Superconducting quantum computing (SQC), one of the several approaches to realizing a quantum computer, relies on superconducting electronic circuits to implement a quantum processor. Ever since Japanese physicist Yasunobu Nakamura created a simple superconducting quantum bit (qubit) in 1999, SQC has been making rapid advances and has emerged as one of the foremost candidates for scalable quantum processors.
Multibillion-dollar corporations like Google, IBM, Intel, Microsoft, and Amazon, and startups like Rigetti Computing, Alice&Bob, IQM, Oxford Quantum Circuits, and others are at the forefront of SQC. Notably, Google’s declared demonstration of “quantum advantage” was performed on a superconducting quantum system.
In this post we discuss the fundamental concepts of SQC, the types of superconducting qubits, the advantages and challenges of the superconducting quantum modality, and its commercial scope.
To make our technical explanation generally accessible, we assume no prior knowledge of superconductivity or electronics on the reader’s part and introduce the necessary ideas and terms as we go along.
Superconductivity is a phenomenon characterized by the total disappearance of electrical resistance in certain materials called superconductors when they are cooled below a “critical” or “transition” temperature Tc. The critical temperature varies from one superconductor to the next, but is in most cases below 20 K (−253°C).
Superconductivity was first discovered in 1911 by the famous Dutch physicist Heike Kamerlingh Onnes (1913 Nobel Prize). While studying the properties of matter at very low temperatures, Onnes and his team found that the electrical resistance of mercury dropped to zero below 4.2 K (-269°C). This was the earliest observation of superconductivity. At zero resistance, a current can circulate inside a material without dissipating energy.
Furthermore, as observed by German physicists Walther Meissner and Robert Ochsenfeld in 1933, external magnetic fields, if weak enough, do not penetrate a superconductor, but rather linger near its surface. This so-called Meissner effect is at the heart of the phenomenon of superconductivity. (When the strength of the magnetic field passes above a critical threshold, the superconductor undergoes a phase transition back to a regular conductor, even if cooled below the critical temperature.)
The difference between superconductors and non-superconductors is best understood by looking at a plot of resistance over temperature. Note that in non-superconductors, electrical resistance does not drop to zero even at zero Kelvin due to the absence of the Meissner effect.
For conventional superconductivity to occur, very low temperature is insufficient: the ambient magnetic field and the electrical current in the superconducting metal must not exceed certain low critical levels above which superconductivity disappears.
Here is another way of visualizing the superconductivity threshold.
Superconductivity is a “macroscopic” quantum phenomenon, meaning that it is a quantum behavior that is observable at the macroscopic or “classical” scale. The quantitative analysis of macroscopic quantum phenomena is extremely hard. Following the discovery of superconductivity, some of the brightest minds in physics, including Albert Einstein, Niels Bohr, Felix Bloch, and Richard Feynman, struggled to formulate an adequate theoretical explanation of this exotic property. Initially, numerous attempts at achieving a “microscopic” understanding of superconductivity proved unsuccessful. Einstein himself admitted as much in 1922: “With our far-reaching ignorance of the quantum mechanics of composite systems we are very far from being able to compose a theory out of these vague ideas.”
It was impossible to have a proper theory of superconductivity without the formulation of the laws of quantum mechanics by Erwin Schrödinger and Werner Heisenberg in 1925-6. Indeed, it was not until 1957, over four decades after the discovery of superconductivity, that three American physicists – John Bardeen, Leon Cooper, and John Schrieffer – provided the first successful microscopic theory of superconductivity.
The solid can be seen as a rigid lattice of positively charged ions submerged in a pool of floating electrons. According to their “BCS theory,” at near 0 K temperatures electrons become bound remotely into “BCS pairs” or “Cooper pairs” through interactions with the positively charged ionic lattice. Excitations of the crystal lattice that act as quasi-particles are termed phonons. This condensation of electrons into Cooper pairs is a part of the mechanism that causes the metal’s phase transition from the normal to the superconducting state.
The phonon expresses the collective motion of the somewhat elastic crystal lattice, making a rigorous quantum explanation possible. In simplified, classical terms, as an electron passes through the lattice, it attracts the positive ions, triggering a slight distortion of the lattice. This movement creates an electrically positive region in the lattice which, in turn, attracts another passing electron.
Cooper pairs circulate inside the superconducting solid without any resistance. Their electrons are entangled in the lowest energy state. (See our Introduction to Quantum Computing Basics post for an explanation of quantum entanglement.)
Geek note: The elementary particles are divided into fermions (matter and antimatter particles) and bosons (“force particles” that mediate interactions among fermions). Generally, the fermions have a half-odd-integer spin quantum number, while the bosons have integer spins. As a result, the bosons have symmetric and the fermions antisymmetric wave functions. The electron, with its spin values of ±½, is a fermion. Cooper pairs always have a total spin of zero in conventional superconductors, which means they behave like bosons.
