In a few years, a new generation of quantum simulators could provide
insights that would not be possible using simulations on conventional
supercomputers. Quantum simulators are capable of processing a great amount
of information since they quantum mechanically superimpose an enormously
large number of bit states. For this reason, however, it also proves
difficult to read this information out of the quantum simulator. In order to
be able to reconstruct the quantum state, a very large number of individual
measurements are necessary. The method used to read out the quantum state of
a quantum simulator is called quantum state tomography.

“Each measurement provides a ‘cross-sectional image’ of the quantum state.
You then put these cross-sectional images together to form the complete
quantum state,” explains theoretical physicist Christian Kokail from Peter
Zoller’s team at the Institute of Quantum Optics and Quantum Information at
the Austrian Academy of Sciences and the Department of Experimental Physics
at the University of Innsbruck. The number of measurements needed in the lab
increases very rapidly with the size of the system. “The number of
measurements grows exponentially with the number of qubits,” the physicist
says. The Innsbruck researchers have now succeeded in developing a much more
efficient method for quantum simulators.

### Efficient method that delivers new insights

Insights from quantum field theory allow quantum state tomography to be much
more efficient, i.e., to be performed with significantly fewer measurements.
“The fascinating thing is that it was not at all clear from the outset that
the predictions from quantum field theory could be applied to our quantum
simulation experiments,” says theoretical physicist Rick van Bijnen.
“Studying older scientific papers from this field happened to lead us down
this track.”

Quantum field theory provides the basic framework of the quantum state in
the quantum simulator. Only a few measurements are then needed to fit the
details into this basic framework. Based on this, the Innsbruck researchers
have developed a measurement protocol by which tomography of the quantum
state becomes possible with a drastically reduced number of measurements. At
the same time, the new method allows new insights into the structure of the
quantum state to be obtained.

The physicists tested the new method with experimental data from an ion trap
quantum simulator of the Innsbruck research group led by Rainer Blatt and
Christian Roos. “In the process, we were now able to measure properties of
the quantum state that were previously not observable in this quality,”
Kokail recounts.

### Verification of the result

A verification protocol developed by the group together with Andreas Elben
and Benoit Vermersch two years ago can be used to check whether the
structure of the quantum state actually matches the expectations from
quantum field theory. “We can use further random measurements to check
whether the basic framework for tomography that we developed based on the
theory actually fits or is completely wrong,” explains Christian Kokail.

The protocol raises a red flag if the framework does not fit. Of course,
this would also be an interesting finding for the physicists, because it
would possibly provide clues for the not yet fully understood relationship
with quantum field theory. At the moment, the physicists around Peter Zoller
are developing quantum protocols in which the basic framework of the quantum
state is not stored on a classical computer, but is realized directly on the
quantum simulator.

## Reference:

“Entanglement Hamiltonian tomography in quantum simulation” by Christian
Kokail, Rick van Bijnen, Andreas Elben, BenoĆ®t Vermersch and Peter Zoller,
24 June 2021, Nature Physics.

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