Not all operators can be prepared as vectorized operators on a QC efficiently - otherwise we'd be able to solve very hard problems. In our work, we vectorize time-evolved Heisenberg operators, which is efficient when U and U^dag can be quantum-simulated efficiently 🙂
Huge thanks to my amazing colleague and supervisors at EPFL (@aangrisani.bsky.social, @qzoeholmes.bsky.social , @gppcarleo.bsky.social) for making my first paper as a PhD here possible. Feel free to contact me e.g. via email 🙂
We also illustrate how it can be experimentally implemented on existing quantum devices featuring 2D connectivity, to simulate a Hamiltonian with 2D connectivity.
This would enable studies of operator growth/hydrodynamics using quantum computers.
With this framework, we unify/formalize many existing protocols (e.g. for computing OTOCs), and obtain new/improved algorithms for other tasks. C.f. the paper for precise complexities.
In fact, any Heisenberg-picture task can be converted to a Schrodinger-picture task, and thus solved on QCs!
The question: can quantum computers also do the same?
The answer turns out to be yes!
We achieve this via the vectorization map, which treats operators as quantum states living in a doubled Hilbert space. This encoding is also very natural on quantum computers, preserving entanglement and magic.
Many physically interesting phenomena can be defined/studied naturally in the Heisenberg picture. For example, classical numerical methods based on Pauli propagation and Matrix Product Operators (MPO) work "natively" in the Heisenberg picture by evolving operators instead of quantum states.
Excited to share about our work on quantum simulation and algorithms, just out on arXiv!
📜 Scirate link here: scirate.com/arxiv/2602.2...
In a nutshell: we show how quantum computers can be used to perform (quantum) simulations in the Heisenberg picture naturally.
