Where to learn quantum, sorted
Courses, papers, books and tools the community actually uses, grouped by area and marked by level. Start at Foundations if you're new.
Foundations
5- CourseBasics of Quantum Information John Watrous, IBM Quantum LearningThe cleanest free start: qubits, measurement and entanglement, with the maths shown properly.Beginner
- CourseQuantum Country Andy Matuschak and Michael NielsenEssays with built-in spaced repetition, so what you read actually sticks.Beginner
- CoursePennyLane Codebook XanaduShort lessons where you write the code as you go, from single qubits to Shor.Beginner
- BookQuantum Computation and Quantum Information Michael Nielsen and Isaac Chuang"Mike and Ike". The textbook the whole field learned from.Intermediate
- CourseLecture notes for Physics 219/229: Quantum Computation John Preskill, CaltechFree, rigorous notes from one of the people who named the field's big ideas.Advanced
Algorithms
7- ToolQuantum Algorithm Zoo Stephen JordanA catalogue of every known quantum algorithm and the speedup it offers.Intermediate
- PaperPolynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer Peter Shor, 1994Shor's algorithm. The paper that made everyone take quantum computing seriously.Advanced
- PaperA fast quantum mechanical algorithm for database search Lov Grover, 1996Grover's search: a square-root speedup for unstructured search, in five pages.Intermediate
- PaperQuantum algorithm for solving linear systems of equations Harrow, Hassidim and Lloyd, 2008HHL. The root of most claims about quantum speedups for linear algebra.Advanced
- PaperA variational eigenvalue solver on a quantum processor Peruzzo et al., 2013VQE, the hybrid quantum-classical loop behind most chemistry work today.Intermediate
- PaperA Quantum Approximate Optimization Algorithm Farhi, Goldstone and Gutmann, 2014QAOA, the go-to algorithm for optimisation problems on near-term hardware.Intermediate
- PaperQuantum Computing in the NISQ era and beyond John Preskill, 2018Where the term NISQ comes from, and an honest look at what near-term machines can do.Beginner
Hardware and error correction
5- PaperThe Physical Implementation of Quantum Computation David DiVincenzo, 2000The DiVincenzo criteria: what any physical system needs to be a quantum computer.Beginner
- PaperA Quantum Engineer's Guide to Superconducting Qubits Krantz et al., 2019How transmons are designed, controlled and read out. The engineer's reference.Advanced
- PaperQuantum supremacy using a programmable superconducting processor Arute et al. (Google), Nature 2019Sycamore, and the first claim of a quantum computer beating a classical one at anything.Intermediate
- PaperSurface codes: Towards practical large-scale quantum computation Fowler et al., 2012The long, careful introduction to the error-correcting code most hardware is betting on.Advanced
- PaperQuantum error correction below the surface code threshold Google Quantum AI, 2024Willow: adding qubits finally made the logical qubit better, not worse.Advanced
Quantum machine learning
5- PaperAn introduction to quantum machine learning Schuld, Sinayskiy and Petruccione, 2014A gentle survey to read before anything else in QML.Beginner
- PaperQuantum Machine Learning Biamonte et al., Nature 2017The widely cited review of where quantum could help machine learning.Intermediate
- PaperSupervised learning with quantum enhanced feature spaces Havlíček et al., 2018Quantum kernels and variational classifiers, run on real hardware.Intermediate
- PaperBarren plateaus in quantum neural network training landscapes McClean et al., 2018Why many quantum neural networks are hard to train, and the problem the field is still working on.Advanced
- ToolPennyLane demos XanaduHundreds of runnable notebooks covering QML, chemistry and optimisation.Beginner
Cryptography
5- PaperQuantum cryptography: Public key distribution and coin tossing Charles Bennett and Gilles Brassard, 1984BB84, the first quantum key distribution protocol. Short and readable.Beginner
- PaperQuantum cryptography based on Bell's theorem Artur Ekert, 1991E91: key distribution secured by entanglement itself.Intermediate
- PaperHow to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits Craig Gidney and Martin Ekerå, 2019A concrete estimate of what it would take to break RSA, and why it matters now.Advanced
- ToolPost-Quantum Cryptography NISTThe standards process choosing the encryption that should survive quantum computers.Beginner
- PaperFIPS 203: Module-Lattice-Based Key-Encapsulation Mechanism NIST, 2024ML-KEM (Kyber), the first finished post-quantum encryption standard.Advanced
Tools and SDKs
8- ToolQiskit IBMThe most widely used quantum SDK, with free access to IBM's real hardware.Beginner
- ToolCirq Google Quantum AIGoogle's Python framework for writing and simulating circuits close to the hardware.Intermediate
- ToolPennyLane XanaduDifferentiable quantum programming that plugs into PyTorch and JAX.Beginner
- ToolCUDA-Q NVIDIAGPU-accelerated simulation and hybrid quantum-classical programming.Intermediate
- ToolAmazon Braket AWSOne SDK for hardware from several vendors: ions, neutral atoms and superconducting.Intermediate
- ToolQuTiP QuTiP communitySimulate open quantum systems: noise, decay and the physics under the qubits.Advanced
- ToolQuirk Craig GidneyA drag-and-drop circuit simulator in the browser. The fastest way to build intuition.Beginner
- VideoQiskit on YouTube IBMYears of lectures, summer school recordings and coding walkthroughs.Beginner
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