Computation is often perceived as something abstract that exists only in ideas, far removed from the physical world. A computer program typically draws on mathematical laws rather than physical ones.
However, in reality, any computation requires a physical system to perform the task, making use of the laws of physics to manipulate information represented by the state of a device.
For instance, the orientation of magnetization at certain points on a hard drive or the conductivity of transistors in a memory chip are physical states that correspond to the binary values of “0” and “1.”
Every 1 and 0 starts with a physical flip somewhere (Photo: Alamy)
Quantum Information and Its Representation
In quantum computing, information is represented by physical states that are extremely tiny and isolated, governed by the laws of quantum mechanics. A single electron’s spin or the state of an individual ion could serve as a quantum bit, or qubit.
At present, no one knows which system will be the best for storing quantum information, so let us imagine a scenario where information is represented by coins placed on a table.
The coins can show heads (“1”) or tails (“0”), but in a quantum computer, the coins would represent quantum states, with heads and tails being quantum mechanical possibilities.
The Fragility of Quantum States
A regular coin on a table can only display heads or tails, meaning the bit it represents is either 1 or 0. On the other hand, quantum mechanics allows quantum coins to display both heads and tails simultaneously (similar to Schrödinger’s famous cat being both dead and alive). This phenomenon occurs to varying degrees.
When the coin is measured, it will randomly choose one of the two states. For example, a coin can be prepared to show 75 percent heads and 25 percent tails. Upon measurement, it will collapse into one of the two possible states, with heads being more likely.
The coin’s random behavior is not due to a lack of understanding; rather, it only decides on a state once it is measured. Until that point, the state is fully defined by the degree of its heads orientation.
The strange part is that simply observing the coin changes its state. This is a result of the delicate nature of quantum states. Any interaction with the outside world can affect them, and measurement involves such interaction.
A quantum coin is bound to collapse into a pure heads or tails state if any information about it is made available to the outside world. Hence, a quantum computer must maintain strict isolation of its qubits for proper functioning.
When considering two quantum coins, there are four potential outcomes from measuring their states: both heads (1,1), both tails (0,0), and the combinations of one head and one tail (0,1 and 1,0). Quantum mechanics allows us to assign any probability to these combinations, as long as the total probability sums to 100 percent.
Therefore, describing the states of two coins requires three numbers. For three coins, seven numbers are needed, for four coins it’s 15, for five it’s 31, and so on. The complexity of the quantum state grows exponentially: to describe just 100 quantum coins would require over 1.26 quintillion numbers—far beyond the storage capacity of all computers ever made.
The Potential and Challenges of Quantum Computing
Now, although such a quantum state may hold a vast amount of information, much of it would remain inaccessible. Despite the vast storage capacity of the quantum system, attempting to read the state would force each coin into a definite heads or tails state, resulting in just 100 bits of information.
Quantum coins play by different rules from regular ones (Photo: Getty Images)
However, the power of quantum computing lies in its ability to manipulate these quantum states without observing them directly. Operations like flipping or swapping the coins can be carried out without knowing the exact state of each coin.
Remarkably, flipping and swapping operations are sufficient for performing any arbitrary computation with the coins, even if partial flips and swaps are allowed. For example, flipping a coin that is 100 percent heads will result in a coin showing 75 percent heads and 25 percent tails.
Additional operations can complete the flip to a 100 percent tails state. Because the quantum system of 100 coins can represent all possible 100-bit numbers in parallel, these computations can be processed at once in a single step. This parallelism is the key to quantum computing’s power.
Quantum Efficiency in Cryptography
Consider a central challenge in modern cryptography: the factorization of large numbers. In traditional computing, the most efficient method involves testing every possible divisor smaller than the square root of the number.
This process becomes increasingly time-consuming as the number of digits increases. A quantum computer can perform the test for all potential divisors simultaneously, making the factorization problem much easier to solve in comparison.
Challenges in Quantum Computing Development
Developing efficient quantum algorithms presents a major challenge, and only a few, such as the factorization algorithm, are currently known. Building a fully operational quantum computer is equally difficult due to the extreme sensitivity and complexity of the quantum states that form its core.
As such, quantum computing remains one of the most demanding intellectual challenges of our time and is likely to continue to be a major area of research in the years to come.