Note that Cooper pairs are weakly bound and can be easily split up by thermal energy, which increases and speeds up the vibrations of the ionic lattice. This explains why superconductivity usually occurs at very low temperatures. (That being said, the BCS theory does not explain the occurrence of superconductivity at higher temperatures.)
In our earlier post on quantum computing hype, we talked about the problem of decoherence in quantum systems. Decoherence produces “noise,” resulting in information loss. In order to preserve coherence, interactions between individual electrons and between electrons and phonons must lend themselves to tight control. Since Cooper pairs resist decoupling unless exposed to a certain amount of energy, superconducting qubits make it relatively easy to extend quantum coherence.
A fundamental component of superconducting qubits is the Josephson junction (JJ). The “Josephson effect,” discovered in the early 1960s by Welsh theoretical physicist Brian D. Josephson, refers to the quantum tunneling of Cooper pairs across a very thin insulating barrier inserted into the superconducting material.
A Josephson junction is constructed by sandwiching the insulator (such as aluminum oxide) between two superconducting layers. The insulator being just a few nanometers thick, the Cooper pairs tunnel through it and couple the respective superconducting wavefunctions on either side of the insulating barrier.
Almost all circuits for superconducting qubits today consist of Josephson junctions.
The Josephson junction can be used to vary the coupling between different components of the circuits, making superconductive circuits essentially lossless at frequencies well below the superconducting gap.
From the Quantum Harmonic Oscillator to Superconducting Qubits
Quantum process architecture based on superconducting qubits is tied to the idea of a quantum oscillator, which stores a tiny amount of electrical energy.
A quantum harmonic oscillator (QHO) is the quantum-mechanical analog of the classical harmonic oscillator, defined as a particle subject to a restoring force that is proportional to the displacement of the particle. (A restoring force is always directed toward the equilibrium position.)
Intuitively, one can visualize the classical harmonic oscillator as a particle with mass suspended and continuously bouncing up and down on a spring, while a quantum harmonic oscillator can be visualized as a particle continually bouncing back and forth within a one-dimensional impermeable box.
A simple QHO can be made with a linear LC circuit consisting of an inductor (represented by the letter L) placed in parallel with a capacitor (represented by the letter C). We want the wire, the inductor, and the capacitor to be superconducting.
The inductor is usually a coiled wire that stores electrical energy in a magnetic field when an electric current passes through it. A capacitor stores electrical energy in an electrical field, typically within metallic plates attached to the capacitor’s two terminals and separated by a dielectric.
It is a useful feature of both the inductor and the capacitor that they can quickly release the stored energy back into the circuit in the form of electrical current, smoothing out interruptions in the supply. The properties that the two devices contribute are called inductance and capacitance, respectively. Working together, they produce a periodic, oscillating electronic signal within the QHO.
At resonance, energy in the HQO sloshes between a charging energy and an inductive energy, just as it oscillates between kinetic energy and potential energy in a spring-mass system.
The energies of the QHO are quantized, meaning that only discrete energy values (called energy eigenstates) are possible, which is true of any quantum-mechanical system based on a confined particle.
However, the energy levels of the QHO are spaced apart equidistantly or “harmonically.” As a result, we cannot define a unique transition for any two levels. Therefore, the QHO is insufficient as a candidate for a qubit.
To design a two-level qubit circuit, we replace the inductor with a Josephson junction. Acting as a non-linear inductor and bringing about a sinusoidal potential well with energy levels that are distributed “anharmonically” (non-equidistantly), the Josephson Junction is an essential building block for making a superconducting qubit.
Types of Superconducting Qubits
Superconducting qubits are divided into three main types, namely: charge qubit, phase qubit, and flux qubit. The three types of qubits are distinguished from each other according to the ratio of Josephson energy EJ (i.e. the energy stored in a Josephson junction in the event of a supercurrent passing through it) to charge energy EC (i.e. the energy stored in the electrical field between the plates of the capacitor). The ratio determines whether the behavior of the qubit is governed by phase fluctuations or charge fluctuations.
The Charge Qubit
The charge qubit, also known as a Cooper pair box (CPB), was one of the first developed superconducting qubits. Designed with a Josephson junction in the circuit, this qubit consists of a small superconducting island (black dot with node flux φ); the “island” denotes a specific superconducting area connected to the circuit in a manner that facilitates the manipulation of the number of Cooper pairs in the area.
The external voltage Vg controls the number of Cooper pairs flowing into and out of the island. Consequently, a certain number of Cooper pairs are trapped inside the island. The number of Cooper pairs trapped will be determined by quantum fluctuations, which, causing an oscillation, will manifest themselves in the form of energy levels used to represent the qubit.
