dynamics of the system to be restricted to only the 2-qubit states. The Josephson junctions are necessary to produce the qubits; otherwise, the superconducting loop would just be a circuit. The point is that the linear inductors in a traditional circuit are replaced with the Josephson junction, which is a nonlinear element that produces energy levels with different spacings from each other that can be used as a qubit. Josephson (after whom the Josephson junction is named) was awarded the Nobel Prize in Physics in 1973 for work predicting the tunneling behavior of superconducting Cooper pairs.
As an example of a superconducting system, Google’s qubits are electrical oscillators constructed from aluminum (niobium is also used), which becomes superconducting when cooled to below 1 K (−272°C). The oscillators store small amounts of electrical energy. When the oscillator is in the 0 state, it has zero energy, and when the oscillator is in the 1 state, it has a single quantum of energy. The two states of the oscillator with 0 or 1 quantum of energy are the logical states of the qubit. The resonance frequency of the oscillators is 6 gigahertz (which corresponds to 300 millikelvin) and sets the energy differential between the 0 and 1 states. The frequency is low enough so that control electronics can be built from readily available commercial components and also high enough so that the ambient thermal energy does not scramble the oscillation and introduce errors. In another example, Rigetti has a different architecture. This system consists of a single Josephson junction qubit on a sapphire substrate. The substrate is embedded in a copper waveguide cavity. The waveguide is coupled to qubit transitions to perform quantum computations (Rigetti et al., 2012).
3.3.2.1Superconducting materials
Superconducting materials is an active area of ongoing research (Table 3.2). The discovery of “high-temperature superconductors” in 1986 led to the feasibility of using superconducting circuits in quantum computing (and the 1987 Nobel Prize in Physics) (Bednorz & Muller, 1986). Before high-temperature superconductors, ordinary superconductors were known materials that become superconducting at critical temperatures below 30 K (−303°C), when cooled with liquid helium. High-temperature superconductors constitute advanced materials because transition temperatures can be as high as 138 K (−135°C), and materials can be cooled to superconductivity with liquid nitrogen instead of helium. Initially, only certain compounds of copper and oxygen were found to have high-temperature superconducting properties (for example, varieties of copper oxide compounds such as bismuth strontium calcium copper oxide and yttrium barium copper oxide). However, since 2008, several metal-based compounds (such as iron, aluminum, copper, and niobium) have been found to be superconducting at high temperatures too.
Table 3.2. Superconducting materials.
Experimental, of interest is a new class of hydrogen-based “room-temperature superconductors” (i.e. warmer than ever before) that have been discovered with high-pressure techniques. In 2015, hydrogen sulfide subjected to extremely high pressure (about 150 gigapascals) was found to have a superconducting transition near 203 K (−70°C) (Drozdov et al., 2015). In 2019, another project produced evidence for superconductivity above 260 K (−13°C) in lanthanum superhydride at megabar pressures [Somayazulu et al., 2019]. Although experimentally demonstrated, such methods are far from development into practical use due to the specialized conditions required to generate them (a small amount of material is pressed between two high-pressure diamond points (Zurek, 2019)).
3.3.3 Superconducting circuits: Quantum annealing machines
Within the superconducting circuits approach to quantum computing, there are two architectures, the standard gate model (described above) and quantum annealing (invented first, but more limited). The two models are used for solving different kinds of problems. The universal gate model connotes a general-purpose computer, whereas the annealing machine is specialized. Quantum annealing machines have superconducting qubits with programmable couplings that are designed to solve QUBO problems (quadratic unconstrained binary optimization), a known class of NP-hard optimization problems that minimize a quadratic polynomial over binary variables.
In quantum annealing, the aim is to harness the natural evolution of quantum states over time. A problem is set up at the beginning and then the system runs such that quantum physics takes its natural evolutionary course. There is no control during the system’s evolution, and ideally, the ending configuration corresponds to a useful answer to the problem. As compared with quantum annealing, the gate model aims to more fully control and manipulate the evolution of quantum states during the operation. This is more difficult given the sensitivity of quantum mechanical systems, but having more control implies that a bigger and more general range of problems can be solved. The difference in approach explains why quantum annealing machines appeared first and have been able to demonstrate 2048 qubits, whereas only 30–70 qubits are currently achieved in the standard gate model.
Quantum annealing is an energy-based model related to the idea of using the quantum fluctuations of spinning atoms to find the lowest energy state of a system (Kadowaki & Nishimori, 1998). Annealing refers to the centuries-old technique used by blacksmiths to forge iron. In the thermal annealing process, the iron becomes uniformly hot enough so that the atoms settle in the lowest energy landscape, which makes the strongest material. Similarly, quantum annealing is based on the idea of finding the lowest energy configuration of a system.
Quantum annealing is deployed as a method for solving optimization problems by using quantum adiabatic evolution to find the ground state of a system (adiabatic means heat does not enter or leave the system). Run on a quantum computer, the quantum annealing process starts from a ground state which is the quantum mechanical superposition of all possible system states with equal weights. The system then evolves per the time-dependent Schrödinger equation in a natural physical evolution to settle in a low-energy state. The computational problem to be solved is framed in terms of an energy optimization problem in which the low-energy state signals the answer. (The quantum annealing process is described in more detail in Chapter 10.)
Overall, the quantum annealing process allows the system of spins (spinning atoms of qubits) to find a low-energy state. Superconducting circuits in the quantum annealing model can be thought of as programmable annealing engines (Kaminsky & Lloyd, 2004). Optimization problems are framed such that they can be instantiated in the form of an energy landscape minimization. Although annealing machines are not general-purpose quantum computers, one advantage is that since annealing systems constantly attempt to reach the lowest energy state, they are more tolerant and resistant to noise than gate model systems and may require much less error correction at large scales.
3.3.4 Ion trapping
Another prominent approach to quantum computing is trapped ions. In these quantum chips, ions are stored in electromagnetic traps and manipulated by lasers and electromagnetic fields. Ions are atoms which have been stripped of or received electrons, which leaves them positively or negatively charged and therefore more easily manipulatable. The advantage of ion trap qubits is that they have a long coherence time (making calculations easier) and (like annealing machines) may require less error correction at large scales. A single qubit trap may accommodate 30–100 qubits, and 23 qubits have been demonstrated in a research context (Murali et al., 2019).
The IonQ quantum chip uses ytterbium ions, which unlike superconducting qubits, do not need to be supercooled to operate. Bulky cryogenic equipment is not required, and the entire system occupies about one cubic meter, as opposed to a much larger footprint for superconducting circuit machines. The chip is a few millimeters across. It is fabricated with silicon and contains 100 electrodes that confine and control the ions in an ultrahigh-vacuum environment.
To operate, the ion trap quantum computer holds the ions in a geometrical array (a linear array for IonQ). Laser beams encode and read information to and from individual ions by causing transitions between the electronic states of the ion. The ions influence each other through electrostatic interactions and their coupling can be controlled.