I've spent the beginning of the summer in Beijing (China), on a conference on "The Frontiers of Quantum Matter", and currently on Stockholm (Sweden) on another conference with title "Entanglement Dynamics: Open Quantum Systems, Monitored Circuits, and Topological Order". A moment on which to exchange ideas and fervent discussions, socialize with other physicists and update each other about our most recent accomplishments, and in many cases, failed attempts. On both occasions I talked about an ongoing unfinished work I will tell you about on a future post.  

In this post I will rather focus on the informal discussion we had last Friday on the use of quantum computers for quantum many body physics (I won't mentioned names to respect people's privacy). Our facilitator asked us (among other questions) the following one: "If you had 10k (say logical) qubits tomorrow, what would you do with them?". This is a question that often comes up in panel discussions of this type, but unlike in other occasions, the crew were mostly (perhaps only!) physicists with a condensed matter background. One suggested option was quantum chemistry. Then we briefly discussed whether we should care that these problems are rigorously proven to be classically hard or not. This time though I had an answer: I would start revisiting those assumptions we once had to assume to make progress, e.g., the Born Oppenheimer approximation, scaling up the system one qubit at a time and in various scenarios to see when it breaks down. At the end of the day, we are physicists who want to unerstand how Nature works (I was then bold to think that the book by Ashcroft and Mermin on solid state physics, should have many similar such examples). And as a second use case, and once the lattice gauge theory simulations community works out how to deal with the gauge fields in a quantum simulator, the phase diagram of quantum chromodynamics in those regimes of temperature and barionic density for which no other classical method appears to work and for which we still lack a clear understanding (such an advantage is also expected to be the case for quantum dynamics).

After we finished this discussion it occurred to me, can we provide a list of well defined open problems in quantum many body physics for which we believe (beyond rigorous proofs) that a quantum computer would make a difference? And what about those problems for which we don't expect that even a quantum computer could help us?

Now, I need to start packing.