Circuit Layer Operations per Second

Circuit Layer Operations per Second (CLOPS) is a benchmarking metric of quantum computers developed by IBM in 2021.^[1] While Quantum volume is more indicative of a qubit's performance and quality, CLOPS is a measure of a quantum computer’s execution speed. CLOPS incorporates both the time to run a circuit as well as the real-time and near-time classical computation, enabling it to serve as a holistic single measure of speed. CLOPS in conjunction with the number of qubits and the quantum volume was originally envisioned by IBM to be the 3 core metrics for comparing quantum devices.^[2]

Redefinition

Originally CLOPS was designed to be related to quantum volume, in the sense that each circuit layer was idealized square quantum volume circuits.^[3] However, in 2023 IBM created a new definition of CLOPS which is related to a specific hardware layer. The different versions are differentiated with a subscript: CLOPS_v for virtual and CLOPS_h for hardware. Functionally, the core difference is that instead of using quantum volume in the calculation, a different metric known as layer fidelity is used instead, measured by the error per layered gate (ELPG) protocol. This enables different hardware with different quantum volumes to be more accurately compared.^[4]

Mathematical explanation of the benchmark

• Define M template circuits; each one composed of K different quantum circuits
• S is the number of shots to run
• D is the quantum volume as log₂
• T is the total amount of time in seconds taken for execution, including the data transfer, transpilation, measurements, resets, and delays

CLOPS_v = ${\displaystyle {\bigl (}M*K*S*D{\bigr )} \over T}$ ^[5]

The main update in CLOPS_h was to replace the quantum volume metric D above with the something IBM termed the layer fidelity, which according to IBM "provides a benchmark that encapsulates the entire processor’s ability to run circuits while revealing information about individual qubits, gates, and crosstalk." Layer fidelity is measured by the error per layered gate (EPLG). ^[4] This inflates the CLOPS score for quantum computers that are sparsely connected.

Table of measured CLOPS

Date	Company	QPU	CLOPSv	CLOPSh
October 2021[6]	IBM	Bogota	1419
October 2021[6]	IBM	Toronto	951
October 2021[6]	IBM	Brooklyn	753
August 2023[7]	Qutech	Starmon-5	372
August 2024[8]	IQM Quantum Computers	Garnet	2600
February 2025[6]	IBM	Heron r2	2400	195000
February 2025[6]	IBM	Heron r1	2400	210000