Definition of the computing unit for the LRZ Quantum Systems

While for HPC hardware there is more or less general consensus about a unit of measurement for the computing resources (e.g. the core-hour, used at LRZ), in the QC operation one can find in the community and by the cloud service providers several definitions based on different units (tasks, shots, gates, to name a few).

For our quantum hardware, keeping in mind the operation of integrated HPCQC systems, we have defined a new unit, based on time. The equivalent qubit-second (eqs) is defined on a quantum system S as

$\begin{array}{l}\displaystyle eqs(S) = t \times n(S) \times \frac{T_{1qg}(Q\text{-}Exa)}{T_{1qg}(S)}\end{array}$

where:

t is the computational wall-clock time spent on the QPU, as measured by the Munich Quantum Software Stack,

n(S) is the number of qubits in the system S,

T_1qg(S) is the one-qubit gate time of system S (as taken by the vendor specifications) and

T_1qg(Q-Exa) is the one-qubit gate time of Q-Exa, taken currently as reference, because it is the first quantum hardware offered to the LRZ user community.

Every unit can have pros and cons, but in this definition, we see the following advantages:

it considers resources on large quantum systems as more costly, because of the factor n(S);
it encourages users to use a large number of qubits, because the computing time t is multiplied by the total number of qubits n(S) of the system. We can reconsider this point, if at some time we will move away from a usage model where a user has exclusive access of quantum hardware;
within a given qubit modality (e.g., superconducting, ion-trap, …), it considers resources on more modern systems (presumably, with shorter gate times T_1qg) as more costly;
up to system constants, eqs(S) is proportional to the wallclock time t, which is easy to be measured and understood.

The adopted values for the constants in the formula for the eqs(S) are:

Q-Exa: n = 20, T_1qg = 40ns (source: IQM website, technical specifications for the 20-qubit IQM Radiance system: https://meetiqm.com/products/iqm-radiance/ )
AQT: n = 16, T_1qg = 15μs (source: AQT website, technical specifications for Marmot: https://www.aqt.eu/products/marmot/ )

Examples of computation:

On the AQT system, the average time per circuit during the Friendly User Pilot Phase was about 30s. Applying the formula, the duration in equivalent qubit-seconds is

$\begin{array}{l}\displaystyle eqs(AQT) = 30 \times 16 \times \frac{40\ \text{ns}}{15\ \mu\text{s}}\end{array}$

which is equal to 1.28s.

On the Q-Exa system, the median time per circuit during the Friendly User Pilot Phase was 2.5s. In equivalent qubit-seconds this is

$\begin{array}{l}\displaystyle eqs(Q\text{-}Exa) = 2.5 \times 20 \times \frac{40\ \text{ns}}{40\ \text{ns}}\end{array}$

namely 50s.