Quantum computing and quantum computers

What is Quantum Computing? Why do we need quantum computing? According to Moore’s law (“The complexity of a microcircuit, measured for example by the number of transistors per chip, doubles every 18 months and therefore quadruples every 3 years”), the density of transistors per unit area on a computer chip doubles every year and a half, which poses two main problems for traditional computers. First, on the computing side, high-density transistors will face the problem of power consumption and thermal effects. Second, downsizing will cause classical transistor theory to fail and performance to deviate from the original design.

Both of these issues will limit further transistor shrinkage, thus ending Moore’s Law. However, although the traditional computer develops to the end of Moore’s Law, it is still unable to cope with many problems that need to be solved. Let’s say we are calculating the ground state energy of N coupled two-level systems, since the number of unknowns will be proportional to 2^N. The current simulation time required for IBM’s supercomputer is 2.5 days for a specific calculation on Google’s 53-qubit quantum computer, which takes about 200 seconds. Qubit is the contraction of quantum bit, a term coined by Benjamin Schumacher to designate the quantum bit, that is to say the basic unit of quantum information.

As the number of qubits continues to increase, conventional computers will soon reach a bottleneck. However, almost all conventional calculations involving quantum mechanics face the same problems. This is why many researchers started thinking about how to use quantum properties themselves as computational resources as early as 1970, which was later summarized by Richard Feynman in 1982.

So what are the advantages of qubits over traditional computing? The most surprising is none other than the properties of quantum superposition and quantum entanglement. Quantum superposition is a non-classical state which contrasts with empirical intuition and the metaphor is Schrödinger’s cat which is both alive and dead.

The superposition state, however, is an actual state for qubits at microscopic or mesoscopic scales (spatial scales, viewpoints, etc., intermediate between macroscopic and microscopic scales). Qubits can be found in the superposition of two characteristic quantum states, and this state of superposition is a non-classical state in which being and non-being coexist in the quantum world. In this state the qubit is neither 0 nor 1, but it is not in a state in which both sides (0 and 1) are uncertain, but rather with equal probability, like a coin before landing on the palm of the hand.

Whereas in visible nature it is possible to observe a phenomenon without substantially influencing it by mere observation (i.e. solely by looking at said phenomenon) – in atomic physics and quantum mechanics, a finite perturbation – and up to a certain point – invisible is linked to each observation. The uncertainty principle is the recognition of absolute chance and arbitrariness in natural phenomena. On the other hand, as will become clear later, quantum mechanics does not predict a single well-defined outcome for observation or for any observer.

The fact that qubits can undergo quantum evolution in a set of superposition states – which is neither 0 nor 1 – implies quantum parallelism in the calculation concerned. The evolution of each qubit is however not sufficient to build all the possible evolutions of a multi-qubit system. So we have to

also interact with different qubits so that they can be interleaved to build a satisfactory algorithm for such a calculation. This special superposition is precisely called the entangled quantum state.

Let’s take two qubits as an example, which is a typical entangled state. Between them, the state representing the first qubit is connected to the state of the second qubit. The two connections are in quantum superposition and therefore we cannot speak of the state in which the two qubits are at this moment – we therefore speak of entanglement.

There is a more practical view of entanglement in quantum computing, that is, entangled states usually result from the control of one qubit (control qubit) over another (target qubit). The relationship between the control qubit and the target qubit is similar to the aforementioned Schrödinger’s cat. According to this view, if the controlling part is in a state of superposition, the controlled part will be in a superposition of different controlled situations.

This entanglement process is an important part of quantum computing. It can be said that layering and entanglement synergistically weave together the varied parallel evolution of quantum computing. Each measurement can only compute one of the possible states, and the superposition state no longer exists after the first measurement. Therefore, in order to get the statistical information we need in the overlay state, we have to calculate and measure the results again.

