The big question is how will they change things? Here is a small introduction:
Quantum computing is built upon the principles of quantum mechanics and computer science.
Today, many are familiar with algorithms such as Deutsch-Jozsa, Grovers, Shor´s, QFT algorithms which were actually invented back in the 1990s. However, they are starting to have a significant impact today because quantum computers are becoming more powerful.
Transitioning from bits (0 and 1) to quantum bits or qubits (|0⟩ and |1⟩ = Basis state) represents a substantial shift.
A qubit can take various forms, such as a photon, an electron, trapped ions, superconducting electronic circuits, and more. A qubit is often represented as bra-ket, see more here. The vector representation of a single qubit appears as follows:
Figure 1 – Vector representation
v0 and v1 represent the weights/probability of the qubit.
Qubits can exist in many possible states. By adding two or more quantum states together, they form another quantum state known as a tensor state. This represents a quantum superposition of the original two states. Typically, a superposition state is expressed as α|0⟩+β|1⟩, where α²+β²=1. For instance, an example of a qubit superposition could be 0.6|0⟩+0.8|1⟩.
A qubit can be thought of as having a value of both 0 and 1 simultaneously, with the weights α and β being controllable. When a qubit is measured, it yields the bit 0 with a probability of α² and the bit 1 with a probability of β². After measurement, the qubit collapses into one of the basis states.
The process of measuring and collapsing from a superposition state to a classical state is determined by probability and the control of α and β weights.
Quantum entanglement is another concept where particles become entangled after being split, rendering them dependent on each other. This means that the quantum state of one particle can impact the other, even over long distances.
Notable experiments, such as those involving the satellite Micius and other developments in quantum internet, have demonstrated the phenomenon of entanglement. In quantum communication systems and quantum teleportation, this strategy is heavily utilized. However, these systems have not achieved faster-than-light (FTL) communication. Sending classical information via entanglement remains unattained, and it is believed that a hypothetical FTL particle, known as a Tachyon, would be required. Consequently, there is still no tachyonic antitelephone for interplanetary real-time communication. Bitcoin can still scale to the moon, read more here.
A digital quantum computer is constructed using a set of quantum logic gates. These gates can include single-bit gates, two-bit gates, three-bit gates, and so on.
Figure 2 – Quantum gates
A single-bit gate takes a single qubit as input and produces a single-bit output. Quantum gates are reversible and unitary transformations that can manipulate the qubit’s state.
A quantum circuit is a sequence of quantum gates applied to qubits to perform a computation. Read this small article.
Figure 3 – Quantum computer properties and metrics used to asses resource costs of quantum circuits,
Quantum algorithms
Quantum algorithms have already demonstrated their ability to potentially surpass classical “secure” algorithms. A quantum register is a system consisting of a set of n qubits (multiple qubits) and is also known as the quantum counterpart of the classical processor register. It allows for the operation on multiple states simultaneously, specifically 2^n (where n represents the number of qubits), while a classical register can store only a single value from the 2^n possibilities.
With a classical 2-bit register, there are four possible states: 00, 01, 10, and 11. In contrast, a quantum 2-bit register can exist in all four states (2^2) simultaneously by utilizing quantum superposition of the four states: α|00⟩+β|01⟩+γ|10⟩+δ|11⟩. Measuring the register will yield one of the four states, with the specific probability determined by the weights.
Let’s assume that a 2-qubit system is constructed with α=0, β=0, γ= δ = 1/√2. In this case, there is no chance of measuring 00 or 01. There is a 50% probability of measuring 10 and another 50% probability of measuring 11.
Quantum parallelism is the capability to perform a large number of operations in parallel. For instance, with a quantum register containing 3 qubits and a 3-bit input gate (CSWAP), it can superpose 8 (2^3) states simultaneously and provide 8 different outcomes. In contrast, a classical computer would require 8 rounds of computation to achieve the same result.
It may sound easier than it actually is because when measuring the output quantum register, it provides one answer with certain probabilities, which is known as the measurement problem. If all eight answers are equally weighted at 12.5%, the quantum computer performs on par with a classical computer, as it essentially requires running all eight calculations separately, similar to what a classical computer does.
Quantum algorithms are designed in a way that assigns higher probabilities to the output weights, ensuring the “correct” answer is obtained with a high likelihood.
