Aerospace & Defense Technology - September 2023 - 19

RF & Microwave Technology
neither a spin-up or spin-down state, but
in-between or a superposition of the two
states. While superposition is fundamental
to the operation of a quantum
computer, we have what is referred to as
the " measurement problem. " A state of
superposition only can exist if you don't
" observe " it - the idea behind the popularized
Schrödinger's cat example. In a
quantum system, observation is synonymous
with measurement. As a physicist
would say, the measurement causes the
particle to be projected to one of its
eigenstates or as an electronics engineer
would say back to the logical 1 or 0.
There are many implementations of
quantum bits, ranging from solid-state
superconducting qubits to photon-based
systems using lasers and modified crystals.
Now, let's discuss the Transmon solid-state
implementation. A Transmon or
Transmission Line Shunted Plasma
Oscillation qubit, is a type of solid-state
qubit. Fundamentally, it is a tuned LC
circuit connected to a transmission line,
which resonates when an appropriate
frequency is applied.
Figure 2 represents an actual quantum
system. As the spin and energy level
change with the application of certain
frequencies, a qubit is fundamentally
based on several microwave resonant circuits
connected via transmission lines,
for both qubit control and measurement.
The inductive component in an actual
qubit is replaced with a Josephson junction.
While still fundamentally an LC
structure, this modifies the inductive
properties of the circuit so only two resonant
or energy states can occur - since
the system must be constrained to two
levels, 1 and 0. The circuit is packaged in
a protective shield with the RF connectors
exposed, then is cooled to about
minus 450 degrees Fahrenheit to ensure
the system exhibits quantum behavior.
One of the key behaviors to establish
for a quantum bit is to determine its resonant
characteristics and determine at
what frequencies it will exhibit quantum
behavior. The que of the resonator is
usually very high so the experimentalists
will want to sweep a range of frequencies
through the devices operating range to
determine the exact resonant frequency.
Once the resonance is known we need
Electron in the excited state
Magnetic Moment
Facing Upwards
eV
Electromagnetic Energy ( f )
Electron in the ground state
Magnetic Moment
Facing Downwards
Figure 1. Electron energy states as measured in electron volts.
E0 or 0
f
E1 or 1
E1 - E0
ħ
Essentially a microwave
resonant circuit
Implemented as a hybrid
superconductor/semiconductor
circuit
Cooled to <-450 degrees f
(milli-kelvin)
Figure 2. A quantum computer.
tum behavior. This is established with
the Rabi Oscillation Measurement. If a
frequency for a specific amount of time
is applied, a pulse, you can make the
electron move from the ground state to
the excited state, and back again. This is
often also referred to as a rotation, with
the excited state being 180 degrees of
rotation and back to the ground state
360 degrees of rotation. A physicist often
refers to the pulse of durations as Pi, 2Pi
or even Pi/2. Pi is the time it takes to
rotate the electron 180 degrees and 2Pi
360 degrees. In the Rabi oscillation measurement,
we vary the pulse width to
determine the exact length of Pi.
So now we know the exact resonant
to determine if the device exhibits quanAerospace
& Defense Technology, September 2023
frequency and the time it takes the electron
to spin-up and spin-down. The next
step is to determine how long the device
can maintain quantum behavior. This is
the Relaxation Time measurement. To
do this we apply a pulse of time length
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Pi, and steadily move the readout further
and further away from the pulse to produce
a decay curve. This is a true quality
metric for qubits, as the longer it can
maintain a quantum state the more
effective it is at performing calculations.
Figure 3 shows the Tabor Quantum
Computing Measurement Control and
Measurement System.
Quantum computers, like all computers,
utilize gates. While a classical computer
utilizes NAND gates, built from
transistors, quantum computer gates are
realized from the electrical pulses with
specific frequencies and lengths. A simplified
example would be a 'not' gate
implementation, this would be the application
of a Pi pulse or inverting the spin.
We can add another gate to the sequence,
the 'Hadamard' Gate or a Pi/2 pulse. As
the qubit is in a state of superposition at
this point it is neither a 1 or 0, if we measure
(or observe) the state of the qubit, it
19
Orbits, shells or Energy Levels
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Aerospace & Defense Technology - September 2023

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