Promising implementations of quantum computers

Quantum computers have raised a lot of interest and funding over the last few years, as they are expected to unlock an entirely new set of answers in the fields of physics, computer science, chemistry and material science. In a previous post I wrote about how we should define a quantum computer in theoretical terms, stepping away from definitions based on the hardware. Its implementation in practice is subject to wide debate, as the scientific community does not agree on which physical system constitutes the best option for the implementation of quantum information processors, and there are currently a few candidates that show promise.
Choosing the physical system that will ultimately be the main platform for quantum computers is not easy. Technological problems that may seem insurmountable today might be solved in a few years time. However, as quantum computers are physical devices, the laws of physics ultimately dictate what they can do or not. The amount of information that classical computers are capable of processing and the rate at which they do so has doubled every 18-months for the last 40 years, which is known as Moore’s law. However, Moore’s law is not a law of Nature and rather an observation of human ingenuity (and economic power), and it is expected it will soon reach saturation: Intel has already confirmed that their cadence in chip production has slowed.
The largest transistor count in a single CPU today is of 5.5 billion transistors, with current transistors being of the size of ~O(10)nm, we can imagine that even if we have quantum processors, machines with more than a trillion components do not seem physically feasible. There are other types of constraints too: if all our components need to be at mK temperature, the size of the quantum computer will be restricted by cooling ability (It is true that there exist large scale machines which operate at ~2K such as CERN, but they would not be considered efficient in the sense we describe here) the clock speed (number of operations per second) will be limited by the amount of available energy in the system, but more energy means more noise and entropy limits the amount of information that can be processed. The ultimate limits of computation are given by the laws of physics, but there is no guarantee that these limits can really be reached.

Various quantum technologies have been considered as good candidates for building quantum computers. They each have their own advantages and challenges, and it is not clear today which will be the final technology; it might not even be just one but a combination of several. In this entry, I will briefly mention the four technologies that (in my view) are most promising. Despite their differences, they have one significant factor in common: they are compatible with microfabrication techniques which will allow each architecture to become modular and be made from regular-sized chips.

Ion traps with photonic links

Charged atoms can be controlled and manipulated in macroscopic traps with a very high degree of accuracy. Excellent control has been achieved in macroscopic ion traps with nearly 100% fidelity in all gates, however for current implementations there exists a harsh scalability factor: only a bounded number of ions can be trapped and individually addressed in the trap. The networked model for quantum computation, in which cells with a small number of qubits are interconnected to perform quantum computation, is particularly well suited for this technology and full-scale architectures have been proposed. The entanglement between different cells is obtained via entangling operations on photons emitted by ions in the different traps. This operation is very slow, however (~300 times slower than any other gate) and uses large photonic switching networks which rapidly increase the photon loss rate. New very low-loss photonic switches and better entangling operations are needed for this technology to be feasible on a large scale. A new approach to overcome the scalability factor is that of integrated ion traps, in which standard semiconductor processing techniques can be used to fabricate micrometer-scale surface-chip traps.

Superconducting qubits

Superconducting systems exhibit generic quantum properties commonly associated with atoms, such as quantized energy levels, entanglement, and superposition of states. As such, artificial- atoms can be engineered from these systems and exquisite control can be achieved by using electromagnetic pulses. Recent demonstrations show the ability to perform single qubit gates with 99.92% fidelity and two-qubit gates with 99.4% fidelity. Moreover, these fidelities are within the fault-tolerant threshold for the surface code which has allowed the experimental implementation of a small surface code implementation of five qubits. Although this implementation of quantum computing benefits from microfabrication of the devices, it has a number of shortcomings. The most important are the cross-talk between nanowires, which hinders the construction of three-dimensional qubit structures (which are considered more advantageous for the implementation of fault-tolerance) and the fact that they operate at mK temperatures, which limits the number of qubits that can be implemented due to the limited cooling capacity.

Linear optics

Single photons are very good carriers of information with low decoherence rates and very high single-qubit gate fidelity. Non-deterministic two-qubit operations and photon loss are a challenge for current technologies, but a series of theoretical breakthroughs in recent years (in which the resources required have been lowered several orders of magnitude) together with technological advances make this physical system a competitive candidate for quantum computing. This architecture uses a percolation approach to the measurement-based model in order to counteract the effect of loss and probabilistic entangling operations. Integrated optical devices can be nano-fabricated, the ability to miniaturize (~1M) linear optical elements on a single chip, is a very promising sign for the construction of linear optical quantum computers with millions of elements per silicon chip in the future. An advantage of this type of architecture is that low temperatures are only required for the single photon detectors, and it is envisioned that in the near future, the entire architecture can be implemented at room temperature.

Spin donors in silicon

Solid-state systems of spin donors in silicon can be used to build quantum computers. Quantum information can be encoded in single phosphorus atoms embedded in a silicon substrate, and qubit gates can be implemented by controlling the spin resonance of the donors and the exchange interaction between different donors. Excellent control fidelity has been shown for single qubit gates, the achieved 99.6% fidelity falls within the requirements of fault-tolerant quantum computing. A scalable integrated two-qubit gate with high enough fidelity is yet to be demonstrated, however, remarkable process has been done in recent years towards this goal. An architecture resembling the networked model has been proposed, completely in silicon, in which donors are laid out in a 2D array. In each cell, single qubit gates are performed by low-power electric and magnetic drive at microwave frequencies, while two-qubit gates are mediated by the induced electric dipole. The cells are connected via long range (mm distance) two-qubit gates enabled by microwave resonators and photonic links.

On a series of posts over the next few weeks, I will study each of these four proposals in detail, attempting to answer the questions:

  • What are the resources used?
  • What are the key results of this architecture?
  • How do the different elements integrate together?
  • What are the open problems, and why are they open?
  • What is the rough resource count for implementing a particularly interesting problem?

Please comment below if there are any other questions you’d like me to (attempt to) answer! For each architecture, I will also provide a list of academic papers where more detailed information can be found.

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