The surface code is the default, but it is not the only option — and at scale, its overhead is brutal. This note compares five architectures racing to lower that cost: cat qubits, GKP codes, color codes, quantum LDPC codes, and IQM's directional tile codes — what each does, how much hardware it needs, and which qubit platform it fits.
Our first application note explained why quantum computers need error correction: physical qubits err roughly once every 1,000 operations, and a useful algorithm needs millions of operations in sequence. The fix is to spread one protected logical qubit across many noisy physical qubits, so errors can be detected and corrected faster than they accumulate.
The dominant recipe is the surface code: a 2D grid of qubits where errors are caught by repeatedly measuring "syndrome" checks. It is popular because it tolerates a relatively high error rate (~1% per gate) and needs only nearest-neighbour connections — a perfect match for chip-style hardware. But it is expensive. At the error rates useful algorithms demand, a single logical qubit can consume hundreds to a thousand physical qubits. A machine with 100 logical qubits could need ~100,000 physical ones.
That overhead is the single biggest obstacle between today's hardware and commercially useful quantum computing. Every architecture below is, at heart, an attempt to pay less for the same protection — and they split into two camps.
Make the physical qubit better (cat & GKP codes bake error-resistance into the hardware itself, so the code on top can be small), or make the code smarter (color, qLDPC and tile codes pack more logical qubits into the same physical qubits). The frontier increasingly combines both.
A cat qubit (named for Schrödinger's cat) is a "bosonic" qubit: instead of one electron or junction, it stores information in the two opposite-phase states of microwave light trapped in a superconducting resonator. By continuously pumping the resonator with engineered two-photon dissipation, the hardware actively stabilises those states.
The payoff is biased noise. One error type — the bit-flip — is suppressed exponentially as you add photons, while the other — the phase-flip — only grows slowly. In practice Alice & Bob have pushed bit-flip lifetimes past one hour (from milliseconds in ordinary qubits). When one error channel is essentially switched off, you no longer need a full 2D surface code to mop up both — a simple 1D repetition code handles the remaining phase-flips.
Alice & Bob shipped Helium, an on-premise system encoding a logical qubit in ~18 cat qubits, in June 2026, and published "Elevator Codes" claiming a ~15:1 physical-to-logical ratio. The trade-off: this only works where you can build high-quality bosonic modes, and gates between cat qubits remain the hard, unfinished part of the story.
Best suited for: Superconducting (cavity/bosonic) — the approach is intrinsic to microwave-resonator hardware.
The Gottesman–Kitaev–Preskill (GKP) code is the other major bosonic approach. Rather than two states, it encodes a qubit in a grid of many evenly-spaced peaks in an oscillator's phase space. Because real errors tend to be small shifts in that space, the grid lets you detect and undo them by snapping back to the nearest grid point — error correction built into a single mode.
GKP is the most "hardware-efficient" code on paper: one well-made oscillator is a protected qubit. The catch is that making a high-quality GKP state requires a lot of squeezing or photons, and the quality of that state — not the qubit count — becomes the bottleneck.
It is also the most platform-flexible code here. It has been error-corrected past break-even in superconducting cavities (Yale), realised in trapped ions, and is the centrepiece of Xanadu's photonic architecture: their Aurora system stitches together 35 photonic chips with 13 km of fibre, using Gaussian boson sampling to convert squeezed light into GKP qubits — all at room temperature. Xanadu's 2025 on-chip GKP qubit (published in Nature) was a milestone; reducing optical loss to reach fault-tolerant GKP quality is the remaining hurdle.
Best suited for: Photonic Superconducting (cavity) Trapped ions — anywhere you have a clean bosonic mode.
Color and surface codes are cousins — both 2D topological codes — but the color code packs its checks more tightly and, crucially, supports transversal Clifford gates. That means an operation like a Hadamard can be applied to a logical qubit by acting on each physical qubit independently, with no error-amplifying choreography. The surface code can't do this in 2D, so it leans on slower "lattice surgery." The price of the color code is higher-weight checks (each stabiliser touches more qubits), which demands very good qubits and rich connectivity.
That makes it a natural fit for trapped ions, where any qubit can talk to any other and gate fidelities are the highest in the industry. Quantinuum's results have been the headline demonstrations: the [[7,1,3]] Steane code (the smallest color code) for fault-tolerant logical teleportation, code-switching to a Reed–Muller code for a transversal T gate, and — on its Helios system in late 2025 — 48 logical qubits from 98 physical ions, the best encoding ratio any platform has shown.
A 2:1 physical-to-logical ratio is real but achieved at small code distance on ultra-high-fidelity ions — excellent for near-term logical demonstrations, not yet the same thing as a deep, billion-operation fault-tolerant qubit. Cross-platform overhead numbers are rarely apples-to-apples (see the comparison caveat below).
Best suited for: Trapped ions Neutral atoms — high-connectivity, high-fidelity platforms.
The most direct attack on overhead is the quantum low-density parity-check (qLDPC) family. (You may see it written "LDPC," borrowed from classical coding.) Where the surface code stores one logical qubit per patch, qLDPC codes encode many logical qubits together and share the protection — dramatically raising the "rate" (logical per physical).
