Strong empiricalClifford circuit benchmark
Clifford brickwork benchmark · 3 qubits
A deterministic H/S/CNOT brickwork circuit suited to stabilizer and compiler regression checks.
Explore quantum algorithms and circuits, with resource estimates, verification evidence, and sources.
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The defining behavior was checked exactly: a mathematical identity, a full statevector or stabilizer simulation, or an exhaustive basis-state truth table.
The design was verified by construction plus measured evidence: statistical re-execution, small-instance analytic agreement, sub-block, echo, or invariant checks. Scale-specific bugs can still survive.
The record rests on external authority: peer-reviewed papers, standard textbooks, expert review, or evidence carried over from related verified entries. Nothing here was re-executed by this catalog.
Only automated (LLM-assisted) review or an unreviewed community submission backs this record so far. Treat it as a starting point, not evidence.
A deterministic H/S/CNOT brickwork circuit suited to stabilizer and compiler regression checks.
A linear graph-state preparation circuit using one Hadamard per qubit and nearest-neighbor CZ edges.
A cyclic graph-state preparation circuit with Hadamards followed by CZ interactions around a ring.
The canonical resource state for one-way (measurement-based) quantum computing: qubits in |+⟩ entangled by CZ along a line.
A controlled version of the Pauli-Y gate that flips the target bit and attaches a ±i phase exactly when the control qubit is |1⟩, completing the CX/CY/CZ family of controlled Paulis.
A diagonal two-qubit entangling gate that applies a -1 phase exactly when both qubits are |1⟩, and is symmetric between the two qubits it acts on.
A two-qubit permutation gate defined as two CNOTs with reversed control and target applied back to back — a genuinely different two-CNOT gate from SWAP (which uses three), and notable for not being self-inverse.
A graph state built on a 4-cycle rather than an open chain, illustrating how stabilizer generators follow directly from graph adjacency.
The single-qubit no-op gate that leaves every state exactly unchanged, used as a placeholder in circuit diagrams, a timing/idle slot on real hardware, and the base case for gate-composition identities.
The joint parity operator Z^{⊗n} and its standard non-destructive ancilla-based measurement circuit, the core primitive behind stabilizer syndrome extraction.
Measure, as a single number, how large a random circuit of equal width and depth a given quantum computer successfully implements, so that progress toward improved system-wide gate error rates can be measured and compared across near-term devices.
Estimate an average error rate for a set of operations (gates) on a quantum information processor, under a noise model general enough to allow errors that depend on both the time and the gate at which they occur.
The Hermitian conjugate (and inverse) of the S gate, applying a -π/2 phase to |1⟩ and undoing whatever an S gate did earlier in a circuit.
A foundational code record that compares quantum protection with the narrower classical repetition-code idea.
A quarter-turn phase gate that exposes the difference between global and relative phase.
A fault-tolerance record for comparing physical error, syndrome extraction, decoder choice, and logical failure.
A Clifford square root of the Pauli-X gate that is the native physical single-qubit gate (an X_{π/2} pulse) on most superconducting hardware.
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