Quantencomputing

Worum es geht

Quantum computing is a different model of computation, not a faster implementation of the old one. Its state is a vector of complex amplitudes over classical bit strings; its operations are unitary transformations that can make amplitudes cancel; and its output is a single measured bit string drawn from a probability distribution given by the squared magnitudes of those amplitudes. Everything that is interesting and everything that is limited follows from that arrangement. A register of n qubits carries two to the power n amplitudes, which is the source of the popular parallelism story, but measurement returns only n bits and destroys the rest, which is why the story is wrong. The real mechanism is interference: an algorithm earns its speedup by arranging for the amplitudes on wrong answers to cancel and the amplitudes on right answers to reinforce, and that arrangement is only known to be possible when the problem has exploitable structure. Hence the shape of the field. Deutsch defined the model in 1985; Simon and Shor found the structure that period-finding provides, giving an exponential speedup for factoring and discrete logarithms; Grover found a general but merely quadratic speedup for unstructured search, and Bennett, Bernstein, Brassard and Vazirani proved that quadratic is all there is in that setting. Shor, Steane and Kitaev then showed that decoherence is survivable and the threshold theorem showed how cheaply, at the price of an overhead — hundreds to thousands of physical qubits per logical one — that separates every machine now in existence from every machine the famous algorithms require. The present era is what Preskill called NISQ: devices large enough to be hard to simulate and too noisy to run the algorithms the field was built on, surrounded by advantage claims that keep meeting improved classical simulations, and by a genuine engineering turn since 2023 as error correction began working as advertised.

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• Has any quantum device performed a task that classical hardware cannot?

  4 benannte Positionen · live and unfinished; the honest teaching position is that classical baselines are a moving research target, and that no advantage demonstration to date has both survived counterattack and computed anything anyone wanted

• Can a large fault-tolerant quantum computer be built, or does noise scale faster than correction?

  4 benannte Positionen · the sceptical case has weakened materially since 2023 as below-threshold operation was demonstrated, and is not refuted — the demonstrations are at distance seven with one logical qubit, and the disputed regime begins where thousands of logical qubits must run together for hours

• Is the set of useful quantum algorithms small and structural, or will it grow?

  4 benannte Positionen · unresolved and consequential; the defensible present statement is that the proved-useful set is small, structured and dominated by simulation and cryptanalysis, and that this has been true for two decades

• Which physical or mathematical resource is responsible for quantum advantage?

  4 benannte Positionen · interference is the right operational answer for teaching; a general resource-theoretic account of quantum speedup is an open research question, and the many-worlds reading is a live philosophical dispute with no empirical content

• How long until a cryptographically relevant quantum computer exists, and what follows now?

  4 benannte Positionen · migration is proceeding and is justified independently of the timeline; the date is genuinely unknown, and both alarmist and dismissive numbers in circulation come from selective reading of the same resource estimates

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• “A quantum computer tries all possible answers simultaneously and picks the right one, so it solves anything with a large search space instantly.”

  debunked

  The superposition half is right and the extraction half is where the claim collapses. You can apply a function to a register in superposition and obtain a state carrying amplitudes for every input-output pair. Then you measure, and you get exactly one of them, chosen at random according to the squared magnitude of its amplitude, with the rest destroyed. If the amplitudes are uniform, that is an expensively built coin flip and no better than guessing. Holevo's bound makes the accounting explicit: n qubits deliver at most n classical bits per transmission, no matter how many amplitudes they carry. The actual mechanism is interference. Amplitudes are complex numbers and can cancel, which is the one thing classical probability cannot do — nothing is ever less likely because there are more ways for it to happen. An algorithm earns its speedup by arranging the unitary operations so that contributions to wrong answers destructively interfere and contributions to the right answer reinforce, concentrating amplitude before the measurement. That arrangement is only known to be constructible when the problem has exploitable structure: hidden periodicity for Shor (shor-1994), the promise structure in Deutsch-Jozsa (deutsch-jozsa-1992), and a slow rotation toward the marked item for Grover (grover-1996). The decisive evidence against the parallelism reading is a theorem, not a preference: for unstructured search, no quantum algorithm can beat order square-root-of-N queries (bbbv-1997), which is exactly the bound you would not expect if the machine could test every candidate at once. Aaronson's one-sentence version, on the masthead of his blog and in his Scientific American article, is the formulation to memorise — quantum computers would not solve hard search problems instantaneously by simply trying all possible solutions at once (aaronson-2008-limits).

• “Quantum computers will break all encryption, and nothing will be private.”

  debunked-as-stated

  Three separate corrections, and the claim survives none of them intact. First, scope: Shor's algorithm attacks the number-theoretic public-key family — RSA, finite-field Diffie-Hellman, elliptic-curve key exchange and signatures — because all of them reduce to hidden-period problems. That is a large and load-bearing part of deployed cryptography, and it is not all of it. Second, symmetric cryptography and hash functions face only Grover's quadratic speedup, which halves the effective key length in the exponent — AES-256 still faces roughly two-to-the-128 operations, and doubling parameters restores any margin. The practical erosion is smaller even than that arithmetic suggests, because Grover's iterations are inherently sequential and parallelise badly, which is why NIST's own post-quantum call framed attack costs with an explicit depth limit. Third, the replacements exist and are standardised: NIST published ML-KEM, ML-DSA and the hash-based SLH-DSA in August 2024 after an eight-year open competition (nist-fips-203-2024), and hybrid key exchange combining a classical scheme with ML-KEM has been shipping in major browsers and protocols since 2023. And the machine is not close: the 2021 reference estimate for RSA-2048 was twenty million physical qubits running eight hours (gidney-ekera-2021), against hardware with hundreds of physical qubits and one logical qubit. The genuine present-tense threat is narrower and duller than the headline — harvest-now-decrypt-later, in which traffic recorded today is decrypted after migration lags, which is why Mosca's inequality frames the decision without needing a date (mosca-2018). What is being migrated to, and the disputes about its parameters, belong to the cryptography package.

