Fall 2024

Abstract: We analyse the entanglement structure of states generated by random constant-depth two-dimensional quantum circuits, followed by projective measurements of a subset of sites. By deriving a rigorous lower bound on the average entanglement entropy of such post-measurement states, we prove that macroscopic long-ranged entanglement is generated above some constant critical depth in several natural classes of circuit architectures, which include brickwork circuits and random holographic tensor networks.

Abstract: Between NISQ (noisy intermediate scale quantum) approaches without any proof of robust quantum advantage and fully fault-tolerant quantum computation, we propose a scheme to achieve a provable superpolynomial quantum advantage (under some widely accepted complexity conjectures) that is robust to noise with minimal error correction requirements. We choose a class of sampling problems with commuting gates known as sparse IQP (Instantaneous Quantum Polynomial-time) circuits and we ensure its fault-tolerant implementation by introducing the tetrahelix code.

Abstract: TBD

Please make sure you sign up for the seminar even if you are not getting pizza afterwards.  Pizza and drinks will be served after the seminar in ATL 2117.*

Abstract: Arrays of gate-defined semiconductor quantum dots are among the leading candidates for building scalable quantum processors. 

High-fidelity initialization, control, and readout of spin qubit registers require exquisite and targeted control over key Hamiltonian parameters that define the electrostatic environment. 

However, due to the tight gate pitch, capacitive crosstalk between gates hinders independent tuning of chemical potentials and interdot couplings. 

Abstract: We discuss recent progress on entanglement catalysis, including the equivalence between catalytic and asymptotic transformations of quantum states and the impossibility to distill entanglement from states having positive partial transpose, even in the presence of a catalyst. A more general notion of catalysis is the concept of entanglement battery. In this framework, we show that a reversible manipulation of entangled states is possible.

Abstract: We show that there exists a unitary quantum oracle relative to which quantum commitments exist but no (efficiently verifiable) one-way state generators exist. Both have been widely considered candidates for replacing one-way functions as the minimal assumption for cryptography—the weakest cryptographic assumption implied by all of computational cryptography. Recent work has shown that commitments can be constructed from one-way state generators, but the other direction has remained open.

Abstract: A Landau level (which is a flat band) forms only when a magnetic flux with non-zero total flux threads a system. In fact the degeneracy at the flat band is proportional to the flux. So no flat band can form when the magnetic flux averages to zero. We will discuss this and then show otherwise. This is relevant to time reversal symmetric systems that form flat bands such as magic-angle twisted bilayer graphene. In this talk the magic behind those systems will be revealed through the simplest model that gives rise to magical behaviour.

We utilize a notion of "combinatorial gauge symmetry", where the gauge symmetry involves not just local rotations of spins, but also permutations of spins. This allows the construction of exact gauge invariant Hamiltonians using just two-body interactions. Models constructed in this way include the toric code and any Abelian and Non-Abelian generalization.  New models also emerge in this paradigm. An advantage of the exact symmetry: the topological energy gaps need not be limited to a perturbative regime, but could potentially persist for a wider range of parameters.

Abstract: To implement arbitrary quantum interactions in architectures with restricted topologies, one may simulate all-to-all connectivity by routing quantum information. Therefore, it is of natural interest to find optimal protocols and lower bounds for routing. We consider a connectivity graph, G, of 2 regions connected only through an intermediate region of a small number of qubits that form a vertex bottleneck.