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SlotLayer 1

Build logical qubits at a target logical error rate

Encode physical qubits whose error rate pp sits below a code- and decoder-specific threshold into logical qubits meeting a target logical error rate per round, by spending qubits and time on redundancy and decoding syndromes in real time. Which code sits underneath reaches the layers above only as a physical-qubit count and a demand on connectivity.

Takes

A physical error rate pp and noise model; a target logical error rate PLP_L; a connectivity constraint; a measurement and feedback cycle time.

Returns

Logical qubits, together with the code and code distance dd that were chosen for them, a physical-qubits-per-logical-qubit figure, and a decoding latency requirement.

This one, drawn

Build logical qubits at a target logical error rateSurface codeQuantum LDPC codes (bivariate bicycle family)Surface code — click the name to read about itSurface codeQuantum LDPC codes (bivariate bicycle family) — click the name to read about itqLDPC codesPhysical qubits — you start hereLogical qubits — you finish here

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From Physical qubits to Logical qubits

A circle is an object you are holding. Each line between the two ends is one recorded way through this slot; where a way is built from smaller slots, those are its own lines. Circles are named on hover, and each one is a link.

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Why this is a layer

Everything above this layer is written in logical qubits and is indifferent to which code sits underneath; everything below is physics. The competing codes trade threshold against encoding rate against required connectivity. The parameter to watch is the code distance dd: it is an OUTPUT of this layer, solved for from the physical error rate pp and the target logical error rate PLP_L that the algorithm's total operation count demands. Halve pp and dd falls; raise the TT-count and dd rises. A distance quoted on its own, or a physical-per-logical ratio quoted without pp, PLP_L and dd beside it, states nothing.

Ways to do this

2 methods recorded

  • Surface code

    Encode a logical qubit in the homology of a two-dimensional lattice of physical qubits, with weight-4 stabilizers measured by nearest-neighbour circuits. It is the dominant fault-tolerant code because it needs only a 2D nearest-neighbour grid and tolerates a comparatively high physical error rate.

  • Quantum LDPC codes (bivariate bicycle family)

    Trade the surface code's strictly planar layout for slightly richer connectivity, in exchange for a much better encoding rate. Many logical qubits live in one code block instead of one per patch.

Routes that skip this layer

No recorded route avoids this step.

This is a step inside

  • Fault-tolerant compilation (Clifford+T pipeline)

    Decompose to Clifford+T, approximate every continuous rotation by a discrete gate word, optimize for T-count and T-depth, then express the result as a schedule of logical operations on encoded patches — typically Pauli-product measurements under lattice surgery.

In the Atlas

No record in the Atlas covers this yet. The catalogue is circuits and primitives; this part of the literature is not in it.