• “Quantum computers are simply much faster computers — they will speed up everything, and one day they will replace the machine on your desk.”

  debunked

  It is a different model of computation with a different and largely incomparable profile, not a faster instance of the same one. On raw speed, quantum hardware loses badly: superconducting gate times are in the tens of nanoseconds and trapped-ion gates in microseconds, against classical operations at gigahertz, and error correction multiplies every logical operation by a large constant factor. What a quantum computer offers is a better scaling exponent on a short list of problems. Montanaro's survey is the inventory to check any claim against (montanaro-2016): exponential speedups for period-finding and its algebraic relatives and for simulating quantum systems, quadratic speedups from amplitude amplification for problems with a checkable predicate, and a long tail of heuristics with no proof. For sorting, arithmetic, databases, rendering, compilation, web serving and almost everything a computer actually does, there is no known quantum speedup and no reason to expect one. Two deeper points belong here. Nobody has proved that quantum computers are more powerful at all — BQP has not been separated from BPP, and the belief rests on the same kind of unproven hardness assumptions that classical cryptography rests on (bernstein-vazirani-1993). And even a proved asymptotic advantage has to survive slow clocks, error-correction overhead and the cost of moving data in and out, which is why the practical filter concludes that quadratic speedups will not pay for themselves and that credible applications need superquadratic advantage on small inputs (hoefler-haner-troyer-2023). The realistic picture is a coprocessor: a specialised accelerator called by classical software for particular subroutines, the way a GPU is, and useless on its own.

• “Quantum supremacy was achieved in 2019, so quantum computers now outperform classical computers and are ready for real work.”

  debunked-as-stated

  The task was random circuit sampling: apply a randomly chosen sequence of gates to 53 qubits and sample from the resulting output distribution. It computes nothing anyone wants. It was selected precisely because it is hard to simulate classically and for no other reason, and the paper says so (arute-2019). Nothing about it implies that a useful computation is near, and the same processor could not run Shor's algorithm on any interesting integer. That much is not disputed by anyone, including Google. The second half of the correction is more interesting and is not settled. The headline comparison — 200 seconds against an estimated 10,000 years on the Summit supercomputer — did not survive contact with classical algorithm research. IBM showed within days that using secondary storage brought the estimate to about two and a half days (pednault-2019); a Sunway supercomputer simulation won the 2021 Gordon Bell Prize doing it in hours (liu-2021-sunway); and Pan, Chen and Zhang matched the sampling task on a cluster of consumer graphics processors (pan-chen-zhang-2022). The same pattern then repeated on other platforms: photonic advantage claims narrowed under classical spoofing algorithms, and IBM's own 2023 utility claim was reproduced classically within weeks (kim-2023-utility; tindall-2024). Google's position is that the rebuttals attack an estimate rather than the experiment, and that later random-circuit runs on larger processors restored a substantial gap that no classical method has closed — which is a live argument, not a closed one. Two things to carry: the classical baseline is a research target that improves when someone is motivated to attack it, so treat hardness claims as provisional for at least a year; and a milestone in complexity theory is not a product. Harrow and Montanaro set out the criteria two years before Sycamore, and identified verification as the hard part, which it remains (harrow-montanaro-2017).

• “Progress is measured in qubits — a 1,000-qubit machine is roughly ten times as capable as a 100-qubit one, and we just need to keep adding more.”

  debunked-as-stated

  Qubit count matters and it is nowhere near sufficient, for three separate reasons. First, error rates. Circuit depth is limited by accumulated error, so a device with a two-qubit gate infidelity of one percent runs out of coherence after roughly a hundred gates regardless of how many qubits it has; the useful figures are two-qubit gate fidelity, coherence time divided by gate time, and readout error, not the qubit total. Second, connectivity. If qubits interact only with their neighbours, entangling distant ones costs a chain of swap operations, each adding error — which is why 48 logical qubits in 280 neutral atoms with arbitrary connectivity (bluvstein-2024) is a different kind of achievement from the same number of fixed-lattice superconducting qubits. Third, and decisively, the logical-versus- physical distinction. Algorithms are written for logical qubits; hardware provides physical ones; and the surface code's exchange rate is hundreds to thousands of physical qubits per logical qubit at realistic error rates, plus magic-state factories for the non-Clifford gates that make the machine universal (fowler-2012-surface-codes). This is the factor of a thousand that makes headline counts and algorithmic requirements incommensurable: breaking RSA-2048 needs a few thousand logical qubits, which was twenty million physical ones on the 2021 accounting (gidney-ekera-2021). The industry's own behaviour confirms the point — IBM built a 1,121-qubit processor in 2023 and then concentrated on smaller devices with better error rates and on error correction, because adding noisy qubits to a noisy machine buys nothing. The result that actually moved the field was not a qubit count but a demonstration that increasing surface-code distance reduces the logical error rate, and does so below threshold (google-2024-below-threshold). A useful habit when reading any announcement: ask for the two-qubit gate fidelity, the connectivity, and whether the qubits quoted are logical or physical.

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