IBM's bivariate-bicycle "gross code," [[144,12,12]], encodes 12 logical qubits in 144 data qubits (288 physical including checks) — correcting errors as well as a surface code that would need ~2,900 qubits for the same 12. That's roughly 10× fewer qubits. The catch has always been connectivity: qLDPC checks reach beyond nearest neighbours, which is hard on a flat chip.
This is exactly what IQM's directional tile codes (June 2026) solve. They are a way to realise high-rate qLDPC codes on a standard 2D planar superconducting grid, using dynamic syndrome-extraction circuits and nearest-neighbour iSWAP gates — no exotic wiring. IQM reports up to a 1,000× lower logical error rate than the surface code at a comparable footprint of about 30 physical qubits per logical qubit.
qLDPC codes also map beautifully onto neutral-atom machines, whose atoms can be physically rearranged to wire up non-local checks — one reason that platform is moving fast on logical qubits.
Best suited for: Superconducting (planar) Neutral atoms — high-rate codes need either clever circuits (IQM) or movable qubits.
| Code family | Core idea | Overhead (phys : logical) | Best platform | 2025–26 milestone |
|---|---|---|---|---|
| Surface code | 2D grid, both error types, nearest-neighbour | ~hundreds–1000 : 1 | Superconducting Neutral atoms | Below-threshold scaling (Google) |
| Cat qubits | Biased noise + 1D repetition code | ~15–18 : 1 | SC cavity | Helium logical qubit; >1 hr bit-flip |
| GKP codes | Qubit encoded in one oscillator's grid states | 1 mode (analog cost) | Photonic SC cavity Ions | On-chip GKP qubit; Aurora (Xanadu) |
| Color codes | Topological + transversal Clifford gates | ~2 : 1* | Trapped ions Neutral atoms | 48 logical / 98 physical (Quantinuum) |
| qLDPC codes | Many logical qubits share one block (high rate) | ~24 : 1 (12 in 288) | Superconducting Neutral atoms | Gross code [[144,12,12]] (IBM) |
| Directional tile codes | qLDPC on a planar grid via dynamic circuits | ~30 : 1 | SC planar | 1000× lower error vs. surface (IQM) |
These ratios are not apples-to-apples. They sit at different code distances, target error rates, noise models and connectivity assumptions, and a low ratio at small distance (*color codes) is not the same as a deep fault-tolerant qubit able to run a billion operations. Treat the column as direction of travel, not a benchmark.
Codes are not chosen in a vacuum — they are co-designed with the hardware's strengths. Connectivity, gate speed, fidelity and whether qubits can be moved all decide what's practical.
| Platform | Natural code fit | Why |
|---|---|---|
| Superconducting (transmon) | Surface, qLDPC / tile codes | Fast 2D nearest-neighbour gates; tile codes bring high-rate qLDPC to a flat chip (Google, IBM, IQM) |
| Superconducting (cavity) | Cat, GKP | Microwave resonators store the bosonic modes both codes need (Alice & Bob, Yale) |
| Photonic | GKP (measurement-based) | Flying qubits at room temperature; GKP states built from squeezed light (Xanadu) |
| Trapped ions | Color codes, surface, qLDPC | All-to-all connectivity and the highest gate fidelities favour transversal gates (Quantinuum) |
| Neutral atoms | qLDPC, color, surface | Atoms can be physically rearranged to wire up non-local checks (Harvard/QuEra) |
| Spin (silicon) | Surface code (target) | High-fidelity, dense, CMOS-compatible — but qubit counts are still small and QEC demos early (Intel, Diraq) |
There is no single winning code — and that's the point. The surface code is the safe default, but it is being squeezed from two sides. Hardware-level codes (cat, GKP) cut overhead by making the physical qubit intrinsically better, which is why bosonic players advertise 15:1 ratios. Logical-level codes (color, qLDPC, tile codes) cut it by packing logical qubits more efficiently, which is why IBM, IQM and Quantinuum tout 10×–1000× improvements.
For diligence, the useful questions are: does the code match the hardware? (a cat qubit on a photonic machine, or a color code on a low-connectivity chip, is a red flag), and is the headline ratio quoted at a real fault-tolerant distance, or at a small demo distance? The companies converging hardware and code together — Alice & Bob on bosonic, Quantinuum on ions, IQM and IBM on qLDPC, Xanadu on photonics — are the ones turning the overhead curve, and with it the timeline to commercially useful machines.
What is the difference between cat, GKP, color and qLDPC codes?
They are different strategies to cut error-correction overhead. Cat and GKP are bosonic codes that make the physical qubit intrinsically better; color and quantum LDPC (qLDPC) codes pack logical qubits together more efficiently.
Which quantum error-correcting code has the lowest overhead?
Bosonic cat qubits (~15–18 physical per logical) and high-rate codes (IBM's qLDPC gross code ~24:1, IQM directional tile codes ~30:1) use far fewer qubits than the surface code's hundreds-to-one — though the figures aren't directly comparable across code distances and noise models.
What are directional tile codes?
IQM's method for running high-rate qLDPC codes on a standard 2D planar superconducting grid, reporting up to 1,000× lower logical error than the surface code at ~30 physical qubits per logical qubit.
Company dossiers: Quantinuum · QuEra · Xanadu · IBM Quantum. Related explainers: Quantum Error Correction · Trapped-Ion Computing.
← Part 1: Quantum Error Correction — the fundamentals