While it is possible to compute various functions and employ different types of gates in quantum computing, achieving optimal and validated conditions requires certification and benchmarking. Noise is a persistent challenge, although improvements are being explored (as referenced in https://www.nature.com/articles/s41566-023-01190-4).
Repetition of computations is often necessary to obtain accurate results, both due to errors in quantum computations and the probabilistic nature of results.
In essence, quantum algorithms can be viewed as hybrids that combine elements of both quantum and classical computation.
Quantum computers applications
Figure 4 – Quantum applications
Quantum computers combined with machine learning will create new forms of intelligent AI with better natural language processing and new capabilities.
Still experiencing noise and requiring extremely low temperatures?
Quantum computers need to undergo thorough checks to ensure the reliability of their results. To learn more, check this. This process includes identification (Tomography), PAC learning, estimation, certification (verification, self-testing), benchmarking, validation, and authentication.
It’s important to note that achieving a functional quantum computer and algorithm involves various forms of complexity, including measurement complexity (settings and circuit depth/entanglement implementations), sample complexity, qubit complexity, classical complexity (time and space), communication complexity, and synchronization complexity.
It’s worth understanding that the computational power of a quantum computer increases exponentially with the number of qubits.
However, quantum computers face challenges related to error rates and the need for extreme cooling, typically close to 0 Kelvin (except for photons), which currently makes them unsuitable for commercial sale (although new concepts are emerging). Nevertheless, they are currently available as Quantum Cloud as a Service (QCaaS), where users can access quantum computing services on a subscription or pay-per-use basis. Quantum as a Service (QaaS) is also possible through API integration with quantum computers.
Let´s talk more about the market
Numbers of participants in the quantum market have increased during the last years.
Figure 5 – Number of Q-organizations
Most companies are based in hardware components, software and quantum communications and security.
Investments in this sector are also experiencing significant growth.
Figure 6 – Quantum tech investment
Another significant indicator of the quantum computing market is the number of patents. The number of patents has been steadily increasing over the past few years. It is also interesting to track various patent categories, their issuance year, the country of origin, and the associated companies. You can find a detailed table in this report.
Figure 7 – Most active applicants in the field of quantum computing
Figure 8 – Patenting activity related to quantum computing
There is also an informative report available on quantum simulation, and perhaps one on quantum communication will be published in the future. Alternatively, you can conduct a search on your own. You can access the quantum simulation report here.
Additionally, in 2018, Gartner produced an intriguing graph that, while speculative, provides an overview of the various impacts quantum computers may have.
Figure 9 – Qubit timeline
Development in quantum processors
Figure 10 – Development in quantum computing processors – Open question, feel free to answer in the comments section
Most manufacturers use circuit-based quantum processors (CBQP), while others employ Annealing quantum processors (AQP), analog quantum processors (AP), or photonic quantum processors (PQP).
It’s often mentioned that a (digital) quantum computer is constructed using quantum logic gates, as illustrated here:
Figure 11 – Examples of how to make quantum devices
Some companies, however, concentrate on employing (digital)-analog quantum computers that emphasize quantum annealing and quantum simulation.
Figure 12 – The figure gives and overview of the highest number of qubits a company have in a quantum computing system and their technology. Note that many companies have many models of quantum computers with lower amounts of qubits.
Companies are currently in a race to add more qubits, with frequent updates on the horizon.
The urgency to change
The urgency to initiate and complete the transition to quantum-safe cryptography depends on the security requirements and risk tolerance of individual organizations and can be assessed using three simple parameters:
Figure 13 – Urgency to change
• The shelf-life time: The number of years for which the data should be protected.
• The migration time: The number of years required to safely migrate the systems that protect that information.
• The threat timeline: The number of years before relevant threat actors could potentially access cryptographically-relevant quantum computers.
Organizations will not be able to protect their assets from quantum attacks in time if the quantum threat timeline is shorter than the sum of the shelf-life and migration times.
So, what are the solutions?
A. Post-quantum cryptography, conventional hardware, computational assumptions
B. Quantum cryptography, new quantum infrastructure, “unconditional” security.
R&D focused on quantum resistance will strengthen option A. Currently, there is already a range of potential algorithms available, but their implementation is not straightforward. Some important considerations include migration overhead and complexity, scalability issues, large key sizes, and speed, especially when dealing with resource-constrained devices.
You can explore the latest quantum-resistant ideas from NIST here.
Satellite-based communication and quantum repeaters will enhance option B. You can find more information here.
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