How the lessons are built

Every lesson opens with one or two questions about something you haven't been taught yet, marked Guess, not scored. When the lesson reaches the answer, it shows you your guess again. Guessing first, even wrongly, helps you learn the material the question was about (St. Hilaire et al. 2024; Richland et al. 2009). Simulations work the same way: you commit to a prediction and say how sure you are before the experiment runs, then compare it with what happened and read why (predict–observe–explain). Making a prediction first helps you learn from the result, and a wrong prediction helps most (Brod et al. 2018).

No segment lets you read for long without retrieving something: a probability to compute, a state to write down, a circuit to build. Testing yourself beats restudying the same material (meta-analyses put the advantage at roughly a third to a half of a standard deviation: Rowland 2014; Adesope et al. 2017; Yang et al. 2021).

Wrong answers get feedback aimed at the specific mistake: a missing square, a sign error, a swapped qubit, a global phase that doesn't matter. Each recognised mistake gets a short refutation: what the tempting idea is, something you can check that contradicts it, and the correct account. Feedback that explains helps far more than a bare right/wrong (Van der Kleij et al. 2015), and refutations of this kind help correct misconceptions (Schroeder & Kucera 2022). Hints unlock after you've had a go, one step at a time.

You choose Guessing, Fairly sure or Certain when you check an answer. Confident mistakes are the ones people correct best once they see the reason (the hypercorrection effect: Butterfield & Metcalfe 2001), so after a confident error the full solution is offered straight away, without waiting for a second try. Your answers also feed a calibration chart on the home page. Learners who judge their own knowledge accurately remember more, partly because overconfident learners stop studying too soon (Dunlosky & Rawson 2012).

New procedures start as fully worked examples. The last steps turn into “your turn” steps you complete yourself, and if you miss one, a second worked example with different numbers follows before you try one alone. This fading works well for beginners (Renkl & Atkinson 2003; Barbieri et al. 2023). Worked examples help less once you know a topic (Kalyuga et al. 2003), so if a lesson's material is familiar you can test out by going straight to its mastery check.

Each lesson asks you to explain its key idea in a few sentences. Self-explanation reliably improves understanding (Bisra et al. 2018, g ≈ 0.55). When this page runs on claude.ai, Claude reads your explanation against a rubric written for that question and tells you what's solid and what's missing, without handing you the answer; after at most two rounds you see the model answer. Elsewhere you compare against the model answer yourself.

Claude does two jobs here and nothing else: it gives feedback on your written explanations, and it answers up to two questions about the page you're on. It never checks a calculation (the app does that exactly), never hints at an exercise (the hints are written by hand), and is off during mastery checks and reviews. In one large trial, unrestricted AI help raised practice scores but lowered later exam scores (Bastani et al. 2025); in another, a tutor grounded in written solutions that guided students one step at a time produced larger gains than an active-learning class (Kestin et al. 2025).

Each lesson ends with a short mastery check: one try per question, no hints, a couple of questions from earlier lessons mixed in, and new numbers on a retake. If something isn't solid yet, the app points you back to the segment that teaches it (mastery learning: Bloom 1984; Kulik et al. 1990). You can also jump straight to the check to test out of a lesson you already know. Before the summary at the end of a lesson you write down what you remember, then tick off the key points you had: a “brain dump” is retrieval practice too.

When you finish a lesson its key questions join your review queue. They come back after about 2 days (the next day for an idea you missed in the mastery check), then after 5, 12, 30, 75 and 150 days as long as you keep getting them right without guessing. A right answer marked Guessing keeps the same gap; a miss brings the question back the next day and steps it down a level. Each review uses fresh numbers and mixes lessons. Spacing is one of the most reliable findings in learning research (Cepeda et al. 2006 and 2008; Dunlosky et al. 2013), and mixing topics that are easy to confuse helps you tell them apart (Brunmair & Richter 2019). The exact intervals matter much less than having gaps at all (Latimier et al. 2021), so the schedule is kept simple and visible. The tutor stays out of reviews: unassisted practice is what builds independent skill.

States appear as kets, as circle notation (one circle per basis state: the filled radius is the amplitude's size, the needle is its phase), as probability bars, and for single qubits on the Bloch sphere. Each picture has one job, and numbers sit next to every glyph: in a pilot study, students rarely read probabilities off such pictures by eye (Bley et al. 2024). The order of topics is shaped by research on where students struggle. Phase gets its own lesson before the Bloch sphere because it is the idea students find hardest there (Hu et al. 2024), and classical bits come before entangled ones, as Mermin recommends (Mermin 2003).

No streaks, points or leaderboards: the evidence that they help learning is mixed and it is unclear which ingredients matter (Sailer & Homner 2020), and feedback that draws attention to yourself rather than the task can make performance worse (Kluger & DeNisi 1996). Lessons are recommended in order but never locked.

The course follows Chapter 1 of Nielsen & Chuang, Quantum Computation and Quantum Information, but you don't need the book: every lesson stands on its own. If you have a copy, switch on Read along with Nielsen & Chuang on the course page. Each lesson then names the sections and pages it covers, and its summary tells you what to read next and what to look for. A good rhythm is to do the lesson first and read afterwards. With the switch off, which is the default, the lessons leave the book out.

Nielsen & Chuang put the Stern–Gerlach experiment near the end of Chapter 1 (§1.5.1) and reversible classical computing (§1.4.1) after teleportation. Here the Stern–Gerlach experiment opens Lesson 1 as a puzzle to predict and is explained in Lesson 5, and reversible gates come in Lesson 6, before entanglement, because practising tensor products on classical bits first makes the bookkeeping concrete (Mermin 2003). The survey sections (§1.1, §1.4.5, §1.5.2, §1.6) are gathered in Lesson 10.

On ketsandgates.com the site counts a few anonymous milestones to see how the course is used: a visit (once per browser per day), lessons started and finished, and review sessions finished. A visit keeps only the day, the country, the kind of device and the site that linked here. There are no cookies and no identifiers, and nothing is tied to your account. Copies of the course elsewhere, such as on claude.ai, count nothing.