by Max Barry

Latest Forum Topics

Advertisement

Post

Region: The Democratic Republic

Monati

Info tech development (computer advancements - Quantum Computers).

One of the Federation's advanced info tech industries with the essential herculean efforts from Pacifican and Swanoviam exchange scientists helping in UMAF's progress to develop the first ever Quantum computer technologies, as well as other technologies that would help the nation to advance with better and more reliant energy, as well as in defensive capabilities. But for now, the emphasis of the new project, subsidized by the regional government of Japan, is to further improve the capabilities of computing technology. By subsidizing the tech industry and its giant companies with 1 billion ASEAN dollars, a good start was achieved that would increase its progress towards completion in the next decade or three. As a result, many top universities both private and public have begun to adopt Quantum Computing courses to help bring bright minds into further developing Quantum technologies. With the purchasing of existing quantum computing devices, the project seeks to further advance the tech into the regular computers we use today or something better.

Quantum computing is the use of quantum-mechanical phenomena such as superposition and entanglement to perform computation. A quantum computer is used to perform such computation, which can be implemented theoretically or physically.:I-5

The Bloch sphere is a representation of a qubit, the fundamental building block of quantum computers.
The field of quantum computing is actually a sub-field of quantum information science, which includes quantum cryptography and quantum communication. Quantum computing was started in the early 1980s when UMAF physicist Ishaga Askuidotrotz proposed the first quantum mechanical model of the Turing machine. Aisha Britzi and Yuraga Lee then expressed the idea that a quantum computer has the potential to simulate things that a classical computer could not.  In 1994, Ishaga published an algorithm that is able to efficiently solve some problems that are used in asymmetric cryptography that are considered hard for classical computers.

There are currently two main approaches to physically implementing a quantum computer: analog and digital. Analog approaches are further divided into quantum simulation, quantum annealing, and adiabatic quantum computation. Digital quantum computers use quantum logic gates to do computation. Both approaches use quantum bits or qubits.:2-13

Qubits are fundamental to quantum computing and are somewhat analogous to bits in a classical computer. Qubits can be in a 1 or 0 quantum state. But they can also be in a superposition of the 1 and 0 states. However, when qubits are measured the result is always either a 0 or a 1; the probabilities of the two outcomes depends on the quantum state they were in.

Today's physical quantum computers are very noisy and quantum error correction is a burgeoning field of research. Existing hardware is so noisy that "fault-tolerant quantum computing [is] still a rather distant dream". As of April 2019, no large scalable quantum hardware has been demonstrated, nor have commercially useful algorithms been published for today's small, noisy quantum computers. There is an increasing amount of investment in quantum computing by governments, established companies, and start-ups. Both applications of near-term intermediate-scale device and the demonstration of quantum supremacy are actively pursued in academic and industrial research.

Basics
A classical computer has a memory made up of bits, where each bit is represented by either a one or a zero. A quantum computer, on the other hand, maintains a sequence of qubits, which can represent a one, a zero, or any quantum superposition of those two qubit states;:13–16 a pair of qubits can be in any quantum superposition of 4 states,:16 and three qubits in any superposition of 8 states. In general, a quantum computer with {\displaystyle n} qubits can be in any superposition of up to {\displaystyle 2^{n}} different states.:17 (This compares to a normal computer that can only be in one of these {\displaystyle 2^{n}} states at any one time).

A quantum computer operates on its qubits using quantum gates and measurement (which also alters the observed state). An algorithm is composed of a fixed sequence of quantum logic gates and a problem is encoded by setting the initial values of the qubits, similar to how a classical computer work. The calculation usually ends with a measurement, collapsing the system of qubits into one of the {\displaystyle 2^{n}} eigenstates, where each qubit is zero or one, decomposing into a classical state. The outcome can, therefore, be at most {\displaystyle n} classical bits of information. If the algorithm did not end with a measurement, the result is an unobserved quantum state. (Such unobserved states may be sent to other computers as part of distributed quantum algorithms.)

