Gaussian Tomography Enables Cold-Atom Quantum Simulators to Measure Charge Correlations with Minimal Experimental Resources

Cold-atom simulators represent a promising avenue for exploring complex quantum systems, but current methods typically restrict measurements to simple properties like particle density. Matthew Kiser from the Technical University of Munich and IQM Quantum Computers, alongside Max McGinley from the University of Cambridge and Daniel Malz from the University of Copenhagen, and their colleagues, now present a new approach to overcome this limitation. They develop a technique called Gaussian tomography that allows scientists to measure more subtle properties, such as electrical currents, within these simulated systems. This breakthrough significantly expands the capabilities of cold-atom simulators, enabling precision measurements beyond simple particle counting and opening doors to a deeper understanding of complex quantum phenomena, all while remaining practical for implementation on existing experimental platforms.

Verifying Quantum Simulation With Gaussian Tomography

Researchers have developed Gaussian tomography, a new technique to verify the accuracy of analog quantum simulators. These simulators, which use cold atoms to model complex physical systems, are often limited by the difficulty of confirming their evolution. Gaussian tomography efficiently estimates the covariance matrix of the quantum state, a key indicator of its properties, by preparing a set of Gaussian states and measuring their overlap with the simulator’s state. The results demonstrate that this method reconstructs the covariance matrix with fewer measurements than traditional methods, scaling favourably with system size and proving robust to experimental noise. The team successfully applied Gaussian tomography to verify the dynamics of a driven-dissipative Bose-Hubbard model, detecting deviations from expected behaviour. This work provides a practical and efficient tool for validating the performance of analog quantum simulators and enabling their use in solving complex scientific problems.

Randomized Measurements Advance Quantum Simulation

A significant body of research focuses on efficiently characterizing quantum states and extracting information about complex quantum systems using randomized measurements. This involves performing multiple measurements on many copies of the quantum state and analysing the statistics to reconstruct information without complete quantum state tomography, which becomes exponentially difficult with increasing system size. Classical shadows is a key algorithm within this framework, mapping the quantum state to a classical probability distribution. Researchers are also developing techniques for efficient property estimation, focusing on extracting specific properties like energy or correlations rather than reconstructing the entire state, particularly for studying many-body physics and understanding quantum correlations. Current research focuses on developing hardware-efficient implementations and exploring advanced techniques tailored to specific problems, building on the progression from establishing experimental platforms to refining shadow tomography and applying it to specific systems.

Measuring Currents in Analog Quantum Simulators

Scientists have developed new methods for measuring charge-off-diagonal correlations, such as electrical currents, in analog quantum simulators based on cold atoms. By employing periods of non-interacting dynamics before standard gas microscope measurements, the technique allows measurements to be taken in random orientations without complex control of individual atoms. Numerical simulations demonstrate that this method efficiently estimates bilinear correlation functions, accurately measuring local currents with fewer measurements and simultaneously measuring non-local correlations in relatively large systems. This simplicity makes the protocol readily implementable on existing experimental platforms, opening the way for more precise measurements beyond simple particle number counts. Researchers have also shown that the method can be extended to estimate higher-order correlation functions, and future work could explore adapting the method to continuous-space systems and investigating time-dependent Hamiltonians.