Quantum Monte Carlo

You’re an insurer pricing hurricane coverage in Florida.

You have 50 years of historical hurricane data. You want to know the probability of a loss exceeding $10 billion in any given year – the tail you’re pricing into your premium.

Classical Monte Carlo: run 1,000,000 simulated hurricane seasons sampled from that historical distribution. Maybe 47 of them exceed $10 billion. Your estimate: 0.0047%. But is that right? With only 47 hits out of a million you still have substantial sampling error. To halve that error you need four million runs.

Quantum amplitude estimation works like this with a probability distribution. Instead of sampling the distribution repeatedly to build up a picture, it encodes the entire distribution into quantum superposition and extracts the amplitude – the probability – directly. Instead of estimating a probability by sampling it millions of times, quantum amplitude estimation encodes the entire probability distribution as a quantum wave and reads the answer directly from its interference pattern – which converges on the true value four times faster for the same number of ‘runs’.

Quantum Monte Carlo: therefore achieves the same error reduction with one million runs that classical needs four million to match. For a tail probability this small, that difference in precision can shift your premium materially – which on a $50 billion book of business is real money.

The value proposition crossover is: at what point does the cost premium of quantum hardware become less than the corporate EVA gain from more accurate tail pricing?

Your best classical estimate of the catastrophic loss probability carries an unavoidable margin of error. On a $50 billion book of hurricane exposure, that margin of error translates directly into $5m of premium you might be charging too much or too little. Quantum Monte Carlo cuts that margin in half – which means $2.5m of pricing risk taken off the table. If your estimate is wrong by that margin, you’re either leaving $2.5m on the table in underpriced premium, or overcharging and losing business to a competitor who has a better number. Quantum gives you the better number.

But what does the classical alternative actually cost? Four million GPU runs across ten major insurance classes – hurricane, earthquake, flood, wildfire, etc – runs to perhaps $500,000 annually at current cloud compute rates. Quantum needs to beat that cost while delivering the precision gain. The total value on offer is $500,000 in classical compute avoided plus $25m in pricing risk recovered across the book. The crossover question is simply: can quantum do this workload for less than $0.5m per year? At current quantum cloud pricing, no. In five years, plausibly yes.

That’s the crossover calculation. Not a question of quantum being generally cheaper – it’s a question of whether the EVA gain from tail precision on a large enough book exceeds the quantum hardware cost. For a top-ten global reinsurer, that number is already interesting.

If and when the costs are comparable I would go with Quantum because there’s more upside and future in it.

But a quantum computer doesn’t return a definite answer. When you measure a qubit, the act of measurement collapses the superposition – you get a 0 or a 1, probabilistically. Run the identical circuit twice and you may get different answers both times.

So you run the same circuit thousands of times, collect the distribution of outcomes, and infer the answer statistically from that distribution (shit eh?). The quantum result is always an average over many shots, never a single deterministic read. And it always has implied error in it.

This is fundamentally different from a classical computer, which runs a calculation once and returns the same answer every time.