Quantum Simulation Informed by Physical Structure

Abstract

Quantum simulation provides a route to studying the real-time dynamics of strongly correlated quantum many-body systems beyond the reach of classical computation. This thesis focuses on two central obstacles that limit its practical utility: the high cost of implementing the required quantum circuits and the challenge of verifying their output in regimes where classical benchmarks are unavailable. Both issues are addressed by exploiting structure, either through prior physical knowledge of the target system or through special properties of selected quantum states, to reduce simulation overhead and to develop new techniques for quantum verification. The background on which this work rests is assembled first: why classical simulation of quantum many-body systems is hard, why a quantum approach built on real-time evolution offers a way past these barriers, and the recurring tools the thesis relies on, including the thermalization of isolated quantum systems, the stabilizer formalism, and lattice gauge theories. Next, known structure is exploited to reduce the cost of computing spectral densities and response functions, quantities at the heart of the description of nuclear reactions. Recasting the Gaussian integral transform of the response in a Fourier basis turns the moments that determine the spectrum into expectation values of real-time evolution, measurable directly on a quantum computer. Prior knowledge of the low-order energy moments, the mean and variance, then allows the transform to be centered and rescaled so that far fewer evolution times are needed to resolve the response.

Turning from exploiting structure to discovering it, an exactly solvable form of weak ergodicity breaking is identified. In a 2+1-dimensional Z2 lattice gauge theory, a family of quantum many-body scars is shown to be composed entirely of stabilizer states. These scars carry exactly zero magic and exactly zero distillable entanglement, making them classically simple by both resource measures even as they sit within otherwise thermalizing, classically intractable dynamics, and their anomalous behavior is traced to an underlying commutant algebra.

This structure is then put to work as a verification tool. Because the stabilizer scars span a small, dynamically isolated subspace, their evolution can be computed exactly by classical means, and bounds on their non-stabilizerness ensure efficient direct fidelity estimation. Together these properties yield a self-contained and scalable benchmark: the measured fidelity of the scar states, compared against their exact classical prediction, quantifies the accuracy of the simulator and in turn bounds the fidelity of the genuinely intractable, non-scar dynamics run on the same device. The result is a concrete strategy for benchmarking quantum simulation at scale, in the regime where a classical check would otherwise be unavailable.

Finally, these results are drawn together, reflecting on what the shared strategy of exploiting structure achieves and where its limits lie, and sketching directions for extending it to richer systems and harder simulation tasks.