Bank for International Settlements working paper sets out a proof of concept for quantum posterior sampling in Bayesian inference

The Bank for International Settlements published a working paper exploring how quantum computation could be applied to Bayesian inference, including a proof-of-concept quantum algorithm for posterior sampling illustrated with Qiskit code in Python. The paper shows that Bayesian updating can be simulated by encoding a discretised posterior distribution into a quantum state and generating samples through measurement, while stressing that the approach does not yet deliver computational speedups over classical methods such as Markov Chain Monte Carlo, importance sampling or particle filtering. The proposed workflow computes the posterior distribution classically, including the normalisation constant, and then prepares an n-qubit quantum state whose measurement probabilities match the posterior across k = 2^n parameter values. A unitary operator is constructed to map the initial state into the target posterior-encoding state, and repeated preparation and measurement are used to estimate posterior expectations via Monte Carlo sampling, with a simulated example using six qubits and 10,000 measurement shots. The paper identifies quantum state preparation and current hardware constraints as central practical challenges, and frames the approach as groundwork for future research into more scalable state-preparation techniques and hybrid classical-quantum methods that could eventually make quantum-enabled Bayesian inference practical.