Coherence, Decoherence, and Error Correction
A first pass. Incomplete by design.
Coherence
For superposition and entanglement to do work, the qubits must stay in a state where their phases are defined relative to one another. That condition is coherence. Any interaction with the outside world (a stray photon, a vibrating atom, a cosmic ray) acts like a measurement and destroys it. The information is not deleted so much as leaked into the environment, where it cannot be recovered.
Decoherence as the engineering problem
Decoherence times for today's hardware range from microseconds (superconducting circuits) to seconds or longer (trapped ions). A computation must finish, or be corrected, before the phases drift. Every hardware platformNoteGrowingQubit Hardware: The Five Leading ApproachesSuperconducting circuits, trapped ions, photons, silicon spins, and topological qubits: what each is, the trade-off each makes, and who is building it. Originally Appendix C of The Resolution of Reality. is a different bet about how to buy more coherence time or faster gates.
Logical versus physical qubits
Physical qubits fail. A logical qubit is an encoded object spread across many physical qubits so that errors can be detected and undone without measuring the encoded value. The overhead depends on the physical error rate: the lower the error rate, the fewer physical qubits per logical qubit. Estimates in the literature have ranged from about a thousand physical qubits per logical qubit down to far fewer as error rates fall and codes improve. The 4,000 or so logical qubits Shor needs for RSA-2048 therefore translate into a physical machine one to three orders of magnitude larger.
What to watch
The headline number in hardware announcements is usually the physical qubit count. The number that matters is the two-qubit gate error rate, because it sets the physical-to-logical ratio and therefore the size of machine needed for any useful algorithm.
What this note does not yet cover
- The threshold theorem and why it makes error correction possible at all.
- Surface codes versus newer low-overhead codes.
- Current best published resource estimates for RSA-2048.
Review log
- 2026-09-08: seeded from Sections V and VI of The Resolution of Reality. Resource-estimate figures deliberately left qualitative until sourced.
Appears in
Essays that draw on this note.
- The Resolution of RealityA primer on quantum computing: how physical law replaces brute-force search, why the advantage depends on how native the problem is to the machine, and where hybrid classical-quantum architectures fit.
Links out
- Qubit Hardware: The Five Leading ApproachesSuperconducting circuits, trapped ions, photons, silicon spins, and topological qubits: what each is, the trade-off each makes, and who is building it. Originally Appendix C of The Resolution of Reality.
Referenced by
Other notes and pages that link here.
- Entanglement and Bell's TheoremWhy entangled particles are correlated more strongly than any pre-written script allows, shown through the CHSH game, the three-polarizer experiment, and the 2√2 bound. Originally Appendix B of The Resolution of Reality.
- Key Quantum Algorithms: Shor, Grover, and SimulationThe three algorithm families that define what quantum computers are for, the speedup each delivers, and why the speedups differ. Originally Appendix D of The Resolution of Reality.
- Qubit Hardware: The Five Leading ApproachesSuperconducting circuits, trapped ions, photons, silicon spins, and topological qubits: what each is, the trade-off each makes, and who is building it. Originally Appendix C of The Resolution of Reality.
Related
- Superposition and InterferenceA qubit before measurement holds amplitudes for both outcomes; computation is the controlled interference of those amplitudes. The double slit is the physical demonstration.
- Entanglement and Bell's TheoremWhy entangled particles are correlated more strongly than any pre-written script allows, shown through the CHSH game, the three-polarizer experiment, and the 2√2 bound. Originally Appendix B of The Resolution of Reality.