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fault tolerant quantum computing quantum computing glossary 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 company editorial policy search browse courses home glossary fault tolerant quantum computing error correction fault tolerant quantum computing also called ftqc quantum computation using error corrected logical qubits that can run arbitrarily long algorithms despite imperfect physical hardware fault tolerant quantum computing ftqc is the end goal of the field the idea is to build a quantum processor that can run algorithms of arbitrary length and complexity despite the fact that its physical components are imperfect and noisy this requires encoding quantum information redundantly so that errors can be detected and corrected continuously faster than they accumulate we do not have this capability yet current machines are nisq devices noisy uncorrected and limited to shallow circuits ftqc is what comes next the details physical qubits have error rates around 0 1 1 0 1 1 0 1 1 per gate that sounds small but an algorithm requiring one million gates fails with near certainty at a 0 1 0 1 0 1 error rate 1 0 001 1 000 000 5 10 435 1 0 001 1 000 000 approx 5 times 10 435 1 0 001 1 000 000 5 1 0 435 success probability to run deep algorithms you need logical error rates closer to 10 15 10 15 1 0 15 per gate fault tolerance achieves this by encoding one logical qubit across many physical qubits errors in individual physical qubits are detected by measuring stabilizer syndromes collective observables of groups of physical qubits that reveal what error occurred without revealing the logical state a classical decoder processes the syndrome measurements and determines which corrections to apply the threshold theorem provides the theoretical foundation if physical gate error rates fall below a code specific threshold value then by increasing the number of physical qubits per logical qubit the logical error rate can be suppressed exponentially below threshold more redundancy always helps above threshold it makes things worse the leading error correction code is the surface code which has a threshold around 1 1 1 and requires roughly 1 000 1 000 1 000 physical qubits per logical qubit at current error rates running shor s algorithm to factor a 2048 bit rsa key requires approximately 4 000 4 000 4 000 logical qubits implying roughly 4 4 4 million physical qubits operating below the surface code threshold beyond qubit count additional engineering constraints must be satisfied syndrome extraction speed mid circuit measurements must be fast enough that syndrome data is available before the next round of errors occurs classical decoding latency the classical decoder processing syndromes must keep pace with the circuit in real time at scale decoding is itself a hard computational problem magic state distillation some fault tolerant gate sets for universal computation require preparing high fidelity ancilla states which is expensive in qubit overhead the gap between nisq devices and a logical machine the gap between nisq and ftqc is the central organizing fact of the current quantum computing landscape understanding this gap explains why current quantum computers cannot run shor s algorithm at cryptographic scale why the race to improve qubit coherence times and gate fidelities matters why qubit count headlines are misleading without the physical logical distinction why organizations like nist are already standardizing post quantum cryptography timeline estimates range from ftqc demonstrations in the late 2020s to cryptographically relevant computation in the 2030s ibm google quantinuum microsoft and ionq all publish roadmaps toward fault tolerance but those roadmaps have historically been optimistic common misconceptions misconception 1 ftqc just means having more qubits qubit count is necessary but not sufficient you also need error rates below the fault tolerance threshold fast mid circuit measurements high fidelity two qubit gates and a working classical decoder ibm s 1 000 qubit condor chip is not fault tolerant because its gate error rates are too high and there is no active error correction loop misconception 2 once we hit the threshold ftqc is solved being below threshold means logical error rates can be suppressed by adding more physical qubits it does not mean they are already low enough going from a threshold error rate to the 10 15 10 15 1 0 15 needed for shor s algorithm still requires massive physical qubit overhead and engineering work misconception 3 nisq devices will smoothly transition into ftqc devices ftqc requires a fundamentally different architecture active syndrome extraction real time classical decoding and different circuit compilation strategies most current nisq hardware will not simply be upgraded new purpose built fault tolerant systems are being developed alongside see also quantum error correction logical qubit surface code nisq shor s algorithm related terms logical qubit an error protected qubit encoded across many physical qubits capable of surviving long computations the unit of quantum computing in a fault tolerant machine nisq noisy intermediate scale quantum the current era of quantum computing characterised by 50 1 000 physical qubits with no error correction and limited circuit depth quantum error correction techniques for protecting quantum information from decoherence and gate errors by encoding logical qubits redundantly across multiple physical qubits surface code the leading quantum error correction code arranging qubits on a 2d grid and detecting errors via local measurements currently the most practical path to fault tolerant quantum computing used in these tutorials quantum gates hadamard pauli cnot toffoli with diagrams beginner 15 min read quantum gates as matrices the linear algebra behind quantum computing beginner 20 min read quantum annealing vs gate based quantum computing beginner 20 min implementing quantum teleportation in qiskit intermediate 20 min read 17 tutorials mention this learn more ready to go deeper on fault tolerant quantum computing browse structured courses browse courses free tutorials previous fault tolerance threshold all terms next flag qubit 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 an independent catalog of quantum computing courses and tutorials published by hadamard llc 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 company editorial policy faq events 2026 podcasts books contact as an amazon associate quantumcomputingcourses com earns from qualifying purchases 2026 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