Quantum Algorithms and its Advantages

admin — Thu, 24 Mar 2022 17:31:21 +0000

We have talked about quantum concepts and its applications in our previous post. Here we will be talking about applications enablement through quantum procedures, also known as quantum algorithms. We are going to write here about the workings of quantum. In computer programming, an algorithm is a set of well-defined instructions to solve a particular problem. It takes a set of input and produces a desired output. Quantum algorithms are a specific procedure for solving computational problems. These are different from protocols because they are a set of standard rules that allow multiple devices to communicate. The advantages of an effective quantum algorithm are as follows:

Accuracy – solve a problem correctly
Efficiency – solve a problem as fast as possible

Clearly the primary concern for quantum algorithms is its speed of execution. While it is important to solve every problem correctly, the long pole for the quantum algorithm is its efficiency. There is a well defined metric to measure the efficiency of the particular algorithm and it’s called Big-O-Notation. Big-O-Notation is a mathematical notation of the worst case performance of the algorithm relative to the input size (n). It is fundamentally different from runtime complexities because that later is inherently tied to hardware performance.

Using the above criteria, algorithm efficiency is represented in Big-O-Notation in the form of O(f(n)). Here O stands for Order and f(n) is a function of “n” to determine the number of operations that can be done as the input size fluctuates. Figure 1 lists some common functions of input size represented in Big-O Notation.

The main goal of quantum algorithms designers is to create algorithms that can perform any computation exponentially more efficiently on quantum computers than on conventional computers. This can be done by exploiting quantum properties such as superposition, quantum entanglement and many more. Unsurprisingly, some of the quantum algorithms have already achieved this goal. Some of the example of quantum algorithms is as follows:

The Deutsch Jozsa algorithm is a good example. It is the first algorithm that shows the separation between the quantum and classical difficulty of a problem. This algorithm demonstrates the significance of allowing quantum amplitudes to take both positive and negative values, as opposed to classical probabilities that are always non-negative
Shor’s algorithm is used for factoring integers in polynomial time. The computing ability of quantum computers could factor complex RSA encryption thereby undermining the global financial system. Shor’s Algorithm gave credence to the fact that quantum computers could have unforeseen economic impact
Grover’s algorithm is another complex implementation that enables searching of an unordered list in a square root n time. Every element is scanned in an unordered list and a quantum computer could achieve this in a function order of square root

Many algorithms have been developed using quantum concepts, but not all can comply with the requirements of accuracy and efficiency – the two pillars of quantum algorithms. Therefore, not every quantum algorithm is better than classical algorithms. So, a novel approach is to devise hybrid algorithms to take advantage of the best of both worlds of classical and quantum computing. Hybrid algorithms apply concepts of both quantum and classical computing to perform higher computations and obtain better results than on one or the other. It is assumed that hybrid algorithms will become more prevalent in future as they prudently employ both quantum and classical computational power.

We will write on hybrid algorithms soon.

The post Quantum Algorithms and its Advantages appeared first on Welcome to Quantum Guru.

Quantum Cryptography- Now To Be a Reality Soon

admin — Mon, 10 May 2021 10:38:01 +0000

Why Quantum Cryptography is Important?

Users place enormous trust in banks and commercial enterprises to keep sensitive information such as credit card details, social security number etc. information safe while conducting online transactions. What if these enterprises can no longer guarantee the security of the private information, using current encryption methods? Cybercriminals are always trying to gain access to secure data, but when quantum computers come online, that information will be even more at risk of being hacked. In fact, hackers have always had head start as they have been collecting encrypted data, but needs significant computing ability to break the code. While decryption is difficult to do with conventional computing, relatively powerful quantum computer will enable breaking of the existing schemes. However, the twist comes when encryption is done using with quantum encryption, as decryption will not be straightforward.

Quantum Cryptography Definition

Quantum cryptography, also called quantum encryption, applies principles of quantum mechanics to encrypt messages in a way that no one outside of the intended recipient can decipher or read it. It takes advantage of “multiple states” and “no change theory” of quantum.

Performing these tasks requires a quantum computer, which has the immense computing power to encrypt and decrypt data. A quantum computer could quickly crack current cryptography schemes some of which are referred later in the article. Unlike mathematical encryption, quantum cryptography uses the principles of quantum mechanics to encrypt data and make it virtually “unhackable”.

