Quantum Computing

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Information about Quantum Computing

Published on May 15, 2010

Author: jaybhanderi

Source: authorstream.com

Quantum Computing and Quantum Computers : Quantum Computing and Quantum Computers prepared by Jay Bhanderi 07CE05 Slide 2: Overview Limit of today’s Computer architecture What is Quantum Computing ? When will Quantum Computers be available ? What comes after Quantum Computing ? How does Quantum Computing Work ? Projected benefits of Quantum Computing Projected risks of Quantum Computing Conclusion Quantum Computing And Quantum Computers Why Quantum Computing ? Quantum Algorithms Quantum Circuits Quantum Gates Today’s Quantum Computers Slide 3: There’s a joke about personal computers that has been around since they came in the market : You buy a new computer, take it home and just as you finish unpacking it you see an advertisement for a new computer that makes yours obsolete. Speed has always been one of the prime objectives to be improved. And we’ve moved from vaccume tubes to transistors to reduce the size and increase the performance. If you make a chart of the evolution of the computer in terms of processing power, you would see that progress has been exponential. The man who first made this famous observation is Gordon Moore, a co-founder of the microprocessor company Intel. Limit of today’s Computer Architecture Quantum Computing And Quantum Computers Slide 4: Moore’s observation is that the number of transistors on a 1-inch (2.5 centimeter) diameter of silicon chip doubles every 18 or 24 months. It’s said to be a law but its more like an observation. Even a small microprocessor chip today is as powerful as a full-sized chip was a few years ago. Advancements in circuit production make devices like smart phones and notebooks possible. While Moore's original observation focused on technological advances and the economics behind producing circuits. Thousands of transistors vs. years Quantum Computing And Quantum Computers Slide 5: Just compare the very primitive computers and today’s. It means by making the semiconductor devices smaller, we can mount more number of them in the same chip and implement more logic on the same chip and hence can get more processing power from the same sized chip. And till today, we've keep doing that to increase the processing power of microprocessors. But now we've already reduced the size of the devices to such an extent that its almost impossible to reduce the size further. The current computer structure is beginning to reach its’ limits. What will happen in next 20 years if processor development continues to support Moore’s observation. The year 2020 or 2030 will find the circuits on a microprocessor measured on an atomic scale. ENIAC (1946) Today’s Computers Quantum Computing And Quantum Computers Slide 6: In the search for ever smaller and faster computational devices, and the researches on computational power of biological systems such as the brain, one is naturally led to consider the possibility of computational devices of the size of cells, molecules, atoms, or of even smaller scales. Why Quantum Computing ? It has been pointed out that if trends over the last forty years continue, we may reach atomic-scale computation by the year 2010. Transistors with “gate lengths” of 10nm can already be fabricated. Wave-like quantum properties of electrons become important on this length scale. Transistors switchable by a single electron predicted by 2015 or so. Physicist Paul The history of computer technology has involved a sequence of changes from one type of physical realization to another --- from gears to relays to valves to transistors to integrated circuits and so on. Quantum computing is the next logical advancement. At such scales, quantum effects become important whether we want them or not. The natural laws that govern the behavior of particles on extremely small scales. Quantum Computing And Quantum Computers Slide 7: How is Quantum Mechanics different ? A classical system is always (in principle) in a definite state; we “just” have to specify which one. We consider or want a classical bit to be in either 1 or 0 state. The state of a quantum system can involve many different possibilities simultaneously. Quantum bit or ‘qubit’ is 0 and 1 simultaneously, superposition of both. Quantum Mechanics and kets notation Ket notation is mathematical representation of state of the quantum system. “Basis kets” – represent a complete set of possible states for system “Basis vectors” – represent a complete set of possible directions Compare a two-dimensional vector: Quantum Computing And Quantum Computers Slide 8: What is Quantum Computing ? QC can be defined as a device for computation that makes direct use of quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data. The basic principle behind quantum computation is that quantum properties can be used to represent data and perform operations on these data. The Bloch Sphere In the classical model of a computer the most fundamental building block, the bit, can only exist in one of two distinct states, a '0' or a '1'. In a quantum computer the rules are changed. Not only can a 'quantum bit', usually referred to as a ‘qubit’, exist in the classical '0' and '1' states, but it can also be in a superposition of both! In this coherent state, the bit exists as a '0' and a '1' in a manner which may at first seem hard to accept. Let's consider a register of three classical bits: it would be possible to use this register to represent any one of the numbers from 0 to 7 at any one time. If we then consider a register of three qubits, we can see that if each bit is in the superposition or coherent state, the register can represent all the numbers from 0 to 7 simultaneously! Not 0 or 1 but 0 and 1….the superposition principle Quantum Computing And Quantum Computers Slide 9: Quantum Computing And Quantum Computers Slide 10: A processