Distributed scheduling of quantum circuits with noise and time optimization

Consider a set of quantum hardware which a user can access to execute one or more quantum? circuits. How can he choose the appropriate? hardware on which each of his circuits can be run? A naive approach to this is that the user can select his favourite hardware, and execute all the circuits sequentially on it. But this? approach has its limitations as the user may not have sufficient execution budget for this particular? hardware. For example, IBM currently allows 10 mins of free access on its 127 qubit devices for each user in a month. A more pragmatic? approach is to distribute his workload on more than one hardware. This has two benefits — both the execution? time on each hardware? and the overall completion time of running all the circuits is lower?because there is a certain amount of? parallel execution.?

Let us also recall that current quantum devices are noisy. Hence,? it is necessary to select the qubits? from the hardware carefully for placement of a circuit allocated to it in order to incur minimal noise. So how does the user schedule a given set of circuits on a given set of? hardware, so that the execution time budget of each hardware is? maintained, yet the effect of noise is minimized??

When a circuit is executed on a hardware, the error probability depends on the number of? qubits and gates in the circuit, as well as the noise profile of the hardware. The noise profile of the? hardware is available from the calibration data (https://quantumcomputing.ibm.com/services/resources). Therefore, if we assign a circuit to a hardware for?execution, a score,?which is an indicator of the quality of the outcome? expected, can be defined. Naturally, we want to select a hardware for a circuit which gives the best quality of?outcome, while meeting the constraint of execution time budget for each hardware.?

In the table below, we show an example of scoring a 6-qubit quantum circuit on four IBM? hardware. The score is calculated using calibration data (PRX Quantum 4, 010327); the lower the score,? the better is the performance. For these scores,? ?ibmq_hanoi is the best device for? execution of this circuit.

Let us formulate this problem of how? to schedule a given set of circuits on a given set of hardwares? such that the score is minimum with the budget for execution time met for all circuits and hardwares.??

Let X_ij denote an indicator variable whether circuit i is scheduled to hardware j. Let Q_ij be the associated score. Then we want that the overall score after? scheduling all the circuits on the set of hardware is minimised. In other words, we get an objective? function

Note that, we need to ensure that each circuit i is to a? hardware j. Since X_ij is an indicator variable, we need to ensure that it sums up to 1 over all hardware j. In other? words, we have a set of constraints, that for each i

Next, let T_j be the maximum execution time allowed for a hardware j. Let ti denote the execution? time for a circuit? i. We need to ensure that the execution time of all the circuits scheduled on?hardware j does not exceed T_j. Mathematically, this leads to a second set of constraints that for each j

Our scheduler solves this optimization problem to find the best schedule. Before showcasing some? results, we also want to leverage circuit cutting (Phys. Rev. Lett. 125, 150504) since it is already? shown to be a useful method for minimizing noise in the system. In this method, a circuit is? partitioned into multiple smaller subcircuits, each of which can be computed individually. Since? each subcircuit has fewer qubits and/or gates, they are expected to be less susceptible? to noise. We refer the readers to our previous blog for more information on circuit cutting and? distribution of workload using it.?

The table below shows the fidelity (which is a measure of closeness of the obtained result with the ideal result) obtained with and without scheduling for different 10 qubit circuits. Each circuit is? partitioned into 2 subcircuits using circuit cutting, and the subcircuits are scheduled as per previous? discussion.

These circuits are selected from various domains of interest such as algorithms, chemistry,? physics. Without scheduling, all the circuits (including the subcircuit instances arising from circuit cutting) would have been computed on a single hardware. In our experiment, we noticed that the?overall execution time is reduced by almost half via our proposed scheduling. Moreover, in each?of the cases, the table shows that our scheduling leads to a significant improvement in fidelity. In? fact, an average improvement of ~21% is obtained using our proposed scheduler for 10 qubit circuits.?

Current quantum devices are noisy, and a plethora of studies are focused on minimizing the effect? of noise. Our proposed scheduler is shown to improve the fidelity while lowering the overall?execution time. Therefore, we expect this scheduling method to be useful in near-term quantum?computing. Moreover, this scheduling method is independent of, and can work in conjunction with other existing error suppression and mitigation methods. We invite the readers to go through the?related paper for further details on this method, and make use of the scheduler for their quantum?workload.

Title of paper: Distributed scheduling of quantum circuits with noise and time optimization

Authors: Dr. Debasmita Bhoumik , Ritajit Majumdar, Amit Saha , Susmita Sur Kolay

Paper link: https://arxiv.org/abs/2309.06005

Tags: #ibm, #ibmresearch, #IBMResearchIndia, #quantumcomputing, #ibmquantum