The short version
- Unavoidable
- Linear algebra. Quantum states are vectors, gates are matrices, measurements are eigenvalue problems.
- Also essential
- Complex numbers, and Python if you are taking the software track.
- Not needed
- Quantum mechanics, advanced physics and differential equations, on the software track.
- Software track
- Typical ramp-up: 2 to 4 months from scratch.
- Theory track
- Typical ramp-up: 6 to 12 months of serious study.
01 The Three Entry Points
There is no single "quantum computing prerequisites" list because there is no single path into the field. Pick the track that matches your goals.
Most learners start here
The Software Track
Write quantum circuits, use frameworks like Qiskit or PennyLane, and run experiments on real hardware via cloud access. No physics degree required.
You need
- Python (comfortable, not expert)
- Linear algebra (vectors, matrices, eigenvalues)
- Complex numbers (Euler's formula, polar form)
You do NOT need
- Quantum mechanics
- Advanced physics
- Differential equations
For algorithm designers
The Theory Track
Understand quantum algorithms deeply, prove correctness, design new protocols, and work at the boundary of quantum computing and complexity theory.
You need
- Linear algebra (thorough, not just familiar)
- Probability theory
- Some quantum mechanics
- Complexity theory basics (P, NP, BQP)
For engineers and physicists
The Hardware Track
Understand and build quantum processors. Work on superconducting circuits, trapped ions, photonics, or neutral atoms at the physical layer.
You need
- Quantum mechanics (undergraduate level)
- Electromagnetism
- Materials science concepts
- Cryogenics basics (for superconducting systems)
02 Mathematics Requirements
Here is what each math topic actually is, why it matters for quantum computing, what level you need, and where to learn it.
Essential for all tracks
Linear Algebra
What it covers. Vectors, matrices, eigenvalues, tensor products, inner products, and unitary matrices.
Why it matters for quantum. Quantum states are vectors. Gates are matrices. Measurements are eigenvalue problems. There is no shortcut around this one.
Level needed. Comfortable, not just familiar. You need to be able to manipulate these objects without slowing down.
Where to learn it
Essential
Complex Numbers
What it covers. Imaginary numbers, complex arithmetic, Euler's formula (e^{iθ} = cosθ + i sinθ), and polar form.
Why it matters for quantum. Quantum amplitudes are complex numbers. Phase is fundamental to interference, which is what quantum algorithms exploit.
Level needed. Fluent with arithmetic and Euler's formula. This is a 1-2 week topic if you have not seen it.
Where to learn it
Important
Probability and Statistics
What it covers. Probability distributions, expected values, Bayes theorem, and random variables.
Why it matters for quantum. Quantum measurement outcomes are probabilistic. Shot noise is statistical. Understanding variance helps you interpret real hardware results.
Level needed. Solid grasp of probability spaces and expectation values.
Where to learn it
Useful (not essential for software track)
Calculus
What it covers. Derivatives, integrals, and multivariable calculus.
Why it matters for quantum. Variational quantum algorithms (VQE, QAOA) use gradient descent. Continuous optimisation appears throughout quantum machine learning.
Level needed. Basic for the software track. Solid for the theory track.
Where to learn it
Advanced track only
Group Theory / Abstract Algebra
What it covers. Groups, symmetries, and representations.
Why it matters for quantum. The Clifford group, stabiliser formalism, and quantum error correction codes all rely on group-theoretic structure.
Level needed. Introductory understanding is sufficient for most purposes.
Where to learn it
You can learn it concurrently with quantum computing rather than front-loading months of pure math before writing a single circuit.
03 Physics Requirements
Physics requirements depend heavily on your track. The software track needs very little. The hardware track needs a solid undergraduate physics background.
Hardware track essential; software track optional
Quantum Mechanics
What it covers. Schrodinger equation, bra-ket notation, observables, and spin.
Why it matters for quantum. Helps you understand what qubits physically are and why quantum gates work the way they do.
Level needed. At minimum: understand the postulates of quantum mechanics. For the hardware track: undergraduate level.
Where to learn it
Software track essential
Classical Computing / CS Fundamentals
What it covers. Algorithms, data structures, and computational complexity (P vs NP basics).
Why it matters for quantum. Quantum algorithms are always compared to their classical counterparts. Complexity classes (BQP, NP, P) are central to understanding where quantum actually helps.
Level needed. Comfortable with algorithm analysis and big-O notation.
Where to learn it
04 Do I Need X?
Quick answers to the questions beginners ask most often.
- Do I need to know quantum mechanics?
- Not for the software track. You can write and run quantum circuits using Qiskit or Cirq without understanding the physics of how qubits are built. Quantum mechanics becomes important if you want to work in hardware, understand noise at a physical level, or design new gate sets.
- Do I need a physics degree?
- No. Many quantum software engineers come from computer science or mathematics backgrounds. The relevant physics for the software track fits into a few self-study weeks.
- Do I need to be good at math?
- Yes, linear algebra is unavoidable for all tracks. The good news: you can learn it concurrently with quantum computing rather than front-loading months of pure math before writing a single circuit. Start quantum basics early; they will motivate the math.
- Can I start with Python only?
- Yes, as an entry point. Our Python for Quantum Computing tutorial covers the Python foundations you need to run your first circuit. You will need to pick up linear algebra soon after, but you do not have to do it before touching any quantum code. Tutorial: Python for Quantum Computing
- How long does it take to get prerequisites ready?
- For the software track: 2 to 4 months of focused study if starting from scratch. If you already have Python and some linear algebra, you can start writing circuits in a few weeks. The theory track realistically takes 6 to 12 months of serious study to build solid foundations.
05 Recommended Learning Order
The most common case: the software track, starting from a general programming background. Follow this sequence and you will be writing real quantum circuits within a few months.
- Python basics 2-3 weeks (skip if already comfortable) If you are not already comfortable with Python, spend 2 to 3 weeks here. You need lists, functions, NumPy arrays, and basic object-oriented syntax.
- Linear algebra 6-8 weeks The single most important prerequisite. Cover vectors, matrix multiplication, eigenvalues, and inner products. Brilliant or MIT OCW 18.06 both work well. MIT OCW 18.06
- Complex numbers 1-2 weeks Short but essential. Focus on Euler's formula and polar form. This can run in parallel with the tail end of linear algebra.
- First quantum tutorial 1-2 hours Start with what a qubit actually is before diving into circuits. This bridges math to physical intuition. Tutorial: What Is a Qubit?
- Hello World with Qiskit 1-2 hours Write and run your first quantum circuit. From this point, you are learning quantum computing by doing it. Tutorial: Qiskit Hello World
- Follow a structured learning path Ongoing Once you have run your first circuits, choose a path matched to your goals: software, theory, or hardware. View Learning Paths