Algorithms that show what quantum computers are really for
An algorithm is the reason a quantum computer is worth building. A few have rigorous proofs of speedups, many are promising ideas still being tested, and some may never beat a good classical method. We want you to learn all three kinds, and to be able to say which is which. Today's machines are in what John Preskill named the NISQ era: Noisy Intermediate-Scale Quantum devices, with too few qubits and too much noise for the famous algorithms at useful size. The long-term hope, which our 2040 framing points toward, is fault tolerance: error-corrected machines. Google reported in Nature that its error-corrected memory improved as the code grew, a milestone for that road. Real progress is happening, and so are real limits. This page is the I in QUBIT Quest: Industry algorithms.
Read next: Preskill, "Quantum Computing in the NISQ era and beyond" and Google Quantum AI, error correction below the surface code threshold (Nature).
What you'll be able to do
Explain the classic algorithms
Describe what Deutsch-Jozsa, Bernstein-Vazirani, Grover, QFT, phase estimation and Shor do, and what kind of speedup each one really gives.
Explain Shor for security
Say in plain words why a large fault-tolerant quantum computer would threaten RSA and elliptic-curve cryptography, and why NIST is already moving to new standards.
Understand VQE and QAOA
Describe how hybrid quantum-classical loops work, why they suit noisy hardware and why they come with no guaranteed advantage.
Grasp error correction basics
Explain why qubits need many physical qubits per logical qubit, what a code threshold means and why this decides when big algorithms become possible.
Run a small QML model
Train a tiny variational quantum classifier in PennyLane or Qiskit Machine Learning and say honestly what it did and did not show.
Separate hype from progress
Read an industry claim, find the problem size, the baseline and the hardware used, and ask whether it is a demonstration or a business result.
The algorithms, with honest labels
"Speedup" means compared with the best known method for the same task. "Needs fault tolerance" means we do not expect it to run at useful size on today's noisy devices.
| Algorithm | What it does | Honest status | Where to learn (free) |
|---|
| Deutsch-Jozsa | Tells whether a hidden function is constant or balanced in one query | Proven query-complexity gap against deterministic classical methods, but a teaching example with no practical use | IBM: Fundamentals of Quantum Algorithms |
| Bernstein-Vazirani | Finds a hidden bit string with one query | Teaching example that shows interference at work; not a practical tool | PennyLane Codebook: Basic Quantum Algorithms |
| Grover search | Searches an unstructured list | Proven quadratic speedup. In practice the overhead of error correction can eat much of a quadratic gain, so it needs fault tolerance and big problems | PennyLane demo: Grover · Q# Grover tutorial |
| Quantum Fourier Transform (QFT) | A building block that reads out hidden periodic patterns | A subroutine, not a stand-alone application; central to phase estimation and Shor | PennyLane demo: QFT |
| Phase estimation (QPE) | Reads out an eigenvalue of an operator | Key to chemistry and Shor; needs deep, low-noise circuits, so it is a fault-tolerant tool | PennyLane demo: QPE |
| Shor's algorithm | Factors large integers and finds discrete logarithms | Believed to give a super-polynomial speedup over the best known classical methods. Needs a large fault-tolerant machine, which does not exist yet | Shor, original paper · MIT OCW 18.435J |
| VQE | Estimates the lowest energy of a molecule or material with a hybrid loop | Designed for NISQ devices; heuristic, with noise and optimization problems (such as barren plateaus). No proven advantage yet | PennyLane demo: VQE · Peruzzo et al., original paper |
| QAOA | Looks for good (not guaranteed best) answers to optimization problems | Heuristic for NISQ devices; whether it beats strong classical solvers is an open research question | PennyLane demo: QAOA · Farhi et al., original paper |
| Quantum error correction (QEC) | Spreads one logical qubit across many physical qubits to catch errors | Active experimental progress; it is the bridge from NISQ to fault tolerance, and it is costly in qubits | IBM: Foundations of QEC |
Why Shor matters for cryptography
Much of today's public-key security, including RSA and elliptic-curve cryptography, relies on problems that Shor's algorithm would solve efficiently on a large fault-tolerant quantum computer. Nobody has built one. Researchers keep lowering the estimated cost: a 2025 paper from Google estimates that RSA-2048 could be factored with fewer than a million noisy qubits, still far beyond today's machines. Because stolen data can be stored and decrypted later, governments are moving early. NIST has published the first post-quantum standards, including FIPS 203, 204 and 205, and its draft IR 8547 lays out a timeline for retiring quantum-vulnerable algorithms (the draft points to deprecation by 2030 and disallowance by 2035). The "by 2040" idea is our own forward-looking framing of where those timelines point, not a NIST requirement. Our SHIELD 2040 area follows this story from the security side.
