Join us for the last Matter seminar of the year, given by Dr Roopayan Ghosh (IIT Bhubaneswar).
Continuous-time quantum algorithms provide a powerful paradigm for exploiting quantum dynamics in computation. In this talk, I will present two distinct approaches within this framework, spanning both adiabatic quantum annealing and coherent interference in Rydberg atom arrays. In the first part, I will focus on the adiabatic approach. Quantum annealing offers a promising route to quantum speedup for hard combinatorial optimization; however, its performance is typically hindered by exponentially small spectral gaps. I will show how catalyst Hamiltonians can mitigate this bottleneck. After contrasting the key mechanisms behind gap closures in conventional annealing, I will explain how non-stoquastic catalysts address one of these failure modes. I will then turn to the Maximum Weighted Independent Set problem and demonstrate that appropriately designed n-local catalysts can reopen the spectral gap and significantly enhance ground-state preparation. Building on the case of 2-local XX catalysts, I will illustrate how catalyst placement and structure can be tailored to general graph problems, and how these constructions translate efficiently into circuit-model implementations. Remarkably, such mappings lead to dramatic reductions in both gate counts and circuit depths compared with standard encodings. I will conclude this part by outlining prospects for realizing XX-type catalytic terms on near-term quantum hardware and a short discussion of how a shortcoming of such systems becomes useful for quantum sensing. In the second part, I will shift from adiabatic evolution to coherent interference phenomena, discussing our recent experimental-theoretical work on Rydberg atom quantum processors. Here, we demonstrated many-body temporal interference in systems of up to 100 atoms, far beyond traditional Landau Zener St¨uckelberg interference which is fundamentally single-body or few-body in nature. I will highlight how genuine many-body interactions qualitatively reshape the interference landscape, rendering simple PXP descriptions insufficient and revealing the crucial role of long-range interaction tails. By exploring different driving protocols and lattice geometries, we uncover striking dynamical features, including vacuum-state freezing. I will conclude by identifying emerging applications of these interference-based protocols for quantum control, sensing, and state preparation.