Papers › On sampling determinantal and Pfaffian point processes on a quantum computer
On sampling determinantal and Pfaffian point processes on a quantum computer
Rémi Bardenet, Michaël Fanuel, Alexandre Feller
DPPs were introduced by Macchi as a model in quantum optics the 1970s. Since then, they have been widely used as models and subsampling tools in statistics and computer science. Most applications require sampling from a DPP, and given their quantum origin, it is natural to wonder whether sampling a DPP on a quantum computer is easier than on a classical one. We focus here on DPPs over a finite state space, which are distributions over the subsets of {1,…,N} parametrized by an N×N Hermitian kernel matrix. Vanilla sampling consists in two steps, of respective costs 𝒪(N³) and 𝒪(Nr²) operations on a classical computer, where r is the rank of the kernel matrix. A large first part of the current paper consists in explaining why the state-of-the-art in quantum simulation of fermionic systems already yields quantum DPP sampling algorithms. We then modify existing quantum circuits, and discuss their insertion in a full DPP sampling pipeline that starts from practical kernel specifications. The bottom line is that, with P (classical) parallel processors, we can divide the preprocessing cost by P and build a quantum circuit with 𝒪(Nr) gates that sample a given DPP, with depth varying from 𝒪(N) to 𝒪(rlogN) depending on qubit-communication constraints on the target machine. We also connect existing work on the simulation of superconductors to Pfaffian point processes, which generalize DPPs and would be a natural addition to the machine learner's toolbox. In particular, we describe "projective" Pfaffian point processes, the cardinality of which has constant parity, almost surely. Finally, the circuits are empirically validated on a classical simulator and on 5-qubit IBM machines.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Tasks
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Methods
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections