The Institute for Mathematical and Statistical Innovation (IMSI), a Mathematical Science Institute funded by the US National Science Foundation, hosted a Long Program on “Statistical Methods and Mathematical Analysis for Quantum Information Science” from September 16 thru December 13, 2024, at IMSI’s headquarters at the University of Chicago.  This Long Program brought together mathematicians and statisticians who are collaborating with colleagues from physics, engineering, computer science, and other fields to solve major outstanding problems in the theory and applications of quantum information science.  One of the embedded workshops was on Quantum Networks which included a talk by Johannes Borregaard, then at Harvard University and Amazon Web Services (currently at Harvard and Lightsynq) on “Quantum networking for enhanced telescopes and tests of gravity.”  This highlight will discuss the work of Borregaard and his colleagues on how a quantum enhanced telescope might be used for the detection of exoplanets.

 

Exoplanets are planets orbiting a star outside of Earth’s solar system.  Exoplanets are extremely difficult to detect because they are relatively small and dim objects that are very far away, orbiting a much larger and much brighter star.  The challenge in detecting exoplanets is a combined one of angular resolution and discriminating the planet’s optical signal from that of its star.  The technical difficulty of exoplanet detection is such that despite breathtaking advances in astronomy in the second half of the last century, such as those made by the Hubble Telescope, the first exoplanet orbiting a star was not discovered until 1995.  As of April 2025, 5,893 exoplanets have been confirmed and listed in the NASA Exoplanet Archive; still a relatively small number given the phenomenal growth in other astronomical discoveries over that same period.  For example, astronomers estimate there to be at least 200 billion galaxies in the observable universe, and our galaxy – the Milky Way – is thought to have at least 100 billion stars.  These comparisons make the discovery of even one exoplanet seem quite a remarkable achievement.

 

Discovering exoplanets is of broad scientific, technical, and social interest.  Scientifically, the existence of planets orbiting stars outside our solar system gives us a greater understanding of our universe and a sense of the extent to which our solar system may be unique.  Technically, detecting exoplanets requires extremely sensitive observations and data acquisition & analysis systems; and increasingly, as we learned from Borreegaard, a potential application of emerging quantum technologies.  Socially, it is widely assumed that if there is life outside our solar system, it would likely exist on planets with some similarity to Earth, orbiting a star such as our Sun.  Thus, one key strategy of the Search for Extraterrestrial Intelligence (SETI) and similar efforts is first to identify planets that are potential candidates for hosting life.

 

In his talk, Borregaard described one of the common techniques astronomers use to detect exoplanets.  This method, though technically challenging, falls in the realm of classical physics. Optics, detection, and signal processing systems treat the light signal from the star/planet system as a spherical wavefront arriving from a point source at some distance; and once the light is captured via a system of lenses and filters, it is processed using techniques long established in the astronomical literature.  Specifically,  classical exoplanet detection involves using a coronagraph to subtract or block the light of the star from the  incoming signal, so that what is left is the light from the planet.  This involves optical processing and then a considerable amount of signal processing by software.

 

Key to analyzing incoming light in the classical technique is knowing the point spread function (PSF) of the system.  The PSF provides a model of how the light from the star (assumed to be a point source with no nearby light-emitting planet) interacts with intervening space and the telescope optics to result in the blurred spread-out image that is detected.  In a star-planet system then, the PSF is used to discriminate the signal from the star from that of the planet, so that the output after signal processing is the light signal from the planet.  This assumes the signal is linear such that Light (star + planet) = Light (star) + Light (planet) (see Figure 1).  In other words, if the light from the star can be blocked, filtered, or subtracted in signal processing, then the signal that remains should be the light from the exoplanet.  Scientists can then further analyze the spectral components of the exoplanet’s light to determine such things as its orbit and composition (including its atmosphere, if it has one).

 

In describing the potential advantages of quantum enhanced detection of exoplanets, Borregaard explained that one challenge in detecting light from a dim, distant star/exoplanet system is that the incoming light signal can be treated not as an optical wave (subject to lenses and filters) but rather as a low intensity stream of individual photons (i.e., quanta), each of which can be counted and analyzed.  Borregaard explained that an advantage of quantum enhanced detection of photons is that it can lead to improvements in spatial and frequency resolution of the incoming signal which are essential for distinguishing two distant, nearby point sources, one of which, in the case of exoplanets, may be a small dim planet near a large bright star.   

 

Quantum enhanced telescopy involves assuming that the incoming signal has a very strong vacuum term which is essentially noise, combined with light from the star and from the exoplanet.  The quantum enhanced telescope gathers multiple copies of the incoming signal over a 2-D array of encoders that convert the light into qubit registers.  Then quantum principal component analysis (qPCA) and quantum signal processing (QSP) is used to sort the signal into light from the exoplanet and light from the star and to create an image of the star/exoplanet system (See Figure 2).  In this system, no accurate knowledge of the PSF is needed and the telescope does not have to be precisely aligned on the target system. The combination of qPCA and QSP enables the star and planet to be studied at the same time and also enables studying multiple sources.  Mathematically,  qPCA and QSP combined with Gram-Schmidt orthogonalization of the resultant data matrices yields eigenvectors and eigenvalues for the individual sources of light from the signal, which is assumed to be a linear combination of all the sources.  

 

One commonly vexing challenge in classical telescopy that quantum enhanced telescopy can help ameliorate is shot noise.  Shot noise is a phenomenon that is related to detecting low intensities of individual photons in a detector such as one would have in a telescope.  Shot noise is further accumulated during signal processing.  In a quantum telescope though, arriving photons are converted immediately to qubits.  Qubit data is then analyzed using a quantum information processing algorithm, and this information is what is detected.  This process significantly reduces shot noise in the observed signal.  Remaining shot noise is introduced during detection.

 

In concluding, Borregaard noted that exoplanet detection using classical techniques has three technically challenging requirements: 1) careful stabilization and alignment of the telescope, 2) an estimation of the PSF, and 3) a narrow field of view focused on the star/planet system.  On the other hand, quantum enhanced telescopes have the advantage that 1) light can be collected from a large field of view with potentially multiple sources from star/exoplanet systems, 2) qPCA and QSP is used on the signal to discriminate the different sources and separate the exoplanet signal from the star’s signal, and 3) and a quantum advantage can be achieved by working around the accumulation of shot noise.  While Borregaard and colleagues’ current work is focused on applications to exoplanet detection, he speculates that there could be other applications that could benefit from quantum processing enhanced sensing such as imaging molecules in living systems, and sensing and tracking satellites. 

 

Figure 1. A representation of the linear combination of incoming light signals from a star and its companion exoplanet, as detected by a classical telescope. 

Figure 2.  Schematic of a quantum enhanced telescope, illustrating how incoming photons are converted to an array of qubits, which are then processed using various quantum and classical algorithms, information from which is used to create an image of the star and its companion exoplanet.