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maths for quantum computing what you need skip to main content quantumcomputing courses com courses all courses course platforms coursera edx udemy brilliant hardware providers google quantum ai ibm quantum ionq quantinuum amazon braket azure quantum quera rigetti d wave tutorials all tutorials hello world qiskit hello world cirq hello world pennylane hello world braket quantum gates grover s algorithm shor s algorithm reference all frameworks qiskit cirq pennylane amazon braket pyquil tket d wave ocean q explore learn learning paths prerequisites programming guide case studies glossary books quantum news podcasts tools bloch sphere quantum pinball guides algorithm guide hardware guide qubit types framework comparison migration guide language timeline cheat sheets career events 2026 jobs careers certifications salary guide universities interview prep faq troubleshooting about about team search browse courses home maths for quantum computing maths for quantum computing quantum computing has a reputation for requiring heavy mathematics that reputation is partly earned and partly exaggerated here is an honest breakdown of what you actually need at what stage and where to learn it without gatekeeping how much maths do you actually need the answer depends entirely on what you want to do with quantum computing for conceptual understanding grasping superposition entanglement and why quantum computers are interesting you need almost no formal mathematics high school algebra is enough to follow intuitive explanations for gate model algorithms implementing circuits in qiskit or cirq understanding grover s algorithm or quantum phase estimation you need linear algebra and complex numbers these are genuinely necessary a university level linear algebra course or a dedicated self study track of three to five weeks gets you there for variational algorithms and quantum machine learning vqe qaoa quantum neural networks you add multivariate calculus and some probability theory on top these are used in gradient based optimisation of circuit parameters for quantum error correction stabiliser codes surface codes logical qubit design you need group theory and abstract algebra this is research level territory for theoretical research proving complexity bounds developing new algorithms you need a broad mathematical toolkit this is a graduate level pursuit and not what most practitioners need the takeaway most people learning quantum computing for practical or career purposes need linear algebra and complex numbers and that is it for a long time do not let unfamiliar sounding prerequisites stop you from starting the essential topics these are the mathematical building blocks that appear directly in quantum computing theory and practice linear algebra the core language of quantum computing quantum states are vectors quantum gates are matrices specifically unitary matrices measurement is an eigenvalue problem you need vectors and vector spaces matrix multiplication inner products eigenvalues and eigenvectors and the tensor product for multi qubit systems complex numbers quantum amplitudes are complex valued euler s formula e i theta cos i sin is everywhere rotation gates the bloch sphere phase kickback and the quantum fourier transform all use it you need basic arithmetic with complex numbers modulus and argument and euler s formula a few hours covers it probability and statistics quantum measurement is inherently probabilistic the born rule says the probability of measuring a state is the squared modulus of its amplitude you need basic probability expectation values and enough statistics to interpret shot based results from real quantum hardware calculus optional not needed for standard gate based algorithms becomes important when you reach variational algorithms vqe and qaoa use gradient descent to optimise circuit parameters and quantum machine learning uses backpropagation you can safely defer this until you reach variational methods fourier analysis the quantum fourier transform qft is a central subroutine in many algorithms including shor s factoring algorithm and quantum phase estimation understanding the classical discrete fourier transform first makes the quantum version much clearer basic familiarity is useful deep mastery is not required group theory advanced needed primarily for quantum error correction stabiliser codes and the pauli group are described using group theory also useful for understanding symmetry based quantum algorithms this is advanced territory most practitioners never need it outside research the topics you don t need quantum computing sounds intimidating in part because of its name but many mathematical topics associated with physics are not required for computing work quantum mechanics the physics quantum computing borrows the mathematical formalism of quantum mechanics but you do not need to understand the underlying physics you do not need to know about wave particle duality the schrodinger equation or atomic structure the circuit model is an abstraction that sits above the physics differential equations not required for gate based quantum computing the schrodinger equation is a differential equation but quantum computing replaces continuous time evolution with discrete gate operations you will encounter differential equations only if you go deep into hamiltonian simulation or analog quantum computing topology sometimes mentioned alongside quantum computing topological quantum computing is a research approach not relevant for standard gate model or annealing based work you can ignore this entirely unless you are specifically interested in topological qubits real analysis and measure theory these are graduate level pure mathematics topics they underpin rigorous probability theory but are not needed for practical quantum computing if you have taken a real analysis course great but you do not need it to start learning order if you are building your maths skills from scratch alongside learning quantum computing this is a practical sequence that avoids spending time on topics you do not yet need 1 linear algebra basics start here focus on vectors matrices matrix multiplication and eigenvalues brilliant s linear algebra course or the 3blue1brown essence of linear algebra series are both excellent starting points give this two to four weeks of part time study 2 complex numbers short and focused you need to understand complex arithmetic the complex plane modulus and euler s formula this can be covered in a few dedicated hours it does not require weeks of study brilliant s complex numbers course is a good option 3 probability fundamentals enough to understand the born rule and interpret measurement results basic probability events distributions expectation values is sufficient for most gate model work this pairs well with starting hands on circuit work in qiskit 4 calculus for variational methods optional add this only when you reach variational quantum