Classical inside Quantum: why replacement is theoretically plausible but practically impossible today

This text is just my thoughts out loud. I'm only a human being trying to analyze current information and imagine what might happen in the future. My thoughts could be completely wrong or might be just "noise" or they could be food for brainstorming about "what if..." scenarios.

If everything in the universe is fundamentally quantum, a perfect quantum computer could potentially simulate all of reality — including every classical computation ever conceived. So what's stopping us?

A deep-dive into physics, computation theory, and the engineering gap that separates what nature allows from what humans can build.

Reviewed & corrected edition — April 2026

The standard answer to "can quantum computing replace classical computing?" is a confident no. The standard reasons — fragility, error rates, the absence of a quantum operating system — are real and valid. But they miss something deeper. They answer an engineering question while ignoring a physics one.

The physics answer is more radical: classical computing is very likely contained inside quantum computation. It always was. The universe never ran on classical rules — we just built machines that approximated them well enough to be useful.

Everything is quantum, whether we model it that way or not

At the most fundamental level, reality is described by quantum mechanics. Matter is made of particles that behave as probability waves. Energy comes in discrete packets. Interactions are inherently probabilistic. Even the transistors in your laptop — the bedrock of classical computing — only work because of quantum tunneling and quantum band theory.

Classical physics is not a separate regime. It is an approximation that emerges from quantum physics when systems are large enough and warm enough that quantum effects average out. Newton's laws work beautifully at human scales not because nature switched to a different engine, but because the quantum fluctuations became statistically negligible.

This distinction matters enormously for how we think about computation.

"The universe computes itself quantum-mechanically. A perfect quantum computer would be the most faithful model of reality ever built — because it would speak the same language as nature itself."

— Paraphrasing David Deutsch's core thesis in The Fabric of Reality, 1997

Simulation equals computation — and the relationship is asymmetric

In computer science, if system A can perfectly simulate system B, then A can compute everything B computes. This is the foundation of computational universality, captured formally by the Church-Turing Thesis.

Now apply that to quantum and classical machines. The relationship is notably one-sided:

| Direction                      | Can it simulate? | Cost                                                                             |
|---                             |---               |---                                                                               |
| Quantum → Classical            | Yes, efficiently | Proven: P ⊆ BQP — no overhead                                                   |
| Classical → General quantum    | Yes, but at cost | Exponential slowdown for most circuits                                           |
| Classical → Restricted quantum | Yes, efficiently | Some quantum circuits (e.g. Clifford) are classically simulable in polynomial time |

The first point — that quantum can simulate classical efficiently — is formally proven. The complexity class P (classical) sits inside BQP (quantum). A quantum computer can replicate every classical operation without overhead.

The reverse is more nuanced. Not all quantum circuits are exponentially hard to simulate classically. Certain restricted families, such as Clifford circuits, can be efficiently simulated on a classical machine. It is specifically general, deep quantum circuits — those exploiting entanglement and interference at scale — that resist classical simulation and grow exponentially in cost.

What is proven:      P ⊆ BQP
                     (Classical is contained within Quantum)

What is conjectured: P ⊊ BQP
                     (Quantum is strictly more powerful than Classical)

The strict separation — the assumption that quantum offers
irreducible advantages — is one of the most important
open problems in computer science. It is not yet proven.

This is a critical distinction. We are highly confident that quantum computation is strictly more expressive than classical, and quantum algorithms like Shor's (factoring) and Grover's (search) demonstrate concrete advantages for specific problems. But a formal mathematical proof that no classical algorithm can match general quantum computation in principle does not yet exist.

So why haven't we replaced classical machines already?

Even setting aside the theoretical open question, the practical gap is enormous. The issue is engineering.

Qubits must be kept near absolute zero (−273°C) and isolated from every possible source of environmental interference. The moment a qubit interacts with its environment, it "decoheres" — it loses its quantum state and collapses into noise. A qubit's useful lifetime is currently measured in microseconds to milliseconds depending on the technology used.

Raw qubit count alone is a misleading metric. Different qubit technologies — superconducting, trapped-ion, neutral atom — differ dramatically in fidelity, coherence time, and scalability. In September 2025, a Caltech team demonstrated a 6,100-qubit neutral atom array, a record by count. Yet high-fidelity superconducting machines like Google Willow operate with around 105 qubits, prioritizing error rates over raw numbers. Both represent genuine progress toward different parts of the same challenge.

| Requirement                  | Theory needs   | Engineering has (2025–2026)                                                                       |
|---                           |---             |---                                                                                                |
| Fault-tolerant logical qubits | Millions      | ~100–6,100 physical qubits depending on platform; logical qubits still very limited              |
| Error rate per gate          | Near zero      | ~0.1–1% for most systems; best labs reaching ~0.0001% on single qubits                           |
| Operating temperature        | Near absolute zero | Requires entire lab infrastructure                                                            |
| Software ecosystem           | Full OS, compilers, apps | Early-stage; cloud access exists but full stack is embryonic                          |
| Cost to operate              | —              | Tens of millions of dollars per system                                                           |

The error problem is particularly severe. Today's quantum computers spend the majority of their physical qubits not on solving problems, but on error correction: many physical qubits are sacrificed to protect a handful of "logical" qubits that actually compute. Until this ratio improves dramatically, fault-tolerant quantum computing at scale remains out of reach.

An analogy: fusion knows no engineering

We have known since the 1950s that nuclear fusion can power a star. The physics is settled and beautiful. The engineering — sustaining a plasma hotter than the sun inside a machine on Earth — has taken seventy years and is still not commercially viable.

Quantum computing is in a similar position. The physics gives us permission. It tells us what is plausible in principle. Engineering is the long, expensive, painstaking work of making the plausible actual.

The correct statement is not "quantum cannot replace classical." It is: quantum cannot replace classical yet — and that "yet" carries enormous weight.

What happens when the engineering catches up?

If error-corrected, fault-tolerant quantum computers at scale ever arrive, the implications go far beyond faster computation. A machine that can efficiently simulate quantum systems could design drugs and materials at atomic resolution, model climate systems and protein folding with unprecedented fidelity, and break most current encryption while enabling new forms of cryptography.

But perhaps the deepest implication is philosophical. If simulation equals computation, and the universe evolves quantum-mechanically, then a perfect quantum computer would not merely model reality — it would be isomorphic to it. It would compute in the same language nature uses.

The future is almost certainly not quantum versus classical — it is classical inside quantum. That hierarchy appears to be written into the laws of physics. What remains is the engineering to reach it, and the mathematics to prove it.

Sources & references

Church-Turing Thesis (Turing, 1936)
Extended Church-Turing Thesis
P ⊆ BQP (Bernstein & Vazirani, 1997)
Gottesman-Knill theorem on efficient classical simulation of Clifford circuits
Caltech 6,100-qubit neutral atom record, Nature (Sept. 2025)
Google Willow 105-qubit chip (2024)
David Deutsch, The Fabric of Reality (1997)
Shor's algorithm (1994)
Grover's algorithm (1996)