Noise Aware Utility Optimization of NISQ Devices

Qiskit inherently recognizes and categorizes qubits with complete operational failure or significant performance issues as ’faulty’ [8]. These qubits are flagged based on calibration data that suggests they are not meeting the minimum standards required for quantum computations. However, this binary classification—faulty or not—does not encapsulate the gradations of performance degradation that can occur over time as quantum hardware components age as well as between device calibrations.

Our approach introduces a quantum resource pruning method through user-defined error thresholds. Unlike the fixed definition of a faulty qubit, which may exclude only those qubits with extreme deviations in performance, user-defined thresholds allow for a more nuanced and adaptable utilization of the quantum processor’s resources. First, the coupling map –a directed acyclic graph or DAG– of the target quantum device is obtained. In this graph, nodes symbolize the qubits, and edges denote the connections –or coupling– between these qubits. Then, we fetch the target quantum device’s calibration data, allowing us to take into account the current error rates of qubits and their connections. We then use the calibration data to enrich the coupling map with error rates, thus converting it to a weighted network representation of the device’s architecture. In this weighted network representation, the nodes (representing qubits) are assigned weights based on their readout error rates, and the edges (representing qubit couplings) reflect the CNOT error rates. It is important to highlight that modern IBM quantum devices use the Echoed Cross-Resonance (ECR) gate as their native entangling operation rather than the CNOT gate commonly found in theoretical quantum circuit designs [12][13]. The ECR gate, like the CNOT, creates entanglement but through a different mechanism suited to the hardware’s architecture. Consequently, when we refer to the ’CNOT error rate’ in this context, we are actually discussing the error rates associated with ECR operations. Given that quantum circuits are typically designed using CNOT gates and later transpiled to the device’s native gate set, this terminology is used for simplicity.

This integration of user-specified error thresholds with detailed device calibration and coupling constraints in weighted network form is the basis for the following quantum resource selection and optimization process.

With these parameters, our methodology employs a pruning function to sift through the qubits and connections based on their error rates. First, it discards any elements whose error rates exceed the user-defined thresholds. Second, it removes disjoint elements that cannot compose a valid partition. For example, a lone edge cannot be admissible if the nodes it connects are not included. After pruning, we are left with valid partitions that adhere to the error criteria. These partitions contain only the qubits and connections that meet the user-defined thresholds, ensuring that each element within them is within the bounds of acceptable error rates.

Finally, the largest partition is transformed into a valid Qiskit coupling map and returned to the user as the optimal partition. This largest partition not only informs the user about the maximum number of qubits available for their specific computational needs but also highlights the potential for parallel circuit execution. Indeed, smaller partitions, close in size to the largest, might allow for parallel execution of multiple copies of a circuit, optimizing resource use, enhancing computational throughput, and potentially diminishing overall runtime and cost for an experiment.

In our analysis, we apply our methodology to ibm_quebec. The resulting visualizations of the processor’s coupling map—post-pruning—, for varying CNOT and Readout error thresholds are depicted in Figure 3. The result shows a complex yet intuitive trade-off dynamic between error thresholds and resulting partitions. As we impose more stringent fidelity requirements by lowering the acceptable error thresholds, the size of the largest partition decreases correspondingly. For instance, reducing the CNOT error threshold by approximately sixfold, from 1.6% to 0.3%, results in the largest partition shrinking from 55 qubits—nearly half of the machine’s 127 qubits—to a mere 2, a 28-fold reduction. Additionally, as the error thresholds are lowered, there is a noticeable decrease in the average connectivity of the partitions, leading them to increasingly i) resemble linear qubit chains ii) retain very little to no features of the original heavy-hex topology.

To validate the effectiveness of our method, we present experimental results showing its impact on the gate fidelity of long-range CNOT gates. This serves as a benchmark for real-world improvements over the baseline. We choose CNOT chains as our benchmark due to their essential role in quantum circuits, specifically for facilitating the long-range entanglement required by algorithms like Shor’s. Indeed, given the non-fully connected nature of IBM’s superconducting qubits–where each qubit is not directly coupled to all others–, interactions between non-adjacent qubits necessitate chains–or cascades–of CNOT gates to move quantum information across the chip. This, in turn, enables the physical realization of sophisticated quantum algorithms designed with all-to-all connectivity in mind. Consequently, the fidelity of long-range CNOT gates is a critical factor in determining the utility of the quantum device.

Our experimental setup consists of generating random paths across the largest partitions obtained post-pruning, employing a random walk algorithm. Each of those paths will later lead to one circuit being executed on the system. By invoking the initial_layout flag, we direct Qiskit’s transpiler to conform its transpilation process to the generated partitions, ensuring results integrity. Quantum Process Tomography (QPT) is used to estimate the fidelity of quantum gates by reconstructing the quantum process from measurements. This reconstruction involves comparing the theoretical and experimental process matrices, providing insight into how closely the quantum device performs to expectations. Once an estimate of the process fidelity is obtained, a simple linear relationship is used to convert it to gate fidelity: $F_{\textrm{gate}}=(4F_{\textrm{process}}+1)/5$ [14][15]. Gate fidelity is chosen because it provides a scalar value that encapsulates the overall performance of the quantum gate, making it a relevant figure of merit for our method’s effectiveness. Finally, the experiments were run over the course of three weeks on ibm_quebec, totalling 3,000+ circuit executions of 4096 shots each. Overall, those experiments took about 492,000 Qiskit Runtime seconds–roughly 135 hours.

Figure 4 displays the normalized probability density distributions of gate fidelity for random 20-qubit CNOT chains executed within partitions generated by our method, with insets illustrating sample configurations and highlighting both utilized and pruned resources alongside the actual CNOT paths. We establish a baseline fidelity by utilizing all non-faulty qubits of the architecture, irrespective of their individual error characteristics, across 49 samples. To evaluate our method, we execute 249 random 20-qubit CNOT chains, adjusting the CNOT error threshold to confine their execution within progressively smaller partitions produced by our approach. The analysis divides the results into two distinct sub-sampled groups from the original dataset: the ’moderately-pruned’ group, with 49 samples derived from partitions at CNOT error thresholds between 1.32% and 1.39%, and the ’high-fidelity’ group, comprising 41 samples from partitions with thresholds between 0.90% and 1.16%. These groups significantly outperform the baseline fidelity of 0.43, with mean fidelities of 0.62 and 0.71, respectively. The fidelity enhancements demonstrated by these sample distributions underscore the efficacy of our pruning method for 20-qubit CNOT chains. In the following section, we extend our examination to explore how our method impacts CNOT chains of varying lengths.

To comprehensively assess the effectiveness of our pruning method, we expand our investigation to varying the number of qubits in the CNOT chain. The experimental setup remains consistent with that presented in the previous section. Table I presents the aggregated results of this extended evaluation. The table presents the baseline mean fidelity, standard deviation, and sample size for each chain length alongside the corresponding metrics achieved through our method. The final column, ’$\Delta$ Mean,’ highlights the percentage improvement in mean fidelity of our pruning method, underscoring its effectiveness across varying chain lengths. Those results demonstrate a pattern: as the length of the CNOT chains increases, the percentage improvement in gate fidelity also rises. This suggests that our pruning method is particularly beneficial for more complex quantum operations requiring longer entanglement chains. In summary, the extended benchmark reinforces the practical utility of our pruning method, demonstrating its capacity to significantly enhance gate fidelity across a broad spectrum of CNOT chain lengths. These findings affirm the method’s potential to optimize quantum computational tasks of varying complexities, making it a valuable tool.

A pivotal aspect of validating our methodology is the enforcement of an initial_layout. This ensures that our benchmarks accurately reflect the characteristics of the entire partition rather than a biased subset of optimal resources. Without the use of initial_layout, the transpiler defaults to optimizing the initial layout, which, given a particular calibration, would bias our results, offering an incomplete picture of the partition’s overall performance. Future works should focus on integrating our method with existing noise-aware and RL based transpiler optimizations such as [16][17]. Our findings further substantiate the sensitivity of gate fidelity to the variance in noise levels across quantum resources. This insight led to a resource pruning approach, which, by selectively eliminating the most error-prone elements while retaining a large part of the architecture, improves gate fidelity by reducing the partition’s error variance.