A Time Optimization Framework for the Implementation of Robust and Low-latency Quantum Circuits

TL;DR

Problem: incoherent energy-dissipation errors cap quantum computation time while fast pulses introduce leakage. The paper proposes a time-optimization framework that models circuits as a dependency graph and uses the Critical Path Method to place fast gates on the critical path while exploiting idle time to implement longer, noise-robust gates without increasing latency. The main contributions are a polynomial-time algorithm with complexity $O(n_g^2 n_d n_q)$ and randomized benchmarking on IBMQ Brisbane showing absolute success-probability gains exceeding 25%, growing with qubit count. This work demonstrates how to achieve robust, low-latency quantum circuit execution by combining fast and robust pulses at the pulse level, guiding compiler design for larger quantum devices.

Abstract

Quantum computing has garnered attention for its potential to solve complex computational problems with considerable speedup. Despite notable advancements in the field, achieving meaningful scalability and noise control in quantum hardware remains challenging. Incoherent errors caused by decoherence restrict the total computation time, making it very short. While hardware advancements continue to progress, quantum software specialists seek to minimize quantum circuit latency to mitigate dissipation. However, at the pulse level, fast quantum gates often lead to leakage, leaving minimal room for further optimization. Recent advancements have shown the effectiveness of quantum control techniques in generating quantum gates robust to coherent error sources. Nevertheless, these techniques come with a trade-off -- extended gate durations. In this paper, we introduce an alternative pulse scheduling approach that enables the use of both fast and robust quantum gates within the same quantum circuit. The time-optimization framework models the quantum circuit as a dependency graph, implements the fastest quantum gates on the critical path, and uses idle periods outside the critical path to optimally implement longer, more robust gates from the gate set, without increasing latency. Experiments conducted on IBMQ Brisbane show that this approach improves the absolute success probability of quantum circuit execution by more than 25%, with performance gains scaling as the number of qubits increases.

Figures (9)

• Figure 1: Square, Gaussian ($\sigma=12$), Gaussian-Square ($\sigma=30$, $w=60$) and DRAG ($\sigma=30$, $\beta=0.1$) pulse shapes for the implementation of a $\pi/2$ rotation.
• Figure 2: Example of a quantum operation dependency graph construction. (a) An example of a quantum circuit with two idle periods on qubit 2. (b) The quantum operation dependency graph corresponding to the quantum circuit in (a), with the critical path highlighted in red. The ES, EF, LS, and LF times are given in arbitrary units.
• Figure 3: Randomized benchmarking results for static fine-tuned gates. Each bar represents the mean success probability of 10 RB quantum circuits. The success probability $P(0)$ represents the likelihood of measuring the system in the initial state, which is used to evaluate gate fidelity through RB. The Clifford length, shown on the x-axis, represents the number of Clifford layers in the sequence, where each layer corresponds to a random multi-qubit Clifford operation decomposed into a specific number of single- and multi-qubit gates.
• Figure 4: Randomized benchmarking results for static fine-tuned gates in time-scale. The experimental results ($P(0)$), circuit latencies, and decoherence times are averaged. Down-pointing triangles represent the mean $P(0)$ for the default fixed-duration gates, while up-pointing triangles represent the mean $P(0)$ for the pulse scheduling under the time-optimization framework. The $T_1$ and $T_2$ times were obtained from IBMQ jobs and plotted using an exponential decay function $e^{-t/T}$. For the $T_1$ plot, consider the decay from $\ket{1}$ to $\ket{0}$, or equivalently, $P(1)$ on the y-axis.
• Figure 5: Randomized benchmarking results for dynamic quantum gates. Each bar represents the mean success probability of 10 RB quantum circuits. The duration limits are for $\pi/2$ rotations. The success probability $P(0)$ represents the likelihood of measuring the system in the initial state, which is used to evaluate gate fidelity through RB. The Clifford length, shown on the x-axis, represents the number of Clifford layers in the sequence, where each layer corresponds to a random multi-qubit Clifford operation decomposed into a specific number of single- and multi-qubit gates.