Quantum machine learning (QML), carefully
QML asks whether quantum circuits can learn from data in useful ways. It is a lively research area and a great way to learn, but there is no proven practical advantage today. Loading classical data into a quantum state is costly, and good classical methods are hard to beat. Treat QML demos as a way to understand variational circuits, not as evidence that quantum AI is here.
PennyLane QML demos
Provider: Xanadu. You earn: hands-on skill training variational circuits (no certificate). Try the variational classifier, data re-uploading classifier and quantum transfer learning demos, and read the barren plateaus demo to see why training can stall. Cost: Free course · About 6 hours (estimate) · Level: Intermediate
Variational classifierBarren plateaus
Qiskit Machine Learning (course and library)
Provider: IBM and the Qiskit community. You earn: the IBM Quantum Learning course Quantum machine learning covers data encoding, quantum kernels and QVCs and QNNs, with a badge exam at IBM Training (exam price not confirmed). It assumes some familiarity with classical machine learning. The open-source library has tutorials. Cost: Free course · About 8 hours (estimate) · Level: Intermediate
IBM QML courseLibrary tutorials
Industry use cases, without the hype
These are the areas where quantum computing is being studied. For each one, ask: what is the problem size, what is the best classical baseline, and which hardware was used?
Chemistry
Simulating molecules is a natural fit, since molecules are quantum systems. Today, VQE-style experiments handle only small molecules that classical computers also solve. Large, useful chemistry is expected to need fault tolerance.
Optimisation
Logistics, scheduling and routing are often named. QAOA and related heuristics are being tested, but advantage over strong classical solvers has not been shown. Grover gives at most a quadratic speedup for search.
Finance
Risk analysis, option pricing and portfolio optimisation are active research topics. Many proposed speedups rely on large fault-tolerant machines, and the cost of loading data is a known hurdle.
Materials
Batteries, catalysts and superconductors rely on quantum effects that are hard to simulate classically. This is regarded as a likely early beneficiary, once error-corrected hardware exists.
Watch the evidence: IBM quantum advantage tracker (an open community effort that compares advantage candidates with the best classical methods), and IBM: Quantum business foundations for a business view.
Your free course path
Every step below is free. Hours are our own estimates. The IBM badge exams are taken at IBM Training, and their price is not confirmed on the course pages, so we count only the lessons as free.