Quantum algorithms are often probabilistic, in that they provide the correct solution only with a certain known probability. The term non-deterministic computing must not be used in that case to mean probabilistic (computing) because the term non-deterministic has a different meaning in computer science.

An example of an implementation of qubits of a quantum computer could start with the use of particles with two spin states: "down" and "up" (typically written {\displaystyle |{\downarrow }\rangle } and {\displaystyle |{\uparrow }\rangle } , or {\displaystyle |0{\rangle }} and {\displaystyle |1{\rangle }} ). This is true because any such system can be mapped onto an effective spin-1/2 system.

Principles of operation

This section includes a list of references, but its sources remain unclear because it has insufficient inline citations. (February 2018)
A quantum computer with a given number of qubits is fundamentally different from a classical computer composed of the same number of classical bits. For example, representing the state of an n-qubit system on a classical computer requires the storage of 2n complex coefficients, while to characterize the state of a classical n-bit system it is sufficient to provide the values of the n bits, that is, only n numbers. Although this fact may seem to indicate that qubits can hold exponentially more information than their classical counterparts, care must be taken not to overlook the fact that the qubits are only in a probabilistic superposition of all of their states. This means that when the final state of the qubits is measured, they will only be found in one of the possible configurations they were in before the measurement. It is generally incorrect to think of a system of qubits as being in one particular state before the measurement. The qubits are in a superposition of states before any measurement is made, which directly affects the possible outcomes of the computation.

Qubits are made up of controlled particles and the means of control (e.g. devices that trap particles and switch them from one state to another).
To better understand this point, consider a classical computer that operates on a three-bit register. If the exact state of the register at a given time is not known, it can be described as a probability distribution over the {\displaystyle 2^{3}=8} different three-bit strings 000, 001, 010, 011, 100, 101, 110, and 111. If there is no uncertainty over its state, then it is in exactly one of these states with probability 1. However, if it is a probabilistic computer, then there is a possibility of it being in any one of a number of different states.

The state of a three-qubit quantum computer is similarly described by an eight-dimensional vector {\displaystyle (a_{0},a_{1},a_{2},a_{3},a_{4},a_{5},a_{6},a_{7})} (or a one-dimensional vector with each vector node holding the amplitude and the state as the bit string of qubits). Here, however, the coefficients {\displaystyle a_{i}} are complex numbers, and it is the sum of the squares of the coefficients' absolute values, {\displaystyle \sum _{i}|a_{i}|^{2}} , that must equal 1. For each {\displaystyle i} , the absolute value squared {\displaystyle \left|a_{i}\right|^{2}} gives the probability of the system being found in the {\displaystyle i} -th state after a measurement. However, because a complex number encodes not just a magnitude but also a direction in the complex plane, the phase difference between any two coefficients (states) represents a meaningful parameter. This is a fundamental difference between quantum computing and probabilistic classical computing.

If you measure the three qubits, you will observe a three-bit string. The probability of measuring a given string is the squared magnitude of that string's coefficient (i.e., the probability of measuring 000 = {\displaystyle |a_{0}|^{2}} , the probability of measuring 001 = {\displaystyle |a_{1}|^{2}} , etc.). Thus, measuring a quantum state described by complex coefficients {\displaystyle (a_{0},a_{1},a_{2},a_{3},a_{4},a_{5},a_{6},a_{7})} gives the classical probability distribution {\displaystyle (|a_{0}|^{2},|a_{1}|^{2},|a_{2}|^{2},|a_{3}|^{2},|a_{4}|^{2},|a_{5}|^{2},|a_{6}|^{2},|a_{7}|^{2})} and we say that the quantum state "collapses" to a classical state as a result of making the measurement.