Geek note: Google and IBM are using a variant of the charge qubit known as transmons (short for “transmission line shunted plasma oscillation qubit”). It is formed by adding a capacitor CB, parallel to the Josephson junction in the charge qubit circuit. This qubit system is designed to have reduced sensitivity to charge noise, which is achieved by increasing the ratio of Josephson energy EJ to the charge energy Ec. The ratio affects the system’s anharmonicity (anharmonic quantum oscillations) and its sensitivity to charge noise. The energy ratio EJ/Ec= 5 is the transmon regime, where the first two energy levels of the qubit are insensitive to fluctuations for any value of ng. (Where ng represents the induced offset charge, proportional to the number of individual Cooper pairs tunneling across the Josephson Junction: ng = Cg Vg / 2e).
The Phase Qubit
A phase qubit consists of a larger, current-biased Josephson junction than in charge qubits. It is operated in the zero-voltage state with a non-zero current bias. For greater non-linearity, the biased current should be close to the critical current Ic of the junction because the Josephson junction will allow currents up to Ic to pass through without any voltage.
In electronics, biasing refers to the initial operating conditions needed for a particular circuit to function in the right manner; the circuit needs a consistent flow of current or voltage. So when we say that a phase qubit is “current-biased”, it means that it is operated in the zero-voltage state, but with “non-zero” current bias. This has a significant implication: compared to the other two types of superconducting qubits, the “tunability” (tuning the phase of the qubit by changing the frequencies) of the current-biased JJ is the chief advantage of the phase qubit. However, the phase qubit is also vulnerable to fluctuations in current, which may affect its performance.
At present, phase qubits are being tested by the National Institute of Science and Technology in the USA. There seem to be no commercial vendors of phase qubits as yet.
The Flux Qubit
First proposed by Terry P. Orlando et al. at MIT in 1999, flux qubits are loops of superconducting material interrupted by Josephson junctions. The loops are controlled by an external magnetic flux Φext and the bias current Ib. The state of a flux qubit, corresponding to the direction in which the superconducting current passes through the loop, is measured by a SQUID (superconducting quantum interference device), a highly sensitive magnetometer that measures the direction of the current in the qubit and, consequently, its basis state (0 or 1).
The chief advantage of a flux qubit is its large anharmonicity (the approximation of a system to the desired qubit states). Other advantages include easy readout and a relatively weak sensitivity to charge noise (compare this to the charge qubit which is highly sensitive to charge noise). Currently, D-Wave, Rigetti, and MIT are using this approach.
Superconductor-Based Quantum Computing: Pros and Cons
Superconducting qubits offer a range of advantages, but one big “secret reason” they are so popular is that they are implemented as microelectronic components, making their fabrication akin to that of classical chips.
As a consequence, superconducting qubits are remarkably designable and tunable. The energy level of the qubit and its coupling strength can be easily modified by adjusting the microfabrication process to tweak the inductance, capacitance, and Josephson energy, based upon which the Hamiltonian of the qubits can be established. (The Hamiltonian operator corresponds to the total energy of a system.)
Superconductivity is good at preventing errors. In a normal conductor, noise arises from resistance in the device: free electrons, colliding with and bouncing off the positively charged ions of the crystal lattice, transfer some of their kinetic energy into its vibrations (phonons). These vibrations generate heat that carries off information about the scattered electrons before it can be put to computational use. But in superconductors, since Cooper pairs flow through the crystal lattice without resistance, no comparable information loss occurs.
Superconducting qubits are compatible with existing microfabrication technologies, such as cryostats, cabling, amplifiers, and sensors. Superconducting circuitry allows for multi-qubit coupling by means of inductance or capacitance. They enjoy fast gate times (fast operation times in logical quantum gates).
The principal drawback of superconducting qubits is their low coherence time (<300 μs). The difficulty of achieving quantum coherence increases in proportion with the number of qubits. As the qubit count increases, assessing the fidelity of quantum operations across the chip also becomes proportionally harder.
In 2D geometries, coupling is limited to neighboring qubits, meaning that superconducting qubits tend to interact only with their immediate neighbors (unlike trapped ions, for example). This makes it hard for superconducting qubits to effectively run some complex calculations.
Equally, gate fidelities need to be improved both for assessing the competence of prototypical algorithms in the NISQ era and for reducing the high cost of encoding logical qubits in terms of the required numbers of physical qubits.
Energy dissipation due to the quantum system’s environment is one of the major sources of quantum errors. It is hard to maintain a temperature very near absolute zero, so devices like the Josephson junction end up being somewhat dissipative components and may affect the stability of a quantum computer.