Step 1 · IBM Quantum Learning: Fundamentals of Quantum Algorithms
Provider: IBM. You earn: the lessons cover Deutsch-Jozsa and Simon, factoring and phase estimation including Shor's algorithm, and Grover. A digital badge is possible by passing an exam at IBM Training (exam price not confirmed). It is the second course in IBM's four-course series after Basics of quantum information. Cost: Free course · About 15 hours (estimate) · Level: Intermediate
Open the course
Step 2 · IBM Quantum Learning: Variational algorithm design
Provider: IBM. You earn: skill in reference states, ansatze, cost functions and optimization loops, the parts of VQE and QAOA. Badge exam available at IBM Training (price not confirmed). Some experience with quantum computing is expected. Cost: Free course · About 8 hours (estimate) · Level: Advanced
Open the course
Step 3 · IBM Quantum Learning: Foundations of Quantum Error Correction
Provider: IBM. You earn: repetition codes, the 9-qubit Shor code, stabilizer codes, CSS and toric codes and the threshold theorem. Badge exam at IBM Training (price not confirmed). The course is the fourth in the series. Cost: Free course · About 15 hours (estimate) · Level: Advanced
Open the course
Step 4 · PennyLane Codebook, algorithm modules
Provider: Xanadu. You earn: the Codebook lists modules on Quantum Error Correction, Basic Quantum Algorithms, Grover, QFT, Quantum Phase Estimation, Shor, Variational Quantum Algorithms and Hamiltonian Simulation. We did not find a certificate on the page (certificate not confirmed). Cost: Free course · About 20 hours (estimate) · Level: Intermediate
Open the Codebook
Step 5 · Google Quantum AI: Hands-on quantum error correction (Coursera)
Provider: Google Quantum AI on Coursera, taught by Dr. Austin Fowler. You earn: intermediate-level surface code skills with the Stim simulator. The course page lists about 29 hours of work. We could not confirm a free or audit option for this course, so treat it as optional and check Coursera for current access. Cost: Free access not confirmed · About 29 hours (listed) · Level: Intermediate
Check on CourseraStim simulator
Step 6 · Free university lectures and notes
MIT OpenCourseWare 18.435J, Quantum Computation (Fall 2003, Prof. Peter Shor) includes lecture notes, assignments and exams under a Creative Commons license. It is dated, so use it for ideas that have not changed, such as Shor, Grover and error correction. UC Berkeley CS294-2, Quantum Computation (Fall 2004, Umesh Vazirani) has lecture-by-lecture notes covering the QFT, Shor, Grover and error correcting codes. No certificates. Cost: Free course · About 20 hours (estimate) · Level: Advanced
MIT OCW 18.435JBerkeley notes
Hands-on: challenges and community events
Dates were checked in October 2026. Some events have already ended, and we say so, so you can plan for the next round.
QHack 2026 (Xanadu, PennyLane)
Xanadu's coding competition runs October 16 to 23, 2026, so it is in its last day or two as we write. The site welcomes hobbyists, students and curious developers, solo or in teams of up to four, and says registering unlocks free quantum training. No entry fee is stated. Even after it closes, the training and the next edition are worth following.
Visit QHack
unitaryHACK (Unitary Foundation)
An annual virtual hackathon where you contribute to open-source quantum software and can earn bounties. The 2026 edition ran June 3 to 17 and has closed. No 2027 dates are announced yet, so follow the Unitary Foundation and get ready by reading open issues now.
unitaryHACKUnitary Foundation on GitHub
Qiskit Fall Fest 2026 (IBM Quantum)
Student-run events supported by IBM Quantum, listed for October and November 2026 at universities around the world. Each event has its own sign-up page, and IBM's listing does not state a cost, so check each host. Many have public or virtual options.
See Fall Fest events
PennyLane challenges and MIT iQuHACK
PennyLane lists coding challenges on topics from chemistry to machine learning (cost not stated on the page). MIT's iQuHACK ran January 30 to February 1, 2026, and its 2027 dates have not been posted. We did not find a current Kaggle quantum competition, and IBM's spring and fall Quantum Challenge had no confirmed 2026 edition in our search, so we do not list them as active.
PennyLane challengesMIT iQuHACK
For Curiosity Coaches
Discussion prompts
- Grover gives a quadratic speedup, not a magic one. When is "a bit faster" worth a very expensive machine?
- If Shor's algorithm will need a machine that does not exist yet, why is NIST acting now?
- VQE has no proven advantage. What would convince you that it does?
- Read one company announcement: what was the problem size, and what was the classical baseline?
4-week plan (about 1 to 2 hours per week)
- Week 1: Grover and the idea of quadratic speedup, with the PennyLane Grover demo.
- Week 2: QFT, phase estimation and Shor: read the cryptography section and the NIST links.
- Week 3: VQE or QAOA demo, then discuss why noise matters.
- Week 4: One QML demo plus a "hype or progress?" debate on a real announcement.
Level fit: The algorithm overview and the NISQ debate suit curious learners at about 14+ and career changers with no math beyond algebra. The IBM algorithm courses and the university notes need comfort with linear algebra, so recommend QUBIT Quest's math steps first.
Free resource library
Related on this site: Quantum Programming: Qiskit, Cirq, Q#, PennyLane & more.