IEEE Aerospace and Electronic Systems Magazine - November 2020 - 10

Quantum Radar Cost and Practical Issues
If you would like to understand what a QR is in more
detail, you should look at the block diagram (see Figure 1)
in [2]. Also, you should read [3]-[5], which explain how
QR works in terms that are accessible to normal radar
engineers. Moreover, this article is part of a special issue
on QR, and presumably there are several excellent articles
in this special issue that explain QR in much more detail
than given here. In fact, the first draft of this article did
not attempt to describe how a QR works, because I
expected this job to be done by others in this special issue;
however, the IEEE reviewers of this article explicitly
asked me to explain how a QR works, and so I dutifully
followed my orders.

TRANSMIT POWER FOR QR
There are two basic facts about QR that dominate the calculation of transmit power. First, the energy in a single
photon at microwave or millimeter (mm) wave frequencies is extremely small, as shown below. Second, the benefit of QR over CR disappears for more than a few
transmitted photons per mode. For example, see [2, Figure
2], which shows that there is very little benefit of a QR
with more than five photons per mode. This is predicted
by quantum mechanical theory [16], and it is confirmed
by experiments [2]. Both of these important points will be
quantified below. It is obvious that one needs to do something to mitigate this extremely low transmit power for
QR, and we shall discuss the options for such mitigation
below as well. The optimal combination of such mitigation methods will be quantified in Section IV.
The energy of a single photon is given by E ¼ hn, in
which h is Planck's constant and n denotes the frequency
of the photon. The number of modes is roughly the timebandwidth product (tB), and hence, the transmit power
with one photon per mode is approximately P ¼ EB. At
X-band, assuming the maximum possible bandwidth
(100%), and assuming one photon per mode, a simple calculation shows that the optimal transmit power for a single
quantum device (e.g., JPA as in [2] or [3]) is -102 dBm.
That is, the maximum transmit power for a single quantum
transmit device (under the conditions assumed here) is
about ten orders of magnitude below a milliwatt. Such
large bandwidths with good gain and good noise figures at
X-band are indeed feasible with modern cryogenically
cooled LNAs, but unfortunately JPAs currently have
much narrower bandwidths [18].

OPTIMAL QR DESIGN
There are many different ways to increase the performance of a QR and attempt to maintain quantum superiority over CR. In particular, we would like to increase the
SNR of the QR without transmitting more than one photon
10

per mode from a given quantum transmit device. For
example, we can use many quantum transmit devices in
parallel, either in a phased array antenna or in a MIMO
antenna or else in some hybrid combination of phased
array antennas and MIMO antennas. But this obviously
increases the cost of the QR significantly, owing to the
high cost of cryogenic refrigerators (roughly one million
dollars each) as explained below. Second, we could use
very large transmit and receive antennas. But this also
increases the cost of the QR substantially, owing to the
cost of material and electronics and land to accommodate
such large antennas, as explained below. Third, we could
amplify the signal before transmission using cryogenically
cooled low noise amplifiers (LNAs) or JPAs, as in [2]-[5].
Although such amplification certainly results in a larger
SNR, it also implies that the radar is no longer a genuine
QR, because such amplification destroys entanglement of
the photons, as explained in [5] and [15]. We shall consider the optimal combination of such methods below.
We use the randomized Nelder-Mead downhill simplex algorithm to design the minimum cost optimal QR.
We ask for the minimum cost QR to achieve a given
SNR at a given range on a given RCS target at a given
data rate. We assume that the QR is theoretically optimal
in detection performance [16]. This is a nonconvex multivariate optimization problem with roughly a dozen
design variables. These design variables include: number
of quantum signal generators (e.g., JPAs), number of
cryogenic refrigerators, area of the transmit antenna, area
of the receive antenna, number of photons per mode, signal bandwidth, number of subarrays in the antennas,
number of time delay units (TDUs), power for cooling
the radar, LNA gain and LNA noise figure, number of
MIMO degrees of freedom, element spacing in the transmit and receive arrays (i.e., sparse versus dense), quantum waveform parameters, radome characteristics, etc.
The optimal signal bandwidth is limited by the current
JPA technology and the tradeoffs with gain and noise
figure in the LNAs [18], as well as the cost of signal
processing. The TDUs are required because it turns out
that the minimum cost QR has an extremely wide bandwidth and has extremely large antennas. The specific
class of QR assumed in our cost analysis uses random
quantum signals generated by cryogenically cooled JPAs
or JPCs as in [2]-[5]; alternative technologies for microwave QR are surveyed in [6] and [20].
Cryogenic cooling (to roughly 7 mK) is required for
almost all currently postulated QR. Some researchers have
suggested the possibility of room temperature QR, but this
is only a vague theoretical idea today [20]. The cost of
such cryogenic refrigerators is a major component of the
total cost of QR. In particular, the cost of a large cryogenic
dilution refrigerator to achieve 7 mK is roughly one million dollars. If we want to build a large array of quantum
signal sources (e.g., JPAs), then we would need many

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