Quantum Computing
A quantum computer's power is not that a qubit is "both 0 and 1 at once." That phrasing is marketing. The real machinery is interference: amplitudes for wrong answers cancel, amplitudes for right answers add. Whenever this engineering succeeds, certain problems collapse from cosmological time to minutes. Whenever it fails — and most problems do not have this structure — a quantum computer is slower than the laptop you're reading this on.
The catch is thermodynamic. A superconducting qubit lives at 15 millikelvin, colder than the cosmic microwave background. At room temperature it decoheres in nanoseconds. Building a useful quantum computer is the practice of holding a soap bubble together while running calculations on it.
How it actually works
A qubit's state is |ψ⟩ = α|0⟩ + β|1⟩ with complex amplitudes summing to |α|² + |β|² = 1. Measurement collapses the state; before measurement, the qubit has probability amplitudes, not values. Entangle two qubits and the pair can no longer be described as two independent objects — it requires a joint description, which is the resource that lets quantum machines maintain correlations across many qubits at once.
A quantum algorithm is a sequence of gates that sculpts amplitudes so that correct paths interfere constructively and wrong paths destructively. Shor's factoring algorithm, Grover's search, the HHL linear-systems algorithm — each is a different shape of interference. Most computational problems don't have an interference shape that helps. This is why "quantum will speed up everything" is wrong: it speeds up the small set of problems whose mathematics happens to align with quantum mechanics.
The 2025 hardware stack
| System | Qubits | Notable result | Approach |
|---|---|---|---|
| Google Willow | 105 | Random circuit sampling: 5 min vs. 10²⁵ classical years | Superconducting |
| IBM Nighthawk | 120 | 218 tunable couplers, +30% circuit complexity | Superconducting |
| Fujitsu/RIKEN | 256 | 4× their 2023 system; 1,000-qubit target for 2026 | Superconducting |
| Quantinuum Helios | ~50 | Highest commercial gate fidelity, Nov 2025 launch | Trapped ion |
| IonQ + Ansys | 36 | 12% beat over HPC on medical-device simulation, Mar 2025 | Trapped ion |
| Microsoft Majorana 1 | 8 (claimed) | Topological qubits — disputed by independent reviewers | Topological |
Google's Quantum Echoes result (Nature, 2025) is more durable than Willow's headline. It demonstrated a 13,000× speedup on a repeatable algorithm that runs on other quantum platforms — verifiable advantage, not a benchmark artifact. IBM's June 2025 work with RIKEN's Fugaku supercomputer was the first time IBM used the phrase "utility scale" — a quantum-classical hybrid simulating molecules beyond classical reach.
The other 2025 jump was error correction. Roughly 120 peer-reviewed QEC papers in the first ten months, against 36 for all of 2024. QuEra published algorithmic fault-tolerance techniques claiming up to 100× reduction in QEC overhead. Record per-gate error rates hit 0.000015%. The field has been waiting since Shor's 1995 error-correction paper for QEC to cross the break-even line. 2025 was the first year that line looks crossable on a realistic timeline.
What it can and cannot do
Clear quantum speedup, with proofs and demonstrations: molecular and materials simulation (the natural use case — quantum mechanics simulating itself), integer factoring via Shor's algorithm, unstructured search via Grover's (quadratic, not exponential). Quantum key distribution is communication, not computation: it gives provably tamper-evident channels via the no-cloning theorem.
Out of reach today: breaking RSA-2048 needs roughly 4,000 logical qubits, which at current error rates means ~4 million physical qubits. We have around 1,000. This gap drives the "harvest now, decrypt later" threat — adversaries archive encrypted traffic today to decrypt when scale arrives. NIST standardized lattice-based replacements in 2024 (Kyber, Dilithium, FALCON); migration is underway in government and critical infrastructure.
Outside the speedup zone: training neural networks, running classical algorithms, general computation. A quantum computer running a classical workload is a $10M space heater.
