In the first article published earlier, we focused on qubits as "bits" of information for quantum systems and some elements of quantum mechanics. But how are qubits physically realized? How can electronics manage these elements that belong to a quantum ecosystem? In this article, we will start a path to explain in detail all you need to know about digital quantum electronics.

Qubits

The classic computer bits can be 0 and 1, and two bits form four possible states: 00, 01, 10, 11. In general, with n bits, you can build 2n distinct states. How many states can you get with n qubit? The space of the states generated by a system of n qubit has dimension 2n: each vector normalized in this space represents a possible computational state, which we will call quantum register of n qubit. This exponential growth in the number of qubits suggests the potential ability of a quantum computer to process information at a speed that is exponentially higher than that of a classical computer. Note that for n = 200 you get a number that is larger than the number of atoms in the universe.


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Formally, a quantum register of n qubit is an element of the 2n-dimensional Hilbert space, C2n, with a computational basis formed by 2n registers at n qubit. Let's consider the case of two qubits. In analogy with 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 two qubits is an overlapping of the form:

QC1

With the normalization on the amplitudes of the coefficients.

Logical Ports

Like classical computers, a quantum computer is made up of quantum circuits consisting of elementary quantum logic gates. In the classical case, there is only one (non-trivial) one-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 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 property of quantum mechanics that is experimentally justified.

The matrix corresponding to quantum NOT is called for historical reasons X and is defined by:

QC2

With the condition of normalization|α|2 + |β|2 = 1 any quantum stateα |0> + β |1>.

Besides NOT, two important operations are represented by the Z matrix:

QC3

which acts only on the component |1> exchanging its sign, and the Hadamard port:

QC4

This last operation is very often used in the definition of quantum circuits. Its effect is to transform a base state into an overlap that results, after a measurement in the computational base, to be 0 or 1 with equal probability. The effect of H can be defined as a NOT executed in half so that the resulting state is neither 0 nor 1, but a coherent superposition of the two primaries (base) states.

The most important logical ports that implement operations on two classic bits are the AND, OR, XOR, NAND, and NOR ports. The NOT and AND ports form a universal set, i.e., any Boolean function can be achieved with a combination of these two operations. For the same reason, NAND forms a universal set.

The quantum equivalent of XOR is the CNOT (controlled-NOT) port, which operates on two qubits: the first is called the control qubit, and the second is the target qubit. If the control is zero, then the target is left unchanged; if the control is one, then the target is negated, that is:

QC5

Where A is the control qubit, B is the target and ⊕ is the classic XOR operation (Figure 1).

Fig1

Figure 1: CNOT port

Another important operation is represented by the symbol in Figure 2 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.

Fig2

Figure 2: quantum measurement circuit

The CNOT port can be used to create states that are entangled. The circuit in Figure 3 generates for each state of the computational base |00>, |01>, |10> , |11> a particular entangled state. These states, which we indicate with β00, β10, β01, β11, are called Bell or EPR states by Bell, Einstein, Podolsky, and Rosen who first discovered their extraordinary properties.

Fig3

Figure 3: Quantum circuit for the creation of Bell states

Quantum CMOS

The way to encode information in modern digital computers is done through voltages or currents on tiny transistors within integrated circuits that act as digital or analog elements. Each transistor is addressed by a bus that is able to define a state of 0 (low voltage) or 1 (high voltage).

Quantum computers have different similarities, and the basic idea is illustrated in figure 4. In this figure, we observe a superconducting qubit (also called SQUID - Superconducting QUantum Interference Device), which is the basic element of a quantum computer (a quantum 'transistor'). The term 'Interference' refers to electrons - which behave like waves within a quantum wave, interference patterns that give rise to quantum effects.

In this case, the basic element is niobium, not silicon, as in a classic transistor. The property of the material allows electrons to behave like qubits. When the metal is cooled, it becomes known as a superconductor and begins to show quantum mechanical effects.

The superconducting qubit structure encodes 2 states as tiny magnetic fields pointing in opposite directions. By means of quantum mechanics, we can control these states defined +1 and -1 or |ψ> = α |0>+β |1>.

Fig 4

Figure 4: Layout of a superconducting qubit. The arrows indicate the magnetic spin states that code the information bits values. Unlike normal information bits, these states can be put in quantum mechanical superposition [Source: D-Wave].

By means of elements known as superconducting loop couplers, a multi-qubit processor is created. A programmable quantum device can be designed by putting together many of these elements, such as qubits and couplers (Figure 5).

Fig 5

Figure 5: a schematic illustration of 8 qubits. The blue dots are the positions of the 16 coupling elements that allow the qubits to exchange information [Source: D-Wave].

To control the operation of qubits, it is important to have a switch structure consisting of Josephson junctions that direct each qubit (routes pulses of magnetic information to the correct points on the chip) and stores the information in a local magnetic memory element to each device.

The Josephson effect consists in the development of current between two superconductors separated by an insulating junction, called Josephson junction. The effect is due to the tunnel effect of the electron pairs in each of the superconductors. If the insulator is too wide, the probability of tunnel effect is low, and the effect does not occur.

Most Josephson junctions represent a quantum processing unit (QPU). The QPU has no large areas of memory (cache), as they are designed more like a biological brain than the common 'Von Neumann' architecture of a conventional silicon processor. One can think of qubits as neurons and couplers as synapses that control the flow of information between these neurons.

The requirements for a successful quantum implementation are encapsulated in the number of quantum bits that must be large enough for high efficiency. This also implies that you must be probably able to perform a lot of quantum bit operations in a short time. The algorithms require the application of many gates logic on many quantum bits. To keep the probability of error low enough, the various gates must be very precise.

Computer cooling

The quantum structure of the computer needs very cold temperatures to work properly. In particular, a temperature reduction approximately below 80mK is required. The performance of a quantum processor increases as the temperature drops - the lower the temperature, the better. The latest generation D-Wave 2000Q system has an operating temperature of about 15 millikelvins. The QPU and parts of the input/output (I/O) system, which includes about 10 kg of material, is cooled to this temperature.

To reach temperatures close to absolute zero, the systems use liquid helium as a coolant. Liquid helium resides within a closed-loop system, where it is recycled and recondensed using pulse tube technology. This makes them suitable for remote use, as there is no need to replenish liquid helium on site.