Program with Abstracts > Thursday AM

A unifying account of warm start guarantees for patches of quantum landscapes 

Hela Mhiri et al. (LIP6 - EPFL)    —  Th 10:00-10:30

Barren plateaus are fundamentally a statement about quantum loss landscapes on average but there can, and generally will, exist patches of barren plateau landscapes with substantial gradients. Previous work has studied certain classes of parameterized quantum circuits and found example regions where gradients vanish at worst polynomially in system size. Here we present a general bound that unifies all these previous cases and that can tackle physically-motivated ansätze that could not be analyzed previously. Concretely, we analytically prove a lower-bound on the variance of the loss that can be used to show that in a non-exponentially narrow region around a point with curvature the loss variance cannot decay exponentially fast. This result is complemented by numerics and an upper-bound that suggest that any loss function with a barren plateau will have exponentially vanishing gradients in any constant radius subregion. Our work thus suggests that while there are hopes to be able to warm-start variational quantum algorithms, any initialization strategy that cannot get increasingly close to the region of attraction with increasing problem size is likely inadequate.

Quantum Circuit Optimization with Differentiable Projected Entangled Pair States for Ground State Preparation

Baptiste Anselme Martin  (Eviden)    — Th 11:00-11:30

The interplay between quantum computers and tensor networks have been increasingly popular, and can provide pathways to overcome difficult problems inherent to quantum algorithms, such as preparing relevant initial states for further computations. In this work, we utilize tensor networks to optimize quantum circuits for ground state preparation. Specifically, we employ differentiable Projected Entangled Pair States (PEPS) across various topologies to simulate and optimize parameterized quantum circuits for model Hamiltonians. Our approach enables the preparation of ground states with high energy accuracy, even for large qubit systems and connectivities that are beyond one dimension. Furthermore, we demonstrate that PEPS-based optimization may help mitigate the barren plateau phenomenon by providing a warm-start initialization with enhanced gradient magnitudes. We believe this work pushes the potential of quantum computing by leveraging classical pre-processing for both NISQ experiments and FT algorithms and helps to identify which tasks are best suited for classical or quantum resources.

Optimal permutation generation with local quantum gates for quadratic assignment problems

Dylan Laplace Mermoud  (ENSTA)      — Th 11:30-12:00

In this talk, we present a quantum algorithm that generates all permutations that can be spanned by one- and two-qubits permutation gates, which can be directly read as an output of the circuit. The construction of the circuits follows from group-theoretical results, most importantly the Bruhat decomposition of the group generated by CNOT gates. We next use the longest Coxeter word of the Bruhat order of the symmetric group, and assemble everything be leveraging the properties of the presentations of semidirect products of nicely presented groups. The circuits obtained are of linear depth and quadratic size. We use these circuits to build ansatze to tackle optimization problems such as quadratic assignment problems, and two of their refinements, graph isomorphism and heaviest k-subgraph problems. We finally present some results about the performance of the algorithm on the instances of the QAPLib obtained via simulation.

Roundtable  featuring session speakers   —  Th  12:00-12:30