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HIGH-PERFORMANCE COMPUTING
Quantum Computer Design: Electronic Circuits

By Maurizio Di Paolo Emilio

ubits are “bits” of information for quantum systems and which acts only on the component |1> exchanging its sign and the
some elements of quantum mechanics. But how are qubits Hadamard port:
physically realized? How can electronics manage elements
Qthat belong to a quantum ecosystem? In this article, we will
carve a path to explain all you need to know about digital quantum
electronics.
This last operation is very often used in the definition of quantum
QUBITS circuits. Its effect is to transform a base state into an overlap that
The classic computer bits are 0 and 1, and two bits form four possible results, after a measurement in the computational base, in a 0 or a 1
states: 00, 01, 10, 11. In general, with n bits, you can build 2n distinct with equal probability. The effect of H can be defined as a NOT
states. How many states can you get with n qubits? The space of the executed in half so that the resulting state is neither 0 nor 1 but a
states generated by a system of n qubits has dimension 2n: Each vector coherent superposition of the two primary (base) states.
normalized in this space represents a possible computational state, The most important logical ports that implement operations on two
which we will call quantum register of n qubits. This exponential classic bits are the AND, OR, XOR, NAND, and NOR ports. The NOT
growth in the number of qubits suggests the potential ability of a quan- and AND ports form a universal set; i.e., any Boolean function can be
tum computer to process information at a speed that is exponentially achieved with a combination of these two operations. For the same
higher than that of a classical computer. Note that for n = 200, you get a reason, NAND forms a universal set.
number that is larger than the number of atoms in the universe. The quantum equivalent of XOR is the controlled-NOT (CNOT)
Formally, a quantum register of n qubits is an element of the 2n- port, which operates on 2 qubits: The first is the control qubit, and
dimensional Hilbert space, C , with a computational basis formed by 2n the second is the target qubit. If the control is 0, then the target is left
2n
registers at n qubits. Let’s consider the case of 2 qubits. In analogy with unchanged; if the control is 1, then the target is negated. That is:
the single qubit, we can construct the computational base of the states’
space as formed by the vectors |00>, |01>, |10>, |11>. A quantum register
with 2 qubits is an overlapping of the form:

where A is the control qubit, B is the target, and ⊕ is the classic XOR
operation (Figure 1).
Another important operation is represented by the symbol in Figure 2
with the normalization on the amplitudes of the coefficients. and consists of measuring a qubit |ψ> = α |0>+β |1>. The result is a
classic bit M (indicated with a double line), which will be 0 or 1.
LOGICAL PORTS The CNOT port can be used to create states that are entangled. The
Like classical computers, a quantum computer is made up of quantum circuit in Figure 3 generates for each state of the computational base
circuits consisting of elementary quantum logic gates. In the classical
case, there is only one (non-trivial) 1-bit logical port, the NOT port,
which implements the logical negation operation defined through a
truth table in which 1 → 0 and 0 → 1.
To define a similar operation on a qubit, we cannot limit ourselves to
establishing its action on the primary states |0> and |1>, but we must
also specify how a qubit that is in an overlapping of the states |0> and
|1> must be transformed.
Intuitively, the NOT should exchange the roles of the two primary Figure 1: CNOT port
states and transform α |0> + β |1> into β |0> + α |1>.
Clearly, |0> would turn into |1> and |1> into |0>. The operation that
implements this type of transformation is linear and is a general prop-
erty of quantum mechanics that is experimentally justified.
The matrix corresponding to quantum NOT is called for historical
reasons X and is defined by:
Figure 2: Quantum measurement circuit

with the condition of normalization |α|2 + |β|2 = 1 any quantum state
α |0> + β |1>.
Besides NOT, two important operations are represented by the Z
matrix:

Figure 3: Quantum circuit for the creation of Bell states

MARCH 2020 | www.eetimes.eu