Logical vs Physical Qubits

The qubit count on a press release is physical; the number that actually matters is how many reliable “logical” qubits those add up to — often a thousand-to-one.

Quantum Computing · Lesson 32 · 11 min read

You keep hearing “this machine has 1,000 qubits!” — but after the last two lessons you should be suspicious. Those are physical qubits: noisy, error-prone, individually useless for a long computation. What a real algorithm needs is logical qubits: reliable, error-corrected qubits built out of many physical ones (lessons 15, 31). The gap between these two is the single most important — and most abused — number in quantum computing. Get it straight and you can cut through almost any quantum headline. Hold the question: what exactly turns a pile of flaky physical qubits into one trustworthy logical qubit, and how many does it take?

A logical qubit is a team playing one qubit

A physical qubit is a single real device (an atom, a bit of superconducting circuit — next lesson) — noisy and short-lived (lesson 14). A logical qubit is one reliable qubit encoded across many physical qubits using a code like the surface code, with constant error-checking keeping it alive (lessons 15, 31). The logical qubit is what your algorithm actually manipulates; the physical qubits are the redundant hardware underneath, quietly absorbing and correcting errors. So “how many qubits does it have?” is a trick question — you must ask physical or logical? A machine with 1,000 physical qubits and a demanding code might offer just a handful of logical qubits, or even none good enough yet.

Code distance: the dial you turn for reliability

How reliable a logical qubit is depends on a tunable number called the code distance (call it d): roughly, how many physical qubits across the protective grid is — a bigger patch of the surface code. A larger distance means more physical qubits devoted to one logical qubit, and it takes more simultaneous errors to overwhelm the code. Here’s the powerful part: as long as the hardware is below threshold (lesson 15), increasing the distance suppresses the logical error rate exponentially. Add a bit more distance (a modest, linear increase in physical qubits) and the logical error rate drops by a large factor — a fantastic exchange rate. That exponential payoff is the whole reason error correction is viable: you buy dramatic reliability with merely-large (not impossible) overhead.

Turning the distance dial (illustrative):
• Distance 3: a small patch of physical qubits → tolerates a single error, modest protection.
• Distance 5: a bigger patch → tolerates more errors; logical error rate drops sharply.
• Distance 7, 9, …: each step up costs a chunk more physical qubits but slashes the logical error rate by another big factor.
• So you dial the distance up until the logical qubit is reliable enough for your algorithm’s length — paying in physical qubits, winning exponentially in reliability.

Why “logical qubits” is the honest metric

Now the payoff for reading the field. Because a useful algorithm may need thousands of logical qubits, each costing hundreds to thousands of physical qubits (lesson 15’s overhead), a truly useful machine may need millions of physical qubits. That’s why the honest way to size up a quantum computer is not its physical qubit count but roughly how many reliable logical qubits it can sustain, and at what code distance — plus whether its physical error rate is actually below threshold so that scaling even helps. A headline screaming a big physical number while staying silent about logical qubits and error rates is marketing, not progress (the “hype vs reality” discipline from lesson 17). The frontier milestone everyone is racing toward is the first machines with many high-quality logical qubits — that, not raw physical counts, is what will unlock the algorithms from Module 3.

Reading a quantum spec sheet honestly:
1. “1,000 qubits!” → ask: physical or logical? These are physical.
2. What’s the physical error rate — is it below threshold? If not, adding qubits won’t help at all.
3. At the code distance they run, how many logical qubits does 1,000 physical actually yield? Maybe a handful.
4. Compare to the algorithm’s need (often thousands of logical qubits). The honest gap — physical count vs reliable logical qubits — is the real state of the machine.