Quantum Volume Benchmark: Heavy-Output Sampling

Circuit Parameters

Qubits (width m) 3

Per-gate error rate 5%

Benchmark Result

Heavy-output P (noisy)

—

Pass threshold

66.7%

0%2/3 threshold100%

Run a circuit to test it

n = 3 qubits, depth = 3

Quantum Volume Sweep

Achieved Quantum Volume: not yet run

How it works

Quantum Volume (QV) is a single-number benchmark (IBM, 2019) that measures how large a "square" random circuit — width m qubits, depth m layers — a real device can run before noise destroys the result. This simulator implements the protocol exactly, on an ideal state-vector simulator with an injected noise model standing in for real hardware error.

Model circuit: m layers, each a random pairing of qubits;
each pair gets 4 random SU(2) rotations + a CZ entangler.

Heavy set:  probs = |amplitude|² for all 2^m outcomes (ideal, no noise)
            heavy = outcomes with prob > median(probs)

Noisy run:  after every gate, each involved qubit gets a random
            Pauli error (X/Y/Z) with probability p (quantum trajectory /
            Monte-Carlo wavefunction model of a depolarizing channel)

Heavy-output probability = fraction of noisy measurement samples
                            that land in the ideal heavy set
Pass condition:  heavy-output probability ≥ 2/3
Achieved QV:     2^m for the largest m that passes

Run New Circuit — draws one fresh random m-qubit circuit, ideally-simulates it to find the heavy set, then samples 400 noisy trajectories to estimate the heavy-output probability at the current error rate.
Sweep Quantum Volume — repeats this (several circuits per width, averaged) at widths 2→6 until a width fails the 2/3 threshold, then reports 2^m as the achieved Quantum Volume — exactly how IBM, Honeywell and Rigetti report this number.
Purple cubes on the diagram are qubits touched by an entangling pair that layer; the amber line is the CZ interaction; gray cubes are idle single-qubit rotations (only appears with an odd qubit count).

Real-world relevance: Quantum Volume is the standard cross-vendor apples-to-apples metric — a device's raw qubit count means little if gate errors compound faster than useful circuit depth grows, which is exactly what the noise slider here demonstrates.

Entangled-pair qubit Idle single-qubit gate CZ interaction

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