The post NISQ Era appeared first on Welcome to Quantum Guru.

The post Visual Application of Quantum Randomness – Image Coloring appeared first on Welcome to Quantum Guru.

The post Bitcoin Blockchain and Quantum Computer-III appeared first on Welcome to Quantum Guru.

The post Getting ready for post Quantum Era with open Source Software appeared first on Welcome to Quantum Guru.

What is SHA-256 (Secure Hash Algorithm 256-bit)?

Ever since the inception (and continued advancements) of network security, encryption and hashing have been the core principles for developing additional security modules. The secure hash algorithm with a digest size of 256 bits, or commonly referred as SHA-256, is one of the most widely used hashing algorithms. While there are other variants, SHA-256 has been at the forefront of real-world applications.

Bitcoin is a decentralized digital currency that uses public distributed ledger called blockchain to register the transactions. The network nodes confirm the authenticity of the transactions using “cryptography”.  Bitcoin applies SHA-256, a cryptographic hashing function that turns random input data into a 256-bit string (called as the ‘Hash’). This is a one-way function and it is easy to find the hash from an input, but the reverse is not possible.

click here to generate your own SHA-256 HASH

Implementation of Grover’s algorithm in finding the target value

In quantum computing, Grover’s search is sometimes presented as an elixir. It finds with a very high probability the unique input (value) to a black box function that produces a particular output. Hence, it is a perfect solution to finding the target value and has a quadratic quantum speedup. The equation is directly proportional to “t” (time in seconds) and “r” (Hash rate) for quantum miners running Grover’s algorithm. Compared with classical success probability of Trt/2256, the success probability of Grover’s quantum algorithm is sin²(2r_q(T/2²⁵⁶)^1/2), where “r_q” is the number of Grover’s iterations per second or the “quantum hash rate”. Solving for r (Hash rate):

r=sin²(tr_qT^1/2/2¹²⁷)2²⁵⁶/tT; where T!=0

There is a different dynamic between the classical and quantum miner because Bitcoin is designed to find a new block on average every 10 minutes (or 600 seconds). Hence, the nature of the search problem changes in this duration. For high probability of success of Grover procedure, quantum miners should run their algorithm for a time “t” before the problem changes, and then make the measurement. Meanwhile, the classical miner, during this period, has been trying as many nonces as possible. So, the quantum miner is hoping that none of the classical miners have found a solution during the Grover evolution. Since the interval between blocks follows an exponential distribution, the probability that the block is still mineable is t/600 e.

Assuming a constant cost of running a quantum computer for a given amount of time, the profitability of quantum bitcoin mining is then:

Re^-t/600sin²(2r_qt(T/2²⁵⁶)^½)-Ct

where “R” is the reward (currently equal to the price of 12.5 bitcoins plus transaction fees) and “C” is the cost of running the quantum computer.

Is quantum bitcoin mining profitable?

Let us do some estimation to determine whether quantum bitcoin mining is profitable. Assume that the cost of running a quantum computer is the same as that of a classical computer. Using the above equations, it can be determined that quantum mining will be possible at a quantum hash rate of 48 kilo-hashes/s, compared with the existing best classical hardware having 125 kilo-hashes/s.

Classical Bitcoin miners can achieve enormous hash rates because the random guess mining algorithm can be quite easily parallelized. The problem is that the quantum advantage does not exceed the factor of (2²⁵⁶/T)½, irrespective of the number of qubits.  Although there is a quantum advantage, it is not insurmountable enough that classical parallelization cannot beat it.  For a quantum computer with a slower hash rate than the minimally profitable 48 kilo-hashes/s, quantum parallelization seems to be necessary.

For example, for a quantum hash rate of 3 kilo-hashes/s, one would require1300 quantum computers to be on par with classical best mining hardware available today. Thus, profitable quantum mining would need rather fast quantum hash rates, and/or a much more significant quantum speedup. This may still happen in the future, but for now, classical mining seems difficult to beat.

Bitcoin mining and electricity

As of August 2021, the leader of the global bitcoin network hash-rate is the USA (35.4%), followed by Kazakhstan (18.1%) and Russia (11%). According to the New York Times, bitcoin mining consumes 0.5% of global electricity annually (refer to figure 2) and is seven times Google’s yearly energy consumption. To mine one bitcoin, an individual miner could take up to 5 years and consume up to 21900 kWh.

Read next part- Bitcoin Blockchain and Quantum Computer – I

The post Bitcoin Blockchain and Quantum Computer – II appeared first on Welcome to Quantum Guru.

Quantum and its related terms are getting increasingly more eyeballs and mindshare from a wide variety of audiences – from researchers to novice enthusiasts. In this article, QuantumGuru attempts to succinctly introduce the fundamentals of quantum computing and its key principles such as superposition, entanglement, to name a few.  More importantly, we have tried to touch upon and simplify the current and proposed work on quantum. Please share your feedback, your topics of interest, and how you would like us to improve.