An eight-dimensional vector can be specified in many different ways depending on what basis is chosen for the space. The basis of bit strings (e.g., 000, 001, …, 111) is known as the computational basis. Other possible bases are unit-length, orthogonal vectors and the eigenvectors of the Pauli-x operator. Ket notation is often used to make the choice of basis explicit. For example, the state {\displaystyle (a_{0},a_{1},a_{2},a_{3},a_{4},a_{5},a_{6},a_{7})} in the computational basis can be written as:

{\displaystyle a_{0}\,|000\rangle +a_{1}\,|001\rangle +a_{2}\,|010\rangle +a_{3}\,|011\rangle +a_{4}\,|100\rangle +a_{5}\,|101\rangle +a_{6}\,|110\rangle +a_{7}\,|111\rangle }
where, e.g., {\displaystyle |010\rangle =\left(0,0,1,0,0,0,0,0\right)}
The computational basis for a single qubit (two dimensions) is {\displaystyle |0\rangle =\left(1,0\right)} and {\displaystyle |1\rangle =\left(0,1\right)} .

Using the eigenvectors of the Pauli-x operator, a single qubit is {\displaystyle |+\rangle ={\tfrac {1}{\sqrt {2}}}\left(1,1\right)} and {\displaystyle |-\rangle ={\tfrac {1}{\sqrt {2}}}\left(1,-1\right)} .

Operation

Is a universal quantum computer sufficient to efficiently simulate an arbitrary physical system?
(more unsolved problems in physics)
While a classical 3-bit state and a quantum 3-qubit state are each eight-dimensional vectors, they are manipulated quite differently for classical or quantum computation. For computing in either case, the system must be initialized, for example into the all-zeros string, {\displaystyle |000\rangle } , corresponding to the vector (1,0,0,0,0,0,0,0). In classical randomized computation, the system evolves according to the application of stochastic matrices, which preserve that the probabilities add up to one (i.e., preserve the L1 norm). In quantum computation, on the other hand, allowed operations are unitary matrices, which are effectively rotations (they preserve that the sum of the squares add up to one, the Euclidean or L2 norm). (Exactly what unitaries can be applied depend on the physics of the quantum device.) Consequently, since rotations can be undone by rotating backward, quantum computations are reversible. (Technically, quantum operations can be probabilistic combinations of unitaries, so quantum computation really does generalize classical computation. See quantum circuit for a more precise formulation.)

Finally, upon termination of the algorithm, the result needs to be read off. In the case of a classical computer, we sample from the probability distribution on the three-bit register to obtain one definite three-bit string, say 000. Quantum mechanically, one measures the three-qubit state, which is equivalent to collapsing the quantum state down to a classical distribution (with the coefficients in the classical state being the squared magnitudes of the coefficients for the quantum state, as described above), followed by sampling from that distribution. This destroys the original quantum state. Many algorithms will only give the correct answer with a certain probability. However, by repeatedly initializing, running and measuring the quantum computer's results, the probability of getting the correct answer can be increased. In contrast, counterfactual quantum computation allows the correct answer to be inferred when the quantum computer is not actually running in a technical sense, though earlier initialization and frequent measurements are part of the counterfactual computation protocol.

For more details on the sequences of operations used for various quantum algorithms, see universal quantum computer, Shor's algorithm, Grover's algorithm, Deutsch–Jozsa algorithm, amplitude amplification, quantum Fourier transform, quantum gate, quantum adiabatic algorithm and quantum error correction.

Potential

Cryptography

Integer factorization, which underpins the security of public key cryptographic systems, is believed to be computationally infeasible with an ordinary computer for large integers if they are the product of few prime numbers (e.g., products of two 300-digit primes). By comparison, a quantum computer could efficiently solve this problem using Shor's algorithm to find its factors. This ability would allow a quantum computer to break many of the cryptographic systems in use today, in the sense that there would be a polynomial time (in the number of digits of the integer) algorithm for solving the problem. In particular, most of the popular public key ciphers are based on the difficulty of factoring integers or the discrete logarithm problem, both of which can be solved by Shor's algorithm. In particular, the RSA, Diffie–Hellman, and elliptic curve Diffie–Hellman algorithms could be broken. These are used to protect secure Web pages, encrypted email, and many other types of data. Breaking these would have significant ramifications for electronic privacy and security.