Unlike mathematical encryption, quantum cryptography uses the principles of quantum mechanics to encrypt data and making it virtually unhackable.

How quantum cryptography works?

Quantum cryptography or quantum key distribution (QKD) uses a series of photons (light particles) to transmit data from one location to another over a fiber optic cable. By comparing measurements of the properties of a fraction of these photons, the two endpoints can determine the key value and whether it is safe to use. The steps are as follows:

The sender transmits photons through a filter (or polarizer), which randomly gives them one of four possible polarizations and bit designations: Vertical (One bit), Horizontal (Zero bit), 45 degree right (One bit), or 45 degree left (Zero bit)
The photons travel to a receiver, which uses two beam splitters (horizontal/vertical and diagonal) to “read” the polarization of each photon. The receiver does not know which beam splitter to use for each photon and has to guess which one to use
Once the stream of photons has been sent, the receiver inform the sender about the beam splitter used for each of the photons in the sequence they were sent. The sender then compares that information with the sequence of polarizers used to send the key. The photons that were read using the wrong beam splitter are discarded, and the resulting sequence of bits becomes the key

The photon’s state will change if it is read or copied by an eavesdropper and the endpoints will detect the change. In other words, a photon cannot be read, copied or forwarded without being detected.

Following are the list of commonly used encryption schemes

Triple DES

Triple Data Encryption Standard (DES) is a computerized cryptography where block cipher algorithms are applied three times to each data block. The key size is increased in Triple DES to ensure additional security through encryption capabilities. Each block contains 64 bits of data. Three keys are referred to as bundle keys with 56 bits per key.

RSA

RSA encryption is a public-key encryption technology developed by RSA Data Security. The RSA algorithm is based on the difficulty in factoring very large numbers. The RSA encryption algorithm uses prime factorization as the trap door for encryption. Deducing an RSA key, therefore, takes a huge amount of time and processing power. RSA is the standard encryption method for important data, including those transmitted over the Internet.

Blow Fish

Blowfish encryption is a symmetric block cipher (a method that allows encrypting data in blocks) that can be used in place of Data Encryption Standard (DES) or International Data Encryption Algorithm (IDEA). It takes a key that varies in length from 32 to 448 bits. It works for both domestic and exportable use.

Two Fish

Twofish is related to the earlier block cipher Blowfish, which is a 64-bit clock cipher that uses a key length varying between 32 and 448 bits also developed by Bruce Schneir. Twofish is also related to Advanced Encryption Standard (AES), a 128-bit block cipher that the United States government adopted as it’s specification for the encryption of electronic data by the U.S. National Institute of Standards and Technology In 2001. While Twofish was a finalist to become the industry standard for encryption, it was beaten out by AES because of Twofish’s slower speed.

AES

Advanced Encryption Standard (AES) is a cipher, meaning that it is a method or process used to change raw information (usually human readable) into something that cannot be read. This part of the process is known as encryption. The method uses a known external piece of information called “key” to uniquely change the data.

When will Quantum Cryptography become available?

The bigger question is about the availability of quantum computers and how much more time to realize quantum cryptography? There are significant engineering challenges to develop quantum computers that can take decades to solve. The technology is still in its infancy, Google has developed a machine with about 50 qubits and IBM is talking about 70 qubits.

Cracking today’s standard RSA encryption would take thousands of qubits. Adding those qubits is not easy because they are so fragile. Additionally, quantum computers today have extremely high error rates and require even more qubits for error correction. “I teach a class on quantum computing,” says University of Texas’s Brian R. La Cour. “Last semester, we had access to one of IBM’s 16-qubit machines. I was intending to do some projects with it to show some cool things you could do with a quantum computer.” That didn’t work out, he says. “The device was so noisy that if you did anything complicated enough to require 16 qubits, the result was pure garbage.”

Once that scalability problem is resolved, we will be well on our way to having usable quantum computers, he says, but it is impossible to put a timeframe on it. Brian R. La Cour guesses that we are probably decades away from the point at which quantum computers can be used to break today’s RSA encryption. There is plenty of time to upgrade to newer encryption algorithms.