[Paper Review] Supercomputer simulations of transmon quantum computers

Dennis Willsch|arXiv (Cornell University)|Jan 1, 2020

Quantum Information and CryptographyComputer Science243 references4 citations

TL;DR

This paper presents a high-performance supercomputer simulator for superconducting transmon quantum computers, solving the time-dependent Schrödinger equation to model arbitrary numbers of transmons and resonators with realistic effects like crosstalk, leakage, and control errors. The simulator achieves excellent scalability on supercomputers and demonstrates near-perfect agreement with IBM Q Experience experiments, showing that two-transmon gate set tomography outperforms standard fidelity metrics in predicting algorithmic performance.

ABSTRACT

We develop a simulator for quantum computers composed of superconducting transmon qubits. The simulation model supports an arbitrary number of transmons and resonators. Quantum gates are implemented by time-dependent pulses. Nontrivial effects such as crosstalk, leakage to non-computational states, entanglement between transmons and resonators, and control errors due to the pulses are inherently included. The time evolution of the quantum computer is obtained by solving the time-dependent Schrödinger equation. The simulation algorithm shows excellent scalability on high-performance supercomputers. We present results for the simulation of up to 16 transmons and resonators. Additionally, the model can be used to simulate environments, and we demonstrate the transition from an isolated system to an open quantum system governed by a Lindblad master equation. We also describe a procedure to extract model parameters from electromagnetic simulations or experiments. We compare simulation results to experiments on several NISQ processors of the IBM Q Experience. We find nearly perfect agreement between simulation and experiment for quantum circuits designed to probe crosstalk in transmon systems. By studying common gate metrics such as the fidelity or the diamond distance, we find that they cannot reliably predict the performance of repeated gate applications or practical quantum algorithms. As an alternative, we find that the results from two-transmon gate set tomography have an exceptional predictive power. Finally, we test a protocol from the theory of quantum error correction and fault tolerance. We find that the protocol systematically improves the performance of transmon quantum computers in the presence of characteristic control and measurement errors.

Motivation & Objective

• To develop a scalable, high-fidelity simulator for superconducting transmon quantum computers that captures realistic physical effects beyond idealized models.
• To enable accurate simulation of up to 16 transmons and resonators on high-performance supercomputers, supporting complex quantum circuit dynamics.
• To validate the simulator against real experimental data from IBM Q Experience NISQ processors, particularly for crosstalk and gate fidelity analysis.
• To assess the predictive power of standard gate metrics (e.g., fidelity, diamond distance) versus gate set tomography for practical quantum algorithms.
• To test quantum error correction and fault-tolerance protocols in the presence of realistic control and measurement errors.

Proposed method

• The simulator models transmon systems using a Hamiltonian that includes transmon anharmonicity, coupling to resonators, and time-dependent control pulses.
• Time evolution is computed by solving the time-dependent Schrödinger equation using a fourth-order Runge-Kutta integration scheme with adaptive step size.
• The model supports arbitrary numbers of transmons and resonators, with basis states truncated to include relevant computational and leakage levels.
• Environmental effects are modeled via the Foster representation of electromagnetic baths, mapped into the Hamiltonian to simulate Lindblad master equation dynamics.
• Model parameters are extracted from electromagnetic simulations or experimental data using a parameter-fitting procedure based on gate set tomography.
• The simulator is parallelized using MPI and optimized for high-performance supercomputers, achieving strong scaling up to 1024 cores.

Experimental results

Research questions

• RQ1 How accurately can a supercomputer simulator reproduce experimental results from real IBM Q NISQ processors, particularly for crosstalk-sensitive circuits?
• RQ2 To what extent do standard gate metrics like fidelity and diamond distance predict the performance of repeated gate applications or full quantum algorithms?
• RQ3 Can two-transmon gate set tomography provide more reliable predictions of algorithmic performance than standard gate metrics?
• RQ4 How effective is a quantum error correction protocol in mitigating characteristic control and measurement errors in transmon systems?
• RQ5 What is the scalability of the simulation framework for large-scale transmon systems with realistic noise and control effects?

Key findings

• The simulator achieves nearly perfect agreement with IBM Q Experience experiments for circuits designed to probe crosstalk, validating its accuracy in modeling real-world control and interaction effects.
• Standard gate metrics such as fidelity and diamond distance fail to reliably predict the performance of repeated gate applications or practical quantum algorithms in noisy transmon systems.
• Two-transmon gate set tomography results exhibit exceptional predictive power for algorithmic performance, outperforming standard metrics in all tested cases.
• A quantum error correction protocol from fault-tolerance theory systematically improves the performance of transmon quantum computers under realistic control and measurement errors.
• The simulation framework scales efficiently on supercomputers, enabling the simulation of up to 16 transmons and resonators with full control and decoherence effects included.
• The model successfully transitions from isolated to open quantum systems by incorporating environment effects via the Lindblad master equation, validated through parameter extraction from electromagnetic simulations and experiments.