Frequently Asked Questions on Quantum Computing…Part 4

Will a universal quantum computer when realized break any encryption code?

First, the devices currently being built have 50–100 qubits and no error-correction. Running Shor’s algorithm to break the RSA cryptosystem would require several thousand logical qubits. With known error-correction methods, that could easily translate into millions of physical qubits, and those probably of a higher quality than any that exist today. None of the systems we know of is close to that, and we have no idea how long it will take.

Secondly, even assuming we have scalable, error-corrected QCs, on our current understanding they’ll only be able to crack certain codes, not all of them. By an unfortunate coincidence, the public-key codes that they can crack include most of what we currently use to secure online communication. However, symmetric-key crypto should only be minimally affected. There are even ideas of public-key cryptosystems based on lattices that no one knows how to break despite years of trying, and efforts are now underway to migrate to those systems.

Where are we with quantum computing today?

Today’s quantum computers include thousands of parts that work together to harness qubits to perform quantum computations albeit with errors and limitations. It is, however, possible to access real quantum computers through the cloud to optimize their performance, conduct research and explore new problems.

I am familiar with Moore’s law but I now hear there is also Neven’s law?

Unlike Moore’s Law that has predicted classical computing power will approximately double every two years — exponential growth — Neven’s Law describes how quantum computing seems to gain power far more rapidly through double exponential growth.

Doubly exponential growth is far more dramatic. Instead of increasing by powers of 2 (2⁰,2¹,2²…) quantities grow by powers of powers of 2 [(2²)⁰,(2²)¹,(2²)²…]. Doubly exponential growth is so singular that it’s hard to find examples of it in the real world. The rate of progress in quantum computing may be the first. The doubly exponential rate at which, according to Neven, quantum computers are gaining on classical ones is a result of two exponential factors combined. The first is that quantum computers have an intrinsic exponential advantage over classical ones: If a quantum circuit has four quantum bits, for example, it takes a classical circuit with 16 ordinary bits to achieve equivalent computational power. This would be true even if quantum technology never improved.

The second exponential factor comes from the rapid improvement of quantum processors. The best quantum chips have recently been improving at an exponential rate. This rapid improvement has been driven by a reduction in the error rate in the quantum circuits. Reducing the error rate has allowed the engineers to build larger quantum processors. If classical computers require exponentially more computational power to simulate quantum processors, and those quantum processors are growing exponentially more powerful with time, you end up with this doubly exponential relationship between quantum and classical machines. While the exact rate at which quantum computers are closing in on classical ones might be debatable, there’s no doubt quantum technology is improving, and fast.

Is there anything like quantum internet? Why do we need to do that?

The quantum internet is a network for transmitting qubits between distant locations. These “qubits” might be made of photons that are in a combination of two different polarizations. The ability to send qubits from one place to another over fiber-optic cables might not transform society as thoroughly as the classical internet, but it would once again revolutionize many aspects of science and culture, from security to computing to astronomy.

The idea is not to replace the internet we have today but really to add new and special functionality. While it is hard to predict all uses of the future quantum, several major applications seem feasible and these include secure communication, clock synchronization, extending the baseline of telescopes, secure identification, achieving efficient agreement on distributed data, exponential savings in communication, quantum sensor networks, as well as secure access to remote quantum computers in the cloud.

What makes quantum keys so secure?

A good way to understand what a quantum internet can do is to think about “quantum entanglement,” a special property that two quantum bits can have that makes all of this possible. The first property of entanglement is that it’s “maximally coordinated”: Distant qubits entangled through the use of the quantum internet ensure that a measurement on one of the qubits guarantees the same outcome on the other one even though the outcome wasn’t determined ahead of time. In this way, the quantum internet is very good for tasks that require coordination, due to that first property of quantum entanglement. The interesting part is the fact that this entanglement cannot be shared with other people. So the second property of entanglement is that it’s inherently private. Nothing else can have any share of that entanglement. And this is the reason why quantum communication is so good for problems that require security.

Who is driving quantum computing development?

Microsoft, Intel, Rigetti, IonQ, IBM, Google, Alibaba, Hewlett Packard, Tencent, Baidu, and Huawei are investing in quantum computing as organizations.

The European Union in 2018 pledged $US1,1 billion towards research in the field and similar public-investment initiatives from the United States, United Kingdom, Japan, Sweden, Singapore, Canada, Australia, and China are all plowing hundreds of millions of dollars into quantum technologies.

