Quantum Information

Many quantum platforms naturally host Hamiltonians with power-law or even all-to-all connectivity, which may potentially process quantum information in a way much faster than conventional gate-based models. For such non-geometrically-local Hamiltonians, it is then important to both come up with fast protocols and understand the ultimate limit for realizing various information processing tasks. In this talk, I will first overview this quantum speed limit topic, and then dive into the particular task of quantum routing, i.e. permuting unknown quantum states on the qubits. I aim to show [1] a provably optimal Hamiltonian routing protocol on the star graph that is asymptotically faster than gate-based routing; [2] a lower bound on the time to realize the shift unitary using 1d power-law interactions which, perhaps surprisingly, can be much slower than the time for the conventional Lieb-Robinson light cone to spread across the whole system. The latter result shares interesting connections to the classification of 1d quantum cellular automata and symmetry-protected topological order.

---

Zoom link

Hamiltonian simulation of lattice gauge theories (LGTs) is a non-perturbative method of numerically solving gauge theories that offers novel avenues for studying scattering processes in gauge theories. With the advent of quantum computers, Hamiltonian simulation of LGTs has become a reality. Simulating scattering on quantum computers requires the preparation of initial scattering states in the interacting theory on the quantum hardware. Current state preparation methods involve bridging the scattering states in the free theory to the ones in the interacting theory adiabatically. Such quantum algorithms have limitations when applied to LGTs, and they tend to be computational resource intensive, rendering their implementation a challenge on the noisy intermediate-scale quantum (NISQ) era devices. In this work, we propose a wave packet state preparation algorithm for a 1+1D Z2 LGT coupled to dynamical matter. We show how this algorithm circumvents the adiabatic process by building and implementing the wave packet creation operators directly in the interacting theory using an optimized ansatz consisting of hadronic degrees of freedom in the confined Z2 LGT. Moreover, we numerically confirm the validity of this ansatz for a U(1) LGT in 1+1D. Finally, we demonstrate the viability of our algorithm for NISQ devices by comparing the classical simulation with the results obtained using the Quantinuum H1-1 quantum computer upon a simple symmetry-based noise mitigation technique.

---

Zoom link

Minimizing the energy of a many-body system is a fundamental problem in many fields. Although we hope a quantum computer can help us solve this problem better than classical computers, we have a very limited understanding of where a quantum advantage may be found. In this talk, I will present some recent theoretical advances that shed light on quantum advantages in this domain. First, I describe rigorous analyses of the Quantum Approximate Optimization Algorithm applied to minimizing energies of classical spin glasses. For certain families of spin glasses, we find the QAOA has a quantum advantage over the best known classical algorithms. Second, we study the problem of finding a local minimum of the energy of quantum systems. While local minima are much easier to find than ground states, we show that finding a local minimum under thermal perturbations is computationally hard for classical computers, but easy for quantum computers.

---

Zoom link TBA