The fundamental principles of quantum computing stem from the theory of quantum mechanics. A number of unique quantum principles highlight the clear differences between explanations provided by conventional (or classical) physics and quantum physics. Chief among these founding principles are the concepts of superposition and entanglement as well as the intrinsic randomness that appears in quantum mechanical measurements, i.e., the uncertainty principle. The application of these ideas to the theory of information has led to the development of quantum information theory.  According to quantum information theory, quantum computing originates alongside quantum communication and quantum sensing, among many others.

The binary representation of data and instructions formulates conventional computing in which a register element r stores a bit b that may take on a value of either b0 or b1. Quantum computing also requires a physical register r but now the register may take the value of a quantum bit, or qubit, q. Conceptually, the qubit is defined as a normalized superposition over the exclusive outcomes b0 and b1. This hypothesis leads to a diagrammatic representation for the possible values of a qubit given as the surface of the unit sphere. Whereas the opposing north and south poles of the sphere represent the classical bit values of b0 = 0 and b1 = 1, every point on the surface corresponds to a possible qubit (q) value.

The superposition principle extends to more than a single quantum register element. Quantum mechanics permits multiple register elements to store superpositions collectively over multiple binary values. This phenomenon is known as entanglement. Quantum entanglement represents a form of information that conventional bits cannot reproduce. While the register elements remain independently addressable, the information they store is coupled and hence not expressed or represented piecewise. For example, two entangled registers may either both be in the b0 state and in the b1 state, but exclude any possibility of anti-correlated values.

The principles of superposition and entanglement lead to an important conceptual difference in the interpretation of register value. Although the qubit maps to a point on the unit sphere, observing the qubit through measurement results in a projection to either b0 or b1 values. This transition from a qubit to a bit is the infamous ‘collapse’ of the quantum state induced by measurement. The implication is that the value q itself is not observable. Instead, interpret the qubit superposition state, q in terms of the probability to observe either b0 to b1. The probabilities p0 and p1 provide the likelihood that the observed outcome will be b0 and b1, respectively.

Classical computers use electrical signals that are either on or off to convey information as bits, the smallest unit of data on a computer, represented as two binary values, zero (when ‘off’) or one (when ‘on’). Zeros and ones are strung together to form binary codes for text and other data on classical computers. Quantum computers use quantum systems, such as electrons or photons, to represent quantum bits or qubits that can be in a state of 0 or 1, or an arbitrary superposition of them, for example, an equal combination of both. Entanglement occurs when there is a non-separable joint state of multiple qubits in superposition. For example, two distant parties could share a state where both qubits are in a superposition of 0 and 1, but such that they are perfectly correlated — a superposition of both sides having 0 or both sides having 1. Balanced superpositions of this form are known as Bell pairs. Superposition and entanglement are the defining features that distinguish quantum information from classical information. In addition to enabling quantum state teleportation over quantum networks, they underpin the exponential algorithmic power of quantum computers.

Testing these intriguing principles of quantum information depends on the ability to manipulate individual atoms, molecules, electrons, and photons. Building quantum computers is challenging because nature cannot easily discern an ideal qubit. Technology-based on advanced material physics coupled with a great deal of engineering will plausibly isolate this kind of system and yet control them to perform computations with sufficient precision. Numerous different candidate systems are being explored including low-power superconducting circuits, electromagnetically trapped ions, single-atom dopants in silicon lattices, neutral atoms in optical lattices, and vacancy defects in diamond and silicon carbide as well as many, many others.

A key feature in all of these technologies is the use of sophisticated techniques to remove, reduce and control errors. Alongside state-of-the-art efforts in nanofabrication and device physics, thermodynamics control is a common approach to reduce errors. This mainly consists of refrigeration and ultra-high vacuum to isolate the device as much as possible. Shielding from stray radiations, such as magnetic fields, is also important. On top of these coarse-grained efforts, device designers also use sophisticated sequences of control pulses to negate errors. This requires a detailed understanding of device physics and it is necessary to overcome current intrinsic error rates. The methods use quantum error correction schemes to mitigate against decoherence as well as fault-tolerant protocols to extend operational sequences.

Even with the future appearance of fault-tolerant Quantum Processing Units (QPU), there is still the outstanding need to program them for practical purposes. This requires a tightly integrated system design coupled with conventional computing methods to support high-level control of quantum registers. A long history of developing quantum algorithms has provided a number of possible applications(reference to Finance use cases is shown in Figure #3) to explore. Beyond factoring, there are novel algorithms for solving linear systems of equations, simulating quantum dynamics, searching unsorted databases, and teaching machines to classify and detect patterns.

The post Fundamentals and Evolution of Quantum Computing appeared first on Welcome to Quantum Guru.

The post What can quantum computers do for gaming? appeared first on Welcome to Quantum Guru.

The post Financial Institutions looking up towards Quantum appeared first on Welcome to Quantum Guru.

The post Search Engine using Quantum Realm Sounds Interesting! appeared first on Welcome to Quantum Guru.