Quantum computing: algorithms and simulations
The fundamental unit of information processing and storage in classical computers is the binary digit, or ‘bit’, where information is represented as either 0 or 1. However, if one uses quantum objects as a basis for information processing, this permits the formation of quantum bits or ‘qubits’. The closest analogy is that a qubit can be said to be in a state that is a combination of both 0 and 1 (a superposition state). Considerable advantage is gained from swapping classical bits (0 or 1) for quantum bits (superposition of 0 and 1) so that certain calculations can be performed significantly faster. However, depending on what calculation is being performed, this could lead to a sudden reduction in effectiveness of important security protocols.
The best-known example of this is the problem of integer factorization. Public-private key encryption is asymmetric – that is, it can be relatively straightforward to encrypt information, but far more difficult to decrypt the information. These protocols typically rely on the multiplication of two large prime integers (the public and private keys) to create an encryption key – a trivial task in comparison with factorizing the product of those two numbers back into the public and private key. With classical factorization algorithms, the problem becomes practically unsolvable for sufficiently large keys due to the length of computation time it would take to discover the factors. However, by implementing a quantum factorization algorithm (e.g. Shor’s algorithm) on a quantum computer with an adequate number of qubits, the time required for breaking the same strength of public key encryption shortens drastically. The core concern of this technology is a possible ‘Enigma moment’ where a sufficiently capable quantum computer is used to start breaking information encrypted with asymmetric public-private key encryption.
This would have an impact on a number of sectors, as public key encryption authenticates users of the Transport Layer Security (TLS) protocol used to secure data in HTTP connections, which is utilized for online banking, sales and telephone calls. Many cryptocurrency wallets secure the bearer’s currency by means of public key encryption, implying that quantum attacks on those wallets may allow the attacker to ‘pickpocket’ them. Nor is it just public-private key encryption that is potentially vulnerable to a quantum attack – research is being conducted into the application of Shor’s algorithm to other forms of asymmetric encryption. Although symmetric encryption is less vulnerable to quantum attack, the Grover quantum search algorithm can find items in a list of size N (for example, a specific decryption key within a particular key space) in √N attempts as opposed to N/2 attempts on a classical computer.
However, quantum computers are not yet sufficiently complex to accomplish this sort of significant breach of public key encryption. This is a fair comment when one considers the physics involved – qubits, as with any quantum superposition, are quite fragile, with vibrations, heating and electromagnetic disturbances potentially causing the superposition to break down (in effect, the simultaneous 0 and 1 of the qubit suddenly snaps back to either 0 or 1, and it functions essentially like a classical bit). There are means of compensating for this problem of decoherence, such as quantum error correction, which encodes the same information into multiple qubits to minimize information loss via decoherence. It should be noted that this requires the construction of a quantum computer that contains even more functional qubits, which increases the scale of the technical challenge at this stage.
The core concern of this technology is a possible ‘Enigma moment’ where a sufficiently capable quantum computer is used to start breaking information encrypted with asymmetric public-private key encryption.
While sufficiently complex quantum computers capable of cracking widely used encryption protocols do not yet exist, the belief that quantum computers are coming has securitized the issue. Already, major national signals intelligence agencies – such as the US National Security Agency and the British GCHQ – are publicly expressing concern about the development of quantum computers and their effect on cryptographic security. There is also a growth of classical ‘quantum-resistant’ encryption protocols, which are believed to be less vulnerable to quantum decryption algorithms. Symmetric encryption standards, such as the Advanced Encryption Standard (AES) can be strengthened against the Grover quantum search algorithm by increasing the key length. Thus, even if quantum computers may be stuck in a semi-permanent state of being ‘just five years away’, the fear of their emergence is already having a reinforcing impact on encryption by spawning a diversification of encryption protocols.
New quantum communication: encryption and networking
Quantum communication relies on many of the same principles and apparatus as quantum computing. A qubit can be described as a single particle functioning as a mixture or superposition of 0 and 1 simultaneously. A superposition of a system of multiple particles – where the state of one particle intrinsically depends on the state of another particle – is referred to as entanglement.
Two qubits, when entangled, allow the result of the measurement of one qubit to provide information about the state of the other qubit. An extension of this principle allows for the teleportation of a quantum object’s state from one location to another. Entangling two qubits together permits the state of a third qubit to be teleported between them. This is not ‘faster-than-the-speed-of-light’ communication – necessary measurements performed on the system as part of the communications protocol are limited to the speed of light – nor is it the physical teleportation of objects. In quantum communication, ‘teleportation’ enables the state of a qubit to be transferred to another site; it also allows for a transfer of information without needing to physically transport that information. Experiments in this field are pushing the boundaries of entangled communication, a successful Chinese quantum communication test via satellite (claimed in 2017) is a notable example.
It is also possible to use quantum entanglement in a protocol for encryption key exchange. As the entangled system cannot be measured without altering it, this protocol also has enhanced resistance to interception, where the error rate in the protocol may be indicative that the communications channel has been compromised. This holds for all QKD protocols, not only those that utilize entanglement.
These principles facilitate quantum networking, a fundamental part of any future quantum information infrastructure. Limiting factors on the development of these technologies are similar to those for quantum computing – maintaining entanglement over large distances and durations. New quantum encryption protocols will have an impact on international security, in particular by being inherently more resistant to interception. Furthermore, given that quantum key exchange techniques can be developed using a similar technological base to quantum computers – which may facilitate the breaking of existing classical encryption protocols – these technologies, when combined, could put substantial stress on existing communication standards and security. However, such technologies would also enable both the US and EU to create secure quantum information networks of their own.
The US quantum funding stream
In December 2018, the National Quantum Initiative (NQI) Act came into force in the US. The act incorporates research from NIST, DOE and NSF, and funds the NQI. In addition, NIST, DOE and NSF regularly fund quantum research. The NQI Act explicitly encourages collaboration between a number of bodies mentioned therein, and their international partners; the National Science and Technology Council’s Subcommittee on Quantum Information Science and the NQI Advisory Committee are given responsibility for determining opportunities for international cooperation with strategic allies. The NQI was initially advocated by the National Photonics Initiative, which noted that the US lacked a large, centralized quantum research project equivalent in scope to the EU’s Quantum Flagship, or to China’s large-scale investment programmes. The NQI Advisory Committee was officially established by President Donald Trump on 30 August 2019. The Subcommittee on Quantum Information Science, in its strategic overview document published in September 2018, encouraged collaboration with like-minded governments and espoused a science-first approach that welcomes fundamental quantum science research. More detailed information about the US programme, from the perspective of the UK Knowledge Transfer Network, was collated during a Global Expert Mission to the US in November 2019 and was published in Quantum Technologies in the USA 2019.
