A cryptographically relevant quantum computer, or CRQC, is a machine powerful enough to run Shor’s algorithm at the scale needed to break the public-key cryptography that secures almost all digital communication. No such machine exists in 2026, and the largest quantum computers are still many generations short of one. Yet the prospect already drives a global migration to post-quantum cryptography, because data stolen today can be decrypted once a CRQC arrives. This guide explains what a cryptographically relevant quantum computer requires, which companies are closest, what the experts expect, and how to prepare. 1. No CRQC exists yet. Breaking RSA-2048 needs thousands of error-corrected logical qubits running deep circuits, and the best machines today field only dozens of logical qubits. The gap is large. 2. The bar keeps moving. Better algorithms have cut the estimated physical-qubit cost of breaking RSA-2048 from around 20 million to under a million, so the threshold is getting easier to reach even before hardware catches up. 3. The mid-2030s is the consensus window. Most surveyed experts put a meaningful probability on a cryptographically relevant quantum computer appearing within a decade, with the heaviest weight around 2030 to 2035. 4. Harvest now, decrypt later is the live threat. Adversaries can store encrypted data today and decrypt it once a CRQC exists, which puts long-lived secrets at risk right now. 5. The fix is already standardised. The United States finalised post-quantum cryptography standards in 2024, and the migration to them is the practical defence against the quantum threat. 6. Watch logical qubits, not physical ones. Roadmaps from IBM, Google, Quantinuum, IonQ and PsiQuantum should be judged on error-corrected logical qubits, the real measure of progress toward a CRQC. What is a cryptographically relevant quantum computer? A cryptographically relevant quantum computer is defined by capability rather than size,