Therefore, in many quantum algorithms (such as Shor’s algorithm for factoring [which solves the problem of factor decomposition of integer numbers into primes] and numerical quantum simulation), we have to use interference mechanisms after the calculation, so that the information of this phase containing the response in the superposition state is converted into conservation (with the implicit idea of ​​preventing a spillage or final loss) due to constructive interference (i.e. by the immediately following variation of other data produced), while other data is discarded by destructive interference.

In this way, the answer can be obtained with fewer measurements. Most quantum algorithms rely heavily on the phenomenon of fluctuation and interference – so relative phase is very important for quantum computing, called quantum coherence. In the hardware design of quantum computers, there are many considerations related to how to protect the quantum state to extend the coherence lifetime.

Quantum computers have a variety of hardware implementations, but the design considerations are similar. There are three common considerations: operability, measurability, and protection of quantum states. In response to these considerations, a cavity quantum electrodynamics (cQED) system was developed.

A superconducting quantum system can be taken as an example to introduce the implementation of quantum computers. The frequency difference between the resonant cavity and the qubit means that the coupling between the resonant cavity and the qubit tends not to exchange energy quanta, but only to generate entanglement, which means that the frequency of the resonant cavity will shift with the state of the qubit. Therefore, the qubit state can be inferred by measuring the microwave penetration or reflection spectrum near the resonant frequency with the bit read line.

The entanglement mechanism between adjacent qubits is ensured by the coupling with respect to the electric capacitance between cross-type capacitors. The coupling effect is controlled by the frequency difference between adjacent qubits. The oscillating behavior reflects the quantum interference effect and its gradual disappearance leads to the decay of coherence and quantum energy.

The coherent lifetime of qubits is influenced by two factors, one intrinsic and one extrinsic. The extrinsic influence comes mainly from the coupling between the qubit and the quantum state readout circuit. The presence of a filter-like protection mechanism in the microwave cavity between the bit and the read line can provide a qubit-like protection mechanism because the cavity and the qubit have a frequency difference of about 718 MHz. The intrinsic influence comes mainly from the loss of the qubit itself and its frequency sensitivity to various types of noise, which can usually be removed by improved materials and processes and optimization of the geometric structure.

Quantum computing has a wide range of applications, currently involved in the fields of decryption and cryptography, quantum chemistry, quantum physics, optimization problems, and artificial intelligence. It covers almost every aspect of human society and will have a significant impact on human life after practice. However, the best quantum computers are not yet able to express the benefits of quantum computing.

Although the number of qubits on a quantum computer has exceeded 50, the circuit depth required to run the algorithm is far from sufficient. The main reason is that the error rate of qubits in the calculation process is still very high, even if we can use qubit quantum correction and fault-tolerant quantum calculation. In the case of quantum computing, the precision that gradually improves the data will greatly increase the difficulty of realizing the hardware and the complexity of the algorithm.

At present, the implementation of some well-known algorithms has only reached the conceptual demonstration level, which is sufficient to demonstrate the feasibility of quantum computing, but the practical application still has a long way. to browse.

But we should remain optimistic because, although general quantum computing still needs to be improved by quantum computing hardware, we can still find new algorithms and applications. In addition, hardware development can also make great progress, just like the development of traditional computers at the beginning.

In line with this goal, many existing technology industries could be upgraded in the near future. Research is advancing rapidly, also thanks to significant public and private investment, and the first commercial applications will see the light of day in the short term.

Given defense and intelligence issues, many governments are funding research in this area. The People’s Republic of China and the United States of America have launched multi-year plans worth billions of yuan and dollars. The European Union has also set up the Quantum Flagship Program for an investment of one billion euros.

Professor Giancarlo Elia Valori is a world-renowned Italian economist and international relations expert, who is the chairman of the International World Group. In 1995, the Hebrew University of Jerusalem dedicated the Giancarlo Elia Valori Chair of Peace and Regional Cooperation. Professor Valori also holds chairs in peace studies at Yeshiva University in New York and Peking University in China. Among his many honors from countries and institutions around the world, Professor Valori is Honorable of the Academy of Sciences of the Institute of France, as well as Knight Grand Cross and Knight of Labor of the Italian Republic.

Sherry J. Basler