What's contested
Three live disputes worth naming:
The benchmark question. Willow's 10²⁵-year claim solves random circuit sampling — a problem engineered to be hard for classical machines and easy for quantum ones. Critics (notably Scott Aaronson, though he is sympathetic to the field) argue these benchmarks demonstrate hardware coherence but not utility. Google's response is that Quantum Echoes is the more honest result. The disagreement is about what counts as a milestone.
Topological qubits. Microsoft's Majorana 1 announcement in 2025 has been met with skepticism from condensed-matter physicists who note the underlying Majorana zero-mode evidence has been retracted before (most prominently the 2021 Kouwenhoven retraction). If topological qubits work, they cut error-correction overhead dramatically. If they don't, Microsoft has spent two decades on a dead end.
The timeline to RSA-breaking. Estimates range from "before 2030" (alarmist, very few specialists endorse) to "after 2045" (depends on whether logical-qubit overhead can be cut by orders of magnitude). The honest answer is that nobody knows, and the spread is itself the story.
Why this has to do with other realms
Willow's headline result is structurally identical to Turing's 1936 trick in the concept halting problem: construct an artificial problem to expose the substrate. Turing built a self-referential halting test to prove computation has limits; Google built random circuit sampling to prove quantum hardware has powers. Both are honest demonstrations of capability through engineered hardness. Both are useless on their own terms.
The deeper bridge: quantum computing expands the tractable set but not the computable set. Problems Turing proved undecidable remain undecidable on a quantum machine. Gödel's incompleteness doesn't loosen. The frontier here is complexity, not computability — and the distinction matters because much of the public conversation conflates them.
An open question
If a quantum machine can simulate any quantum system, can it simulate a brain — not the computation a brain performs, but the brain itself, including whatever quantum effects (if any) Penrose-Hameroff style theories require? The first credible attempt would be the most consequential experiment in the history of consciousness studies.
Key sources
- Nielsen & Chuang, Quantum Computation and Quantum Information (2010) — the canonical graduate textbook, still the load-bearing reference.
- Google Quantum AI, "Quantum error correction below the surface code threshold," Nature (2024) — the Willow result paper.
- Google Quantum AI, Quantum Echoes paper, Nature (2025) — verifiable-advantage demonstration. To verify: exact title.
- Scott Aaronson's blog, Shtetl-Optimized — the most reliable popular-but-rigorous commentary on quantum-computing claims, including skeptical takes on benchmark results.
- NIST Post-Quantum Cryptography standards (2024) — Kyber, Dilithium, FALCON specifications.
- QuEra's algorithmic fault-tolerance paper (2025) — to verify: exact citation for the 100× overhead reduction claim.
Further reading
- Quantum Computing Since Democritus by Scott Aaronson — the rare book that takes computational complexity, philosophy, and quantum mechanics seriously in the same chapters.
- John Preskill's 2018 essay "Quantum Computing in the NISQ era and beyond" (arXiv:1801.00862) — coined "NISQ" and remains the clearest map of the intermediate-scale phase the field is still in.
- Nature podcast episodes on the Willow and Quantum Echoes results — the principal investigators explaining the work in their own framing.
- The IBM Quantum roadmap page (canonical, updated annually) — the most concrete published trajectory from any vendor.
See Also
- concept quantum error correction — the bottleneck; the reason 2025 mattered.
- concept quantum entanglement — the resource that makes interference at scale possible, and the reason FTL signaling is still impossible.
- concept quantum measurement problem — why does measurement collapse the wavefunction? A separate puzzle from computing, but every quantum algorithm leans on the answer being "shut up and calculate."
- concept halting problem — the structural twin of Willow's benchmark; both engineer artificial problems to reveal substrate limits.
- concept godel incompleteness — quantum machines expand tractability, not provability; the incompleteness frontier doesn't move.
- concept holographic error correction — surface codes have a startling structural kinship with AdS/CFT, suggesting spacetime itself may be error-corrected.
- concept aging telomeres — molecular simulation is the most credible near-term medical payoff; telomere biology is one candidate target.