However, other cryptographic algorithms do not appear to be broken by those algorithms. Some public-key algorithms are based on problems other than the integer factorization and discrete logarithm problems to which Shor's algorithm applies, like the McEliece cryptosystem based on a problem in coding theory. Lattice-based cryptosystems are also not known to be broken by quantum computers, and finding a polynomial time algorithm for solving the dihedral hidden subgroup problem, which would break many lattice based cryptosystems, is a well-studied open problem. It has been proven that applying Grover's algorithm to break a symmetric (secret key) algorithm by brute force requires time equal to roughly 2n/2 invocations of the underlying cryptographic algorithm, compared with roughly 2n in the classical case, meaning that symmetric key lengths are effectively halved: AES-256 would have the same security against an attack using Grover's algorithm that AES-128 has against classical brute-force search (see Key size). Quantum cryptography could potentially fulfill some of the functions of public key cryptography. Quantum-based cryptographic systems could, therefore, be more secure than traditional systems against quantum hacking.

Quantum search
Besides factorization and discrete logarithms, quantum algorithms offering a more than polynomial speedup over the best known classical algorithm have been found for several problems, including the simulation of quantum physical processes from chemistry and solid state physics, the approximation of Jones polynomials, and solving Pell's equation. No mathematical proof has been found that shows that an equally fast classical algorithm cannot be discovered, although this is considered unlikely. However, quantum computers offer polynomial speedup for some problems. The most well-known example of this is quantum database search, which can be solved by Grover's algorithm using quadratically fewer queries to the database than that are required by classical algorithms. In this case, the advantage is not only provable but also optimal, it has been shown that Grover's algorithm gives the maximal possible probability of finding the desired element for any number of oracle lookups. Several other examples of provable quantum speedups for query problems have subsequently been discovered, such as for finding collisions in two-to-one functions and evaluating NAND trees.

Problems that can be addressed with Grover's algorithm have the following properties:

There is no searchable structure in the collection of possible answers,
The number of possible answers to check is the same as the number of inputs to the algorithm, and
There exists a boolean function which evaluates each input and determines whether it is the correct answer
For problems with all these properties, the running time of Grover's algorithm on a quantum computer will scale as the square root of the number of inputs (or elements in the database), as opposed to the linear scaling of classical algorithms. A general class of problems to which Grover's algorithm can be applied is Boolean satisfiability problem. In this instance, the database through which the algorithm is iterating is that of all possible answers. An example (and possible) application of this is a password cracker that attempts to guess the password or secret key for an encrypted file or system. Symmetric ciphers such as Triple DES and AES are particularly vulnerable to this kind of attack. This application of quantum computing is a major interest of government agencies.

Quantum simulation
Since chemistry and nanotechnology rely on understanding quantum systems, and such systems are impossible to simulate in an efficient manner classically, many believe quantum simulation will be one of the most important applications of quantum computing. Quantum simulation could also be used to simulate the behavior of atoms and particles at unusual conditions such as the reactions inside a collider.

Quantum annealing and adiabatic optimization
Quantum annealing or Adiabatic quantum computation relies on the adiabatic theorem to undertake calculations. A system is placed in the ground state for a simple Hamiltonian, which is slowly evolved to a more complicated Hamiltonian whose ground state represents the solution to the problem in question. The adiabatic theorem states that if the evolution is slow enough the system will stay in its ground state at all times through the process.

Solving linear equations
The Quantum algorithm for linear systems of equations or "HHL Algorithm", named after its discoverers Harrow, Hasidim, and Lloyd, is expected to provide speedup over classical counterparts.

America JB and Sudeteland

ContextReport