Junction X OP Pohjola: QSVT4CRA — silver#

Date:

2026-06-09

Tags:

quantum, hackathon, junction, op-pohjola, var, qsvt, npe, factor-copula, sbi

Original post:

LinkedIn

My first time in the quantum world — and we took 2nd place on Junction X OP Pohjola’s challenge with QSVT4CRA: a Quantum Singular Value Transformation pipeline for Value-at-Risk estimation that fuses amortised Bayesian inference with a quantum block-encoding of the learned factor-copula.

This note preserves the LinkedIn write-up and adds a small amount of context. The team, in full: Milla Kolehmainen, Antti Nurminen, Silja Heiskanen — and huge credit to mentor Juha Vesanto.

The LinkedIn post#

I spent the weekend knee-deep in the quantum world, first time for me, and we won 2nd place on Junction X OP Pohjola’s challenge! It couldn’t have been possible without my team Milla Kolehmainen, Antti Nurminen, Silja H. and mentors such as the amazing Juha Vesanto.

We approached the challenge from a real problem: banks like OP run ~10k Monte Carlo simulations daily to estimate tail-risk, VaR and CVaR for different portfolios and assets. Current classical methods:

  1. Scale poorly to higher dimensions O(N·d·exp{c·d})

  2. Have slow error decay O(sqrt{1/N}).

While advanced classical methods such as HMC and SVI offer benefits over the traditional MC we wanted to research if going quantum-native could offer a speedup. We researched Quantum Singular Value Transformations and Quantum Amplitude Estimation for scalable VaR estimation for capital planning and stress testing. We found:

  • Standard QAE requires k expensive ancilla qubits for k assets.

  • QSVT operates updates on single ancilla qubit but produces deeper circuits.

  • State loading eats up all of the quantum advantage if done poorly: k assets get encoded to 2^k amplitudes.

  • Pre-calculated distributions (that would amortize state-prep) such as Gaussian Conditional Independence models scale poorly to Out-of-Distribution regimes (market shocks).

Our pipeline:

  • Train NPE over different regimes to output posterior samples for factor-copula given some data.

  • Block-encode factor-copula params (output of single forward pass on trained NPE) to QSVT unitary.

  • Compile circuit, and run QAE to output VaR+CVaR.

We were able to run our pipeline for a 12-asset portfolio on real IBM hardware (Boston) with ~10% error on VaR estimate. The error is due to decoherence and compounding gate error. Our work is fully open-source and documented in the project repo.

The Heron r3 scaling study#

The chart below is the headline result — a VaR-95 tail-estimate error sweep on IBM Heron r3 as the QSVT polynomial degree grows from 2 to 32, holding the shot budget fixed at 12 repetitions × 4096 shots per degree.

Heron r3 posterior degree-vs-error

Heron r3 VaR-95 tail-estimate error vs QSVT polynomial degree. Error rises with degree and circuit depth, peaking around ~11% at degree 20; the green dashed line is the ideal target (zero error). The right axis shows the transpiled circuit depth growing roughly linearly in degree.#

Honest read: the pipeline runs end-to-end on a real superconducting QPU, but VaR-95 error scales with circuit depth in the regime we tested. Improving the depth-error tradeoff — better state-loading, shallower polynomials, or error mitigation — is the obvious next step.

What carried over from the rest of the work#

The factor-copula + amortised-Bayes framing is the same trick that anchors StimIQ and EASE Health: encode the structure you understand into a forward model, sample parameters from a posterior, and let the downstream algorithm consume those samples. Here the downstream algorithm is a QSVT unitary rather than a clinician-facing optimisation, but the epistemics are the same.

The formal companion to this work is the Lean 4 / Fable 5 proof that any copula vertex lifts to a quantum circuit in O(d²) two-qubit gates. Together, the empirical pipeline (this note) and the formal bound close the copula-to-quantum loop.