Geek note: Several proposals to minimize quantum dissipation have been put forward, such as the use of Purcell filters in superconducting resonators to minimize qubit-environment coupling, and the initiation of “quantum uncollapsing” in a three-qubit superconducting circuit, in which potential errors in the target qubit are detected and defused by the other two qubits.
Additionally, given the extremely low temperatures and very high-frequency electric fields in which SQC circuits operate, most dielectrics (e.g. silicon oxides and silicon nitrides) are subject to error-inducing defects.
Last but not least among the challenges, superconducting qubits are large and hard to miniaturize.
(The following is a photo of Google’s superconducting Sycamore chip which demonstrated “quantum supremacy”.)
Commercial Relevance and Future Prospects of SQC
According to a BCC Research report of January 2022, superconducting quantum computing is expected to grow from $145 million in 2021 to $613 million in 2026. It is arguably just a matter of time before superconducting qubits are harnessed for practical applications, e.g. in sensitive magnetometers using SQUIDs; in superconducting magnets for particle accelerator beam-steering and focusing; in medical MRI and NMR imaging; and in high sensitivity particle detectors, such as transition edge sensors, superconducting bolometers, and so on.
Google, IBM and Rigetti are some of the leading proponents of SQC today. Following Google’s demonstration of “quantum supremacy,” IBM in 2021 launched a quantum processor with 127 superconducting qubits. In February this year, Rigetti Computing announced the commercial availability of its 80-qubit superconducting quantum processor. In March, French quantum computing startup Alice&Bob raised $27 million to build its “first fault-tolerant cat-qubit quantum computer” using the superconducting approach.
Superconducting technology dominates the quantum enterprise chiefly because of its scalability: it allows us to increase the number of qubits without jeopardizing the quantum hardware’s stability. This is important because a quantum computer, to be useful, must be able to handle a large number of qubits.
However, it’s worth pointing out that building a thousand-qubit QC today would be quite cumbersome. Unlike transistors in classical computers, superconducting qubits are measured in millimeters. One of the first breakthroughs toward miniaturization was achieved in January 2022 by researchers at MIT when they used ultra-thin hexagonal boron nitride as the ultra-thin insulator in the capacitors of superconducting qubits.
“The resulting qubit is about 100 times smaller than what they made with traditional techniques on the same chip. The coherence time, or lifetime, of the qubit is only a few microseconds shorter with their new design. And capacitors built with hexagonal boron nitride contain more than 90 percent of the electric field between the upper and lower plates, which suggests they will significantly suppress cross-talk among neighboring qubits,” says Joel Wang, a research scientist at MIT.
One of the challenges in SQC today is designing high-quality quantum gates needed to improve the accuracy of computations. While most superconducting quantum systems today use aluminum and niobium, the presence of impurities in these superconductors tends to affect the performance of the system to the point of triggering decoherence.
A possible solution is creating “artificial atoms” from superconducting qubits. In artificial atoms, the electrons move around the center of the quantum dot, instead of an atomic nucleus. “This allows us to adjust the strength of the qubit-waveguide interactions so the fragile qubits can be protected from decoherence, or a kind of natural decay that would otherwise be hastened by the waveguide, while they perform high-fidelity operations,” reports Michaela Jarvis from MIT.
To that end, in July 2022, researchers at Alibaba Quantum Laboratory developed a quantum processor using fluxonium, a superconducting artificial atom. Compared to transmons, fluxonium qubits have anharmonic energy levels and make use of an inductor instead of a capacitator. This is what would make fluxonium qubits resistant to decoherence and computational inaccuracy.
“When we started our research program, we decided to explore fluxonium as the building block for future quantum computers, deviating from the mainstream choice of the transmon qubit. We believe that this relatively new type of superconducting qubit could go much further than transmon,” says Yaoyun Shi, Director of Alibaba’s Quantum Laboratory.
The use of “unconventional” superconductors, i.e. materials in which Cooper pairs are not bound by phonons, is also being considered in ways that can help us discover new superconducting materials.
Geek note: Scientists at Oak Ridge National Laboratory recently devised a way of measuring the electrical current between an atomically sharp metallic tip and a superconductor. This new method detects Cooper pairs in a superconductor with unparalleled precision by looking for Andreev reflections – special particles released into the metal when Cooper pairs are formed right near the interface of superconductor and metal.
The quantum industry is still far from locking in on a single approach to building a practical quantum computer. While superconducting qubits are appealing, neutral atoms, trapped ions, photons and other quantum modalities all have their own unique sets of advantages and disadvantages. Much as with classical hardware in the mid-20th century, when integrated circuits had not yet been invented, we can expect new dramatic breakthroughs in the world of quantum computing.
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