The Problem-Substrate Mapping: A Framework for Honest Computational Investment

In the paper's words

Phase IV of the Qubit Delusion series. Translates the critique into a concrete investment portfolio: matching computational problem classes (optimization, linear algebra, probabilistic inference, quantum simulation, cryptography, general-purpose) to optimal physical substrates (Ising machines, optical processors, neuromorphic, analog quantum simulators, reversible classical, fault-tolerant QC). Proposes a standardized five-question evaluation framework with red flags and green flags.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. Near-term investment thesis (1-3 years): Deploy neuromorphic processors for edge AI --- always-on sensing, keyword spotting, anomaly detection --- where the energy budget is severely constrained (microwatts to milliwatts).

   from 3.3 Neuromorphic and p-Bit Processors

2. Still --- a 10× to 100× improvement in the energy efficiency of general-purpose computation would be transformative.

   from 3.5 Reversible Classical Computing

3. Long-term investment thesis (7-15 years): Fund fundamental research in reversible and adiabatic computing as the long-term path to energy-efficient general-purpose computation.

   from 3.5 Reversible Classical Computing

4. Google's Willow processor (2024) demonstrated error correction below the surface-code threshold --- a genuine scientific achievement --- but at a scale (105 qubits) that is $10^{5}\times$ smaller than what is needed for useful computation.

   from 3.6 Fault-Tolerant Quantum Computing

5. Computational demands: For 2048-bit RSA, Shor's algorithm requires approximately 4,100 logical qubits and $10^{9}$ Toffoli gates.

   from 2.5 Cryptography and Number Theory

6. The answer, as of 2026, is: not in the next 15 years.

   from 2.5 Cryptography and Number Theory

How it is done

1. Shor's algorithm provides an exponential quantum speedup for these problems.

   from 2.5 Cryptography and Number Theory

2. Memristive neuromorphic systems remain at the research prototype stage but have demonstrated proof-of-concept matrix multiplication at ~10 fJ per operation.

   from 3.3 Neuromorphic and p-Bit Processors

3. Information is never erased except at final readout, so the Landauer bound is paid only once per computation, not once per operation.

   from 3.5 Reversible Classical Computing

4. The joules-per-solution crossover for Shor's algorithm on 2048-bit RSA is estimated at $\sim 10^{7}$ physical qubits, requiring a cryogenic infrastructure of unprecedented scale.

   from 3.6 Fault-Tolerant Quantum Computing

What would falsify it

1. Falsifiable milestones for each allocation.

   from 1. Introduction: From Critique to Portfolio

2. Any technology that cannot state a falsifiable joules-per-solution milestone: This is the acid test.

   from 4.4 What Is NOT in the Portfolio

3. (Not "conventional CMOS" --- the BEST classical alternative, including specialized hardware: FPGA, ASIC, reversible) What is the falsifiable milestone with a specific timeframe?

   from 5.1 The Five Questions

Where the claim stops

1. Approximately 45% goes to thermodynamic and analog computing (Ising machines, p-bit networks, analog quantum simulators), 25% to optical/photonic computing, 20% to neuromorphic, and only 5-10% to fault-tolerant quantum --- a near- inversion of the current allocation, where gate-model quantum computing absorbs roughly 60% of advanced computing investment.

   from 6. Conclusion: The Honest Portfolio

2. The honest portfolio does not promise exponential speedups or revolutionary new industries within five years.

   from 6. Conclusion: The Honest Portfolio

3. This is the one problem class where quantum physics provides a genuine, in-principle exponential advantage --- and it does not require fault tolerance, error correction, or universal gate sets.

   from 2.4 Quantum Simulation

Where to read

1. 1. Introduction: From Critique to Portfolio281 words · 1 min
2. 2. Problem Classes and Their Physical Signatures1,077 words · 5 min
3. 3. The Substrate Portfolio1,232 words · 5 min
4. 4. The Investment Portfolio534 words · 2 min
5. 5. The Evaluation Framework284 words · 1 min
6. 6. Conclusion: The Honest Portfolio393 words · 2 min