Measuring entanglement without destroying it on commercial quantum computers


In quantum mechanics, the act of measurement produces unavoidable perturbation (also called “back-action”) on the state of the measured system. This effect is, in many cases, not desirable, as back-action often limits the precision of repeated measurements. However, so-called Quantum Non-Demolition (QND) measurements ensure that the unavoidable and deleterious back-action is diverted onto other system variables that have no impact on the quantity of interest. In this way, one can repeat the same measurement many times without suffering from random perturbation due to measurement back-action, which has many applications in sensing and metrology. QND measurements are an active research area, yet most implementations so far applied to a single quantum object. 

During his specialization semester at EPFL in the Laboratory of Quantum and Nano-Optics, Master’s student Nicolas Schwaller performed QND measurements on bipartite systems (i.e. consisting of two quantum bits, or qubits) that featured quantum entanglement. His study also explored the relationship between entanglement and the wave-particle duality of each subsystem, using a generalization of Niels Bohr’s duality principle to a “triality” relation between concurrence, predictability and visibility [Opt. Commun. 283 (5), 827-830 (2010) ; Phys. Rev. A 103 (2), 022409 (2021)]. 

The experiment was performed on two commercial quantum computers based on previous theoretical work from De Melo et al. [Phys. Rev. Lett. 98 (25), 250501 (2007)] who proposed quantum circuits dedicated to the QND measurements of these complementary observables quantifying quantum entanglement and wave-particle duality. 

Nicolas Schwaller and co-authors compared the performance of most two most developed quantum computing technologies: superconducting circuits of IBM Q and trapped ions of IonQ. In the first one, the state of one qubit is encoded in the oscillation of electric currents in a superconducting element. The second one is based on individual ions (electrically charged atoms) trapped in vacuum and controlled by laser beams. Despite a totally different approach, quantum computers based on these advances are already available on the cloud, giving anyone the opportunity to experiment with real quantum systems.

Fig. 1: (a) Decreasing amount of entanglement in different states: tomography of input state (empty symbols), followed by QND (filled symbols), and finally on the output state (crosses), for IonQ (left, blue) and IBM Q (right, red). (b) Schematic representation of the qubits of IonQ, interacting with laser beams (red arrows) and through ion-ion interactions (red shade), and (c) linear chain of qubits of the IBM Q circuit used here, with nearest neighours linked with superconducting transmission lines.

Their respective performances were assessed by performing the QND measurement of two-qubit states with every possible amount of entanglement and wave vs. particle character. If the two architectures performed equally well in the initial quantum state preparation stage (Fig. 1a), the extended coherence time and full connectivity (Fig. 1b) of trapped ions gave them an edge over superconducting qubits (Fig. 1c) in the task of QND measurement, resulting in higher fidelity of the output state, especially for highly entangled scenarios (Fig. 1a).

As commercial quantum computers continue to scale up and improve, such studies will start to probe the foundation of quantum mechanics on larger and larger objects, possibly yielding new insights in the quantum measurement problem and the quantum-to-classical transition.

Reference: “Experimental QND measurements of complementarity on two-qubit states with IonQ and IBM Q quantum computers”, Nicolas Schwaller, Valeria Vento & Christophe Galland, Quantum Information Processing 21, 75 (2022);