What can quantum computers do today, and what's still to come?

Each claim on this page gets one of five grades:

• In use: doing a real job today, outside the lab.
• Shown, ahead: run on real hardware, better than the best ordinary method, checked by others.
• Shown, not ahead: run on real hardware, but ordinary computers do as well or better, or nobody has checked yet.
• On paper: worked out for future machines that don't exist yet.
• Press release only: a claim without a paper, or with a paper that doesn't support it.

One question does most of the work: compared with what? Many claims compare a quantum machine with an ordinary method nobody uses for that job.

Quantum technology already works, mostly outside computing:

• First-generation quantum tech (the introduction): lasers (page 14c), computer chips, LEDs and MRI scanners all rely on quantum rules. In use for decades.
• Clocks and sensors (chapter 12): atomic clocks in every GPS satellite. Wearable brain scanners in clinical research. Gravity sensors in field trials. In use, or in trials.
• Random numbers: quantum random-number chips in Samsung phones sold in South Korea since 2020. In use.
• Security (chapter 13): post-quantum encryption, ordinary maths built because of quantum computers, already protects much of the web. In use.

Today they're mostly tools for research and learning. Companies and universities rent time on them over the internet to test ideas and train staff. McKinsey counted more than 300 organisations, from Airbus to JPMorganChase, working with quantum companies in 2026. That's experimenting, not yet relying on them.

Their clearest results so far:

• Test tasks: sampling and physics tasks where quantum machines beat ordinary computers, though some earlier claims later fell to better ordinary methods (chapter 11). Shown, ahead, on made-up tasks.
• Certified randomness (2025): JPMorganChase and Quantinuum produced random numbers that anyone can check came from a quantum process (Nature). A first step towards a practical task. Shown.
• Quantum Echoes (2025): Google measured a physical effect 13,000 times faster than a supercomputer could calculate it, in a way others can check (Nature). Physics, not yet chemistry. Shown, ahead, not yet reproduced classically.

Molecules follow quantum rules. To simulate one exactly, an ordinary computer must track every way its electrons can arrange themselves, and that number doubles with each extra electron orbital (chapter 7's doubling). A quantum computer follows the same rules as the molecule, so its size grows only in step with the molecule. Richard Feynman made this argument in 1981 (page 7c).

The prizes are large: better catalysts for fertiliser and capturing carbon, better batteries, and medicines designed with more confidence (page 14a).

Researchers cost these jobs for future error-corrected machines:

• FeMoco (2017): the molecule bacteria use to turn nitrogen from the air into fertiliser. About 135 error-corrected qubits running for weeks. Later work (2021) cut the cost to about 4 million physical qubits for under four days.
• Cytochrome P450 (2022): an enzyme that breaks down most medicines in your body. About 4.6 million physical qubits for 73 hours at today's best error rates.
• Battery materials (2023): even with better methods, runtimes of thousands of days. More work needed.

Each estimate falls as methods improve. Today's machines have a few dozen error-corrected qubits (chapter 8), so all of this is on paper.

Small steps. In 2025 and 2026 IBM with Japan's RIKEN, Google, and the London company Phasecraft ran chemistry and materials problems on real machines. The results matched or approached the best ordinary methods. None clearly beat them. Shown, not ahead.

Ordinary computers keep improving too. Chemists don't need the exact answer, just a good-enough one, and clever approximations often deliver it. In January 2026 a team led by Garnet Chan reported reaching chemical accuracy on a FeMoco model with ordinary computers (a preprint, not yet peer reviewed). If that holds, the flagship example needs replacing with harder molecules. A 2025 MIT study expects quantum methods to beat the best ordinary ones for small and medium molecules in about 10 years, and the cheaper everyday methods in 15 to 20.

Banks, airlines and logistics firms hope quantum computers will find better schedules, routes and portfolios. The evidence so far:

• HSBC and IBM (September 2025) reported "up to 34%" better predictions of bond-trade outcomes. Experts, including the computer scientist Scott Aaronson (page 16c), challenged it: the gain appeared even against a noise-free simulation of the same circuit, which suggests hardware noise did the work, and ordinary methods could reproduce it. Preprint only, not peer reviewed, disputed.
• IonQ and Ansys (March 2025) reported a blood-pump simulation "12% faster" than ordinary computers. The 12% came from a simulated run, not the quantum hardware. Press release only.

For most optimisation problems, no known quantum algorithm gives a large proven speed-up. Annealers (chapter 10) remain a separate, debated case.

• Machine learning: in 2018 Ewin Tang, an 18-year-old student in Texas, found an ordinary algorithm that matched a celebrated quantum one for recommending products. Similar results followed for other quantum learning methods. No practical quantum advantage for machine learning exists yet. On paper, and shrinking.
• Drug discovery: in 2025 a team in Toronto used a mainly ordinary AI system with a small quantum part to suggest cancer-drug candidates; two looked promising in lab tests (Nature Biotechnology). Nobody showed the system needed the quantum part. No approved medicine depends on quantum computing. Shown, not ahead.
• Breaking encryption: needs far bigger machines (chapter 13). On paper.