QDataSet, quantum datasets for machine learning

Abstract

The availability of large-scale datasets on which to train, benchmark and test algorithms has been central to the rapid development of machine learning as a discipline. Despite considerable advancements, the field of quantum machine learning has thus far lacked a set of comprehensive large-scale datasets upon which to benchmark the development of algorithms for use in applied and theoretical quantum settings. In this paper, we introduce such a dataset, the QDataSet, a quantum dataset designed specifically to facilitate the training and development of quantum machine learning algorithms. The QDataSet comprises 52 high-quality publicly available datasets derived from simulations of one- and two-qubit systems evolving in the presence and/or absence of noise. The datasets are structured to provide a wealth of information to enable machine learning practitioners to use the QDataSet to solve problems in applied quantum computation, such as quantum control, quantum spectroscopy and tomography. Accompanying the datasets on the associated GitHub repository are a set of workbooks demonstrating the use of the QDataSet in a range of optimisation contexts.

Fig. 1

Plot of an undistorted (orange) pulse sequence against a related distorted (blue) pulse sequence for the single-qubit Gaussian pulse dataset with x-axis control (‘G_1q_X’) over the course of the experimental runtime. Here f(t) is the functional (Gaussian) form of the pulse sequence for time-steps t. These plots were used in the first step of the verification process for QDataSet. The shift in pulse sequence is consistent with expected effects of distortion filters. The pulse sequences for each dataset can be found in simulation_parameters =⇒ dynamic_operators =⇒ pulses (undistorted) or distorted_pulses for the distorted case (see Table (1) for a description of the dataset characteristics).

Fig. 2

The frequency response (left) and the phase response (right) of the filter that is used to simulate distortions of the control pulses. The frequency is in units of Hz, and the phase response is in units of rad.

Fig. 3

Plot of average observable (measurement) value for all observables (index indicates each observable in order of Pauli measurements) for all measurement outcomes for samples drawn from dataset G_1q_X (using TensorFlow ‘tf’, orange line) against the same mean for equivalent simulations in Qutip (blue line - not shown due to identical overlap) for a single dataset. Each dataset was sampled and comparison against Qutip was undertaken with equivalent results. The error between means was of order 10⁻⁶ i.e. they were effectively identical (so the blue line is not shown).

Fig. 4

An example of a quantum state rotation on the Bloch sphere. The |0 > 0, |1⟩ indicates the σ_z-axis, the X and Y the σ_x and σ_y axes respectively. In (a), the vector is residing in a +1 σ_x eigenstate. By rotating about the σ_z axis by π/4, the vector is rotated to the right, to the +1 σ_y eigenstate. A rotation about the σ_Z axis by angle θ is equivalent to the application of the unitary $U\left(\theta \right)=\exp \left(-i{\theta }_z{\sigma }_z/2\right)$.