What Quantum Computers Can and Cannot Do: Drawing the Boundary Lines

Forum topic · 小凯 · 2026-10-27

Summary

This zhichai.net article, part four of a quantum computing primer series, separates fact from hype in quantum computing claims. It identifies the one certainty: Shor's algorithm will eventually break RSA and elliptic-curve encryption, making 'harvest now, decrypt later' a present-day threat, which is why NIST published post-quantum cryptography standards in August 2024 and major software has already migrated. The most consensual future use is quantum simulation of molecules like FeMoco for fertilizer chemistry, high-temperature superconductivity, and battery materials, though these require fault-tolerant machines still years away. The author pours cold water on quantum optimization, finance, and quantum machine learning, citing barren plateaus and data-encoding overhead, with no reproducible wins over classical heuristics. It also contextualizes quantum advantage demonstrations: Google's 2019 Sycamore claim eroded from 10,000 years to days, China's Jiuzhang and Zuchongzhi 3.0 (105 qubits, 15 orders of magnitude advantage in random circuit sampling), and Google's October 2025 verifiable quantum advantage on Willow (13,000x faster, published in Nature). A three-question test for evaluating quantum headlines is provided.

What Quantum Computers Can and Cannot Do

> This article is included in the column *From Coins to Error Correction* as extended reading (Q-010) · Column index: https://zhichai.net/topic/178636834

Every few weeks, quantum computing makes headlines wearing one of two faces: "the moment a quantum computer boots up, all encryption instantly becomes obsolete" or "quantum chips crush supercomputers, pharma companies panic." Both deserve scrutiny. This article draws the boundary lines clearly — what's true, what's theoretically valid but far off, and what was wrong from the start. There is only one criterion: who ran it, on what machine, against whom, and won at what?

The Most Certain Outcome: Changing the Locks

Today's internet encryption (RSA, elliptic curves) rests its security on a mathematical wall: factoring the product of two large primes back into its factors, which classical computers cannot do. Shor's 1994 algorithm mathematically marked this wall as "demolishable." What's missing is only a fault-tolerant quantum machine large enough — an engineering estimate on the order of a million physical qubits. It's an engineering problem on a ten-year timescale, not a matter of principle.

The real urgency hides elsewhere: harvest now, decrypt later. Encrypted traffic intercepted and stockpiled today can be re-processed once quantum machines mature a decade from now. For secrets whose confidentiality horizon spans decades — medical records, state archives, trade secrets — the threat is not future; it is present.

So the lock-changing has already begun. In August 2024, the US NIST published three post-quantum cryptography standards, betting security on new mathematical problems that quantum computers also cannot solve. You don't need the algorithm details — just know that some mainstream browsers and chat apps have quietly completed migration, and your phone's recent system update almost certainly contains the new lock. This is the only quantum computing "big event" that has already happened today — it arrived as a threat and landed as a defense.

The Most Consensual Use: Teaching Chemistry

The quantum computer's first irreplaceable application will most likely not be breaking ciphers, but simulating molecules. The reason in one sentence: molecules are themselves quantum systems. Simulating a quantum system with a classical computer is essentially approximating an approximation — large systems inevitably distort; simulating a quantum system with a quantum system means speaking the same language.

This is not a new idea — it was the original motivation for quantum computing in the 1980s. Today's targets have names: the FeMoco molecule at the active center of nitrogenase — the hidden player in the fertilizer industry's core reaction, intractable for classical computers; one accurate quantum simulation could rewrite synthetic chemistry. Also: the mechanism of high-temperature superconductivity; new materials for batteries and catalysts. Academically, there is no disagreement on direction — only on timelines. These applications all require fault-tolerant machines, and fault-tolerant machines need the bodyguard corps described in the previous installment. The paper value is already written; the payout date rests on error-correction engineering.

Three Directions That Need Cold Water

The hottest three words in investment narratives — optimization, finance, machine learning — are precisely the three with the thinnest scientific evidence.

Optimization: You often hear "quantum annealing can solve logistics scheduling." In real head-to-head experiments, classical heuristic algorithms have not been consistently beaten — every time a quantum method has its moment, a classical algorithm catches up. Portfolio optimization in finance belongs to the same category. This doesn't mean never — it means there is still no reproducible report card.

Quantum machine learning: Sounds natural, but practice contains two famous traps. One is *barren plateaus* — as model parameters grow, the gradients of the training signal vanish like into a plateau, and training cannot proceed. The other is the *encoding tax* — classical data must first be stuffed into a quantum circuit to be processed, and the stuffing itself can consume the entire theoretical advantage. To date, no scenario has demonstrated a clear advantage over classical methods.

Neither direction is necessarily a scam, but the distance between "no evidence yet" and "verified" should be measured before you invest money.

Already Happened, But Needs Correct Understanding: Advantage Demonstrations

In 2019, Google's 53-qubit chip ran a specially designed sampling task and announced it finished in 200 seconds what a classical supercomputer would need 10,000 years for. The academic world was shaken — then classical algorithms fought back. Within a year, "10,000 years" was compressed to days. This tug-of-war has never stopped.

This is not a face-slap; it is the norm. Advantage demonstrations are a carefully selected class of tasks: ones quantum machines are naturally good at and classical machines can only brute-force. Their significance lies not in usefulness, but in the nonexistence of a *principled barrier* — proving quantum machines genuinely can do some things classical machines effectively cannot.

The milestones of the Chinese camp lie along the same line: Jiuzhang takes the photonic route and the Zuchongzhi series the superconducting route, each crossing this threshold on sampling tasks; Zuchongzhi 3.0 (105 qubits) pushed the lead in random circuit sampling to 15 orders of magnitude faster than supercomputers. In October 2025, Google ran the first "verifiable" quantum advantage algorithm on Willow, 13,000 times faster than the fastest supercomputer, published in *Nature*. "Verifiable" is the key upgrade — previous sampling tasks were fast, but their results could not be quickly checked. This time, they can.

Closing With Three Questions

Next time you see quantum news, run it through three questions: How many physical qubits did it run on? Was error correction used? Was the opponent the strongest classical algorithm or a straw man? After these three questions, the water in the headline will separate out on its own.

The two most certain facts about this machine today: it will kill today's cryptography — and the lock-changing is genuinely happening; and it has not yet killed anything else — for which error-correction engineers are working overtime.

*(Fourth installment of the quantum primer series, concluding here: Part 1, vocabulary overview; Part 2, interference mechanisms; Part 3, error-correction bodyguards; this one, application boundaries. After four articles, you're probably closer to the truth than most headline writers.)*