Which are the topical areas of quantum information theory?

Quantum physics has taken center stage as a powerful way to harness the laws of nature to solve certain problems. Various professionals from the fields of Physics, Computer Science, Mathematics, Engineering, and Information Theory are coming together to cope with the demands of this new and promising field.

Quantum algorithms & complexity
Quantum processors are very useful in implementing quantum algorithms. Quantum algorithms work on universal quantum computers and allow for processing speeds that exceed known classical algorithms. The development of robust quantum algorithms has been somewhat slow, in part due to the challenge of retrieving the answer from our quantum computer. Popular quantum algorithms include Shor’s algorithm, Grover’s algorithm, Deutsch–Jozsa algorithm, Simon’s algorithm, and Quantum phase estimation algorithm amongst others. Scientists are working on new techniques and protocols. The ability to use a quantum system to perform simulation is very crucial in quantum information theory research. There are a variety of models & architectures for quantum systems available online from a variety of big and small players like Rigetti, Alibaba, IBM, D-Wave among others. These players are provoking renewed interest in science and engineering. Quantum algorithms are being developed and tested and new physical implementations are being considered.

Topological approaches: Topological methods are one of many pathways being considered as the world attempts to build a universal and scalable quantum processor. Their main attraction is based on their intrinsic fault-tolerant properties that make active error detection and recovery unnecessary. However, their drawback is that they have longer operation times, such that there is still so much more work to be done to identify the available schemes that are well suited for quantum computation.
Companies like Microsoft are supporting research efforts in this space.

Quantum simulations: Developments in the field of quantum technology suggest that quantum simulators are becoming the first short-term application of quantum computers. The benefit of quantum simulators stems from the fact that they offer a platform to test thoughts and ideas involving quantum mechanics which their classical peers struggle to handle, and they can deliver on this with modest hardware capabilities. To build a useful quantum processor more stringent requirements have to be met. There are a variety of problems where simulators can be employed immediately like in chemical simulation, drug discovery, artificial intelligence, process optimization, high energy physics, and condensed matter physics.

Quantum error correction & purification: Quantum materials provide the environment where qubits, the elemental unit of quantum information processing, are defined and live. Therefore, quantum materials are the basis of a quantum computer. To have a working quantum computer you need to couple together many qubits, while maintaining their long coherence time. These demands are often in conflict.
Qubits that are hard to couple together have long coherence time because they tend to achieve adequate levels of isolation. On the other hand, systems that are easy to couple together tend to decohere quickly, because they can be perturbed easily by the environment. The precision of the qubit materials is of major importance to solve these two challenging requirements.

Multi-partite entanglement & applications: To build a universal scalable quantum computer, it should be possible to achieve multi-particle entanglement. The ability to achieve that will have a profound impact on the ability to implement novel protocols in quantum information processing. Multipartite entangled states represent keys resources, both for quantum computers and for novel communication schemes with several users such as quantum-secret sharing, quantum voting, etc. Alternatively one can consider multi-partite fingerprinting schemes that would allow for the determination of whether or not many databases are identical with very little resources. Further, solid-state lattice platforms can prove useful in building hybrid quantum systems.

Quantum Communication: For any system to deliver value it has to be scalable. The ability to move quantum data from one place to another within the local system as well as with other remote systems is called quantum communication. At the basic level quantum states encode quantum information: hence quantum communication means the transmission of quantum information as well as the distribution of quantum resources such as entanglement. Quantum Communication covers aspects ranging from elementary physics to practical applications that are relevant to society today. From an application point of view, a major interest has been focused on Quantum Key Distribution (QKD), as this offers a provably secure way to establish a confidential key between distributed partners.

While a quantum computer can use a small number of qubits to represent an exponentially larger amount of data, there is not currently a method to rapidly convert a large amount of classical data to a quantum state (this does not apply if the data can be generated algorithmically). For problems that require large inputs, the amount of time needed to create the input quantum state would typically dominate the computation time and greatly reduce the quantum advantage. While there are proposals for quantum random access memory (QRAM) that can perform this function, it seems there aren’t any practical implementation technologies.

tl;dr. In summary research in the field focuses on quantum computing hardware, software, algorithms, and applications.

Read on Part 5 here