Chapter 3 — Physics for computing
Lesson map
Lesson 03 published. Map, example, EX005.
flowchart TD
N0["Learning outcomes"]
N1["3.1 Qubits and measurement"]
N2["3.2 Entanglement and gates"]
N3["3.3 Decoherence and error correction"]
N4["3.4 Quantum key distribution is different"]
N5["Synthesis"]
N0 --> N1 --> N2 --> N3 --> N4 --> N5
N5 --> EX["Worked example"]
EX --> Q["Exercise EX005"]
Logical drawing
flowchart LR
N0["Learning outcomes"]
N1["3.1 Qubits and measurement"]
N2["3.2 Entanglement and gates"]
N3["3.3 Decoherence and error correction"]
N4["3.4 Quantum key distribution is different"]
N5["Synthesis"]
N0 --> N1 --> N2 --> N3 --> N4 --> N5 --> Q["EX005"]
[Learning outcomes]
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[3.1 Qubits and measurement]
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[3.2 Entanglement and gates]
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[3.3 Decoherence and error correction]
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[3.4 Quantum key distribution is different]
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v
[Synthesis]
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[Worked example] --> [Exercise EX005]
Learning outcomes
You will (1) describe a qubit, superposition, measurement and entanglement in engineering terms; (2) explain decoherence and why error correction dominates the cost of a quantum computer; (3) distinguish physical from logical qubits; and (4) separate quantum computing from quantum key distribution. It builds on Chapters 1–2 and frames the threat used throughout the book.
3.1 Qubits and measurement
A classical bit is 0 or 1. A qubit's state is a combination α|0⟩ + β|1⟩ with complex amplitudes whose squared magnitudes sum to one; measurement returns 0 with probability |α|² and 1 with probability |β|², and destroys the superposition. n qubits are described by 2^n amplitudes, but measurement yields only n bits, so a quantum algorithm must arrange interference so that wrong answers cancel and right answers reinforce. Shor's algorithm does this for periods; for most problems no such arrangement is known, which is why quantum computers are not general accelerators.
3.2 Entanglement and gates
Entangled qubits have correlated measurement outcomes that cannot be explained by independent states. Gates — rotations of single qubits and controlled operations on pairs — build circuits. Algorithms are measured in logical gate counts and circuit depth, the number of sequential layers, which matters because errors accumulate with time.
Depth matters because qubits decohere while they wait: a circuit with many sequential layers must finish before errors overwhelm it, or error correction must keep up. That is why resource estimates report both logical qubits and a runtime figure. Entanglement is a resource algorithms use, not a speed-up on its own; most problems gain nothing from it.
3.3 Decoherence and error correction
Physical qubits lose their state through interaction with the environment (decoherence) and through imperfect gates. Quantum error correction encodes one logical qubit in many physical qubits — in surface-code designs, hundreds to thousands — and continuously measures syndromes to correct errors. This overhead is why estimates for breaking RSA-2048 moved from twenty million noisy qubits (Gidney and Ekerå 2021) to under a million (Gidney 2025) as algorithms and codes improved — and why counts of physical qubits in press releases say little about cryptographic relevance without error rates.
3.4 Quantum key distribution is different
Quantum key distribution (QKD) uses quantum states of light to agree keys, with security grounded in physics, but it needs special hardware, point-to-point links and authenticated classical channels, and it does not provide signatures. Several agencies, including the NSA, recommend PQC rather than QKD for most uses. This book treats QKD as a niche technology and PQC as the migration path.
QKD also leaves authentication to classical cryptography, so a QKD link still needs signatures or pre-shared keys, which brings PQC back into the design. Its distance limits and trusted-node relays add physical security problems. For BPA's customs exchange over the public internet, QKD is not an option, while hybrid TLS with ML-KEM can be deployed on existing servers.
3.5 Worked example
A vendor tells BPA that "a 1,000-qubit machine was announced, so RSA is broken soon". The engineering response: ask for error rates, logical qubit counts and circuit depth; compare with published resource estimates; note that a thousand noisy physical qubits is orders of magnitude short of the estimates; and still migrate, because recorded traffic must stay secret for decades (Chapter 20).
The vendor's number answers none of the questions that matter for RSA-2048. Physical qubits must be turned into logical ones at a ratio of hundreds or thousands, and the circuit must run long enough without failure. Even so, the conclusion is to keep migrating: the case for action rests on how long customs data must stay secret, not on the date of the next announcement.
3.6 Common errors and limits
- Saying quantum computers "try all answers at once".
- Equating physical and logical qubits.
- Presenting QKD as a replacement for PQC.
Superposition does not let a quantum computer read out all answers; measurement returns one result, and only interference designed for a specific structure helps. Physical and logical qubits differ by error-correction overhead, so headlines about qubit counts say little about cryptographic risk. QKD needs dedicated links and leaves signatures unsolved, so it cannot replace PQC across ordinary networks such as the internet links BPA's partners use.
Exercises
- EX005 — Overhead arithmetic. If a logical qubit needs 1,000 physical qubits and an algorithm needs 1,400 logical qubits plus 30% ancilla overhead, how many physical qubits are needed? Rubric: 3 = correct (1.82 million) and comment on assumptions.
- EX006 — Vendor claim. Write three questions that turn a qubit-count announcement into evidence. Rubric: 3 = error rate, logical count, depth/time.
Synthesis
Quantum algorithms exploit interference for special problems; error correction makes useful machines enormous; announcements must be translated into logical resources; QKD is not the migration path.
Continue studying — chapter 03 of 50
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