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arXiv:2012.13131

State-dependent Routing Dynamics in Noisy Quantum Computing Devices

Ronald J. Sadlier, Travis S. Humble

Published Dec 24, 2020• 0 citations
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Abstract

Routing plays an important role in programming noisy, intermediate-scale quantum (NISQ) devices, where limited connectivity in the register is overcome by swapping quantum information between locations. However, routing a quantum state using noisy gates introduces non-trivial noise dynamics, and deciding on an optimal route to minimize accumulated error requires estimates of the expected state fidelity. Here we validate a model for state-dependent routing dynamics in a NISQ processor based on correlated binary noise. We develop a composable, state-dependent noise model for CNOT and SWAP operations that can be characterized efficiently using pair-wise experimental measurements, and we compare model predictions with tomographic state reconstructions recovered from a quantum device. These results capture the state-dependent routing dynamics that are needed to guide routing decisions for near-real time operation of NISQ devices.

DOI
10.48550/arxiv.2012.13131

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Routing plays an important role in programming noisy, intermediate-scale quantum (NISQ) devices, where limited connectivity in the register is overcome by swapping quantum information between locations. However, routing a quantum state using noisy gates introduces non-trivial noise dynamics, and deciding on an optimal route to minimize accumulated error requires estimates of the expected state fidelity. Here we validate a model for state-dependent routing dynamics in a NISQ processor based on correlated binary noise. We develop a composable, state-dependent noise model for CNOT and SWAP operations that can be characterized efficiently using pair-wise experimental measurements, and we compare model predictions with tomographic state reconstructions recovered from a quantum device. These results capture the state-dependent routing dynamics that are needed to guide routing decisions for near-real time operation of NISQ devices.
Placement, routing, and scheduling are essential tasks for near-optimal performance of programs for noisy quantum processors. Reliable execution of an arbitrary quantum circuit on current devices requires routing methods that overcome connectivity limitations while meeting data locality requirements. However, current devices also express highly variable noise levels in both the quantum gates and quantum registers. This requires any routing algorithm to be adaptive to both the circuit and the operating conditions. We demonstrate near-optimal routing methods of noisy quantum states that minimize the overall error of data movement while also limiting the computational complexity of routing decisions. We evaluate our methods against the noise characteristics of a 20-qubit superconducting quantum processor.
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In Noisy Intermediate-Scale Quantum (NISQ) era devices, the output fidelity of a quantum circuit, under plausible assumptions, decreases exponentially with its size and depth. As such, optimizing these aspects becomes paramount. This is especially true for sparsely connected physical architectures where added swap gates are essential to meet device connectivity requirements. In this work, we adapt the Approximate Token Swapping (ATS) algorithm, traditionally used for routing qubits, to handle noisy settings by giving priority to specific swap sequences over others. This priority is partially determined by the error rates of the couplings in the qubit connectivity graph. We refer to this algorithm as Priority-ATS (PATS). We provide theoretical justification for PATS's effectiveness over the ATS algorithm and experimentally demonstrate its ability to improve the output state's fidelity. In our simulations, we employ a depolarizing channel to represent two-qubit gate errors, with each neighboring qubit pair having a distinct CNOT gate error rate. By applying realistic error rates, our results prominently highlight an enhanced output fidelity of the quantum circuit when PATS is employed.
Due to the limited decoherence time of qubits in the Noisy Intermediate-Scale Quantum (NISQ) era, optimizing the size and depth of logical quantum circuits for efficient implementation on sparsely connected physical architectures is crucial. In this work, we extend the Approximate Token Swapping (ATS) algorithm by incorporating qubit priority and the size of permutation cycles to be routed. We refer to this algorithm as Priority-ATS (PATS), which also considers CNOT gate errors while constructing the routing schedule for the qubits. We provide theoretical justification for the superior effectiveness of PATS over ATS and experimentally demonstrate its ability to improve the fidelity of the output state. Furthermore, we use depolarizing error channels to model the noisy CNOT gates, where each adjacent qubit pair has a distinct error rate. By employing realistic error rates, we showcase the robust improvement in output fidelity when using PATS as opposed to a noise-oblivious ATS routing scheme.
Quantum computers with a limited qubit connectivity require inserting SWAP gates for qubit routing, which increases gate execution errors and the impact of environmental noise due to an overhead in circuit depth. In this work, we benchmark various routing techniques considering random quantum circuits on one-dimensional and square lattice connectivities, employing both analytical and numerical methods. We introduce circuit fidelity as a comprehensive metric that captures the effects of SWAP and circuit depth overheads. Leveraging a novel approach based on the SABRE algorithm, we achieve up to 84%84\%84% higher average circuit fidelity for large devices within the NISQ range, compared to previously existing methods. Additionally, our results highlight that the optimal routing choice critically depends on the qubit count and the hardware characteristics, including gate fidelities and coherence times.
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