From compatibility of measurements to exploring Quantum Darwinism on NISQ

TL;DR

This work links Quantum Darwinism with KD quasiprobabilities to diagnose the quantum-to-classical transition on NISQ hardware. By constructing a simple system–environment model with tunable non-classicality and measuring the KD distribution via a cycle test, the authors benchmark IBM’s superconducting and IonQ’s trapped-ion devices while validating simulations. Results show that while simulators align with theory and reveal non-classicality for Darwinism-breaking regimes, real hardware noise obscures the quantitative recovery of non-classicality measures, making this a useful hardware benchmark and a step toward larger-scale studies of emergent classicality.

Abstract

Quantum Darwinism explains how tenets of classical reality, such as objectivity and repeatability, emerge within a quantum universe. As a mathematical framework, Quantum Darwinism also provides guiding principles that determine what physical models support emergent classical behavior, what specific observables obey classical laws, and much more. For instance, in a recent work we elucidated that the limit under which Kirkwood-Dirac quasiprobability distributions become effectively classical coincides with the regime where the underlying physical model obeys the rules of Quantum Darwinism. In the present work, we study the breaking of Quantum Darwinism in a specific model and how that translates to non-classical measurement statistics. Interestingly, this provides effective tools for benchmarking the genuine quantum characteristics of NISQ hardware, which we demonstrate with IonQ's trapped-ion and IBM's superconducting quantum computing platforms.

Figures (5)

• Figure 1: Circuit to measure the real or imaginary part of the quasiprobability corresponding to the measurement outcomes $\dyad{A}$ and $\dyad{B}$ in the state $\ket{\psi}$. Which is measured is determined by the absence (real) or presence (imaginary) of the S gate. The controlled-cycle unitary performs a cyclic rotation of its inputs, taking $\ket{A}\ket{\psi}\ket{B} \to \ket{B}\ket{A}\ket{\psi}$.
• Figure 2: Heatmap of the non-classicality of the KDQ distribution over time for 5000 random settings, for a range of transverse field strengths $\Omega$. The white curve overlaid corresponds to the specific choice of settings used in our experiments, which approximately maximize the non-classicality at $\tau_a = 3.66$ when $\Omega = 1.5$.
• Figure 3: CDF of the distribution of non-classicality values for 5000 random settings with $\tau_a = 3.66$. Note that the probability of obtaining exactly zero non-classicality vanishes, indicating that for this simple system almost all measurement settings and initial conditions allow the failure of quantum Darwinism to be witnessed.
• Figure 4: Circuit diagram showing the complete experimental protocol. The first section of the circuit prepares the desired states in the three-qubit registers representing $\ket{A}$, $\ket{B}$, and $\ket{\psi}$. Then, the state $\ket{A}$ is evolved with the Trotterized propagator $U^\dagger$ to reach the specified measurement time $\tau_a$. Finally, the cycle test of Wagner24 is applied to measure the quasiprobability $q = \mathrm{tr}\left\{BA(\tau_a)\dyad{\psi}\right\}$.
• Figure 5: Scatterplot of the complex quasiprobabilities measured using the circuit of Fig. \ref{['fig:FullCircuit']} for inter-measurement times of (top) $\tau_a = 0$, (middle) $\tau_a = 2.21$, and (bottom) $\tau_a = 3.66$. Results are shown for experiments using the IonQ Aria-1 and IBM Torino quantum computers with $2\times10^5$ shots per quasiprobability, as well as noisy simulations of the same machines with $2\times10^6$ shots per quasiprobability. The numerically exact quasiprobabilities are depicted using crosses, with shaded ellipses denoting the expected $1\sigma,2\sigma,3\sigma,4\sigma$ regions assuming only statistical uncertainty inherent to estimating $q_{ij}$ with finitely many samples.