algorithms at that point you need partial derivatives and gradient descent if you have covered calculus before a quick refresher is enough if not defer it until you are actively working on vqe or qaoa looking for a structured path see the learning paths guide or the prerequisites overview for more detail on building up from the fundamentals courses for maths and quantum computing courses covering the mathematical foundations of quantum computing including linear algebra probability and complex numbers brilliant applied probability build intuition for probability from first principles essential for understanding quantum measurement born s rule and why quantum algorithms work self paced beginner diff easy maths medium code low paid enroll brilliant complex numbers quantum states are described using complex numbers amplitudes phases and the complex plane this course builds the fluency you need before tackling quantum mechanics self paced beginner diff easy maths medium code low paid enroll brilliant computer science fundamentals brilliant s interactive introduction to computer science through algorithms searching sorting big o analysis and graph problems the computational thinking that underpins both classical and quantum computing self paced beginner diff easy maths medium code low paid enroll d wave foundations for quantum programming d wave preparatory course building the math and python skills needed before d wave s quantum programming core covers qubo formulation quadratic models constraint writing and python for optimization optional but recommended for developers without strong math backgrounds 10 hours beginner diff easy maths medium code high 350 enroll d wave getting started with applied quantum optimization learn to identify and describe optimization problems suited for d wave s quantum classical hybrid technology covers problem discovery constraint definition and building a quantum business case no math or physics background required 5 hours beginner diff easy maths medium code low 50 enroll wolfram research introduction to quantum computing with the wolfram language wolfram s quantum computing framework for mathematica and the wolfram language offering a unique symbolic computation approach to quantum circuits ideal for mathematical exploration visualization and analysis without writing low level circuit code 8 hours beginner diff easy maths low code medium free enroll brilliant logic build rigorous logical reasoning from the ground up through interactive deduction puzzles the careful thinking that quantum computing study demands self paced beginner diff easy maths low code low paid enroll brilliant quantum computing interactive brilliant s interactive quantum computing course learn by doing with hands on puzzles and visualisations subscription based covered by brilliant s free trial self paced beginner diff easy maths medium code medium paid enroll microsoft quantum katas self paced quantum programming exercises microsoft microsoft quantum microsoft s free collection of self paced quantum programming exercises in q covers quantum basics through advanced algorithms via hands on kata style challenges with immediate feedback runnable in the browser self paced beginner diff easy maths medium code medium free enroll frequently asked questions do you need a maths degree to learn quantum computing no a maths degree is not required especially for conceptual or introductory study many quantum computing courses are designed for people with only high school algebra for practical work with real algorithms implementing grover s running qiskit circuits understanding quantum machine learning you need linear algebra and a working knowledge of complex numbers that is a fraction of a university maths education and can be picked up in a few weeks with the right resources what linear algebra do you need for quantum computing you need vectors and vector spaces quantum states are column vectors matrix multiplication applying gates means multiplying matrices inner products and norms for calculating probabilities from amplitudes eigenvalues and eigenvectors measurement and hamiltonian dynamics the tensor product combining multi qubit systems you do not need advanced topics like abstract algebra measure theory or functional analysis for most practical quantum computing work are complex numbers required for quantum computing yes complex numbers are unavoidable quantum amplitudes are complex numbers not real numbers the born rule squaring the amplitude to get a probability only makes sense if you understand complex modulus euler s formula e i theta cos theta i sin theta underpins rotation gates the bloch sphere and the quantum fourier transform the good news you only need the basics of complex numbers not complex analysis a few hours of study covers what you need how much calculus do you need for gate based quantum computing very little standard textbook algorithms grover shor quantum phase estimation require almost no calculus calculus becomes important if you work on variational quantum algorithms vqe qaoa or quantum machine learning where gradient descent is used to optimise circuit parameters if you are new to quantum computing you can safely defer calculus and come back to it when you reach variational methods what is the hardest maths concept in quantum computing for most learners the tensor product is the first genuinely difficult concept it explains how multi qubit systems combine and why an n qubit system lives in a 2 n dimensional space rather than an n dimensional one understanding entanglement mathematically requires the tensor product after that spectral decomposition expressing operators in terms of their eigenvectors and eigenvalues is the next conceptual hurdle and it is central to quantum measurement and hamiltonian simulation where to go next if you want to see which courses assume prior maths knowledge check the prerequisites page ready to start learning quantum computing see quantum computing for beginners for an entry level starting point or browse the learning paths for a structured route get one quantum email a week new tutorials courses worth taking and what changed in qiskit cirq pennylane this week no spam unsubscribe anytime email address subscribe 112 courses 220 tutorials 241 glossary terms 26 framework references 34 case studies quantumcomputing courses com free tutorials curated courses framework references and tools for anyone learning quantum computing written and maintained by dr donovan who writes on quantum computing research hardware and industry at quantum zeitgeist learn all courses free tutorials learning paths compare frameworks algorithm guide case studies quantum news reference glossary framework docs hardware guide qubit types history timeline cheatsheets bloch sphere quantum programming careers careers guide salary guide certifications interview questions jobs team training post a job talent pool about about this site editorial 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