students was a 4-week long summer camp aimed at introducing high school students to quantum concepts and careers, including applications spanning quantum computing, sensing, and communication. The program ran for 7 hours/day, Monday-Friday, July 1-26, and included hands-on modules and activities, professional development, and project-based learning. Here we provide details on the camp curriculum and outcomes based on pre and post knowledge and attitudes assessments.

We introduce QCLAB, an object-oriented MATLAB toolbox for constructing, representing, and simulating quantum circuits. Designed with an emphasis on numerical stability, efficiency, and performance, QCLAB provides a reliable platform for prototyping and testing quantum algorithms. For advanced performance needs, QCLAB++ serves as a complementary C++ package optimized for GPU-accelerated quantum circuit simulations. Together, QCLAB and QCLAB++ form a comprehensive toolkit, balancing the simplicity of MATLAB scripting with the computational power of GPU acceleration. This paper serves as an introduction to the package and its features along with a hands-on tutorial that invites researchers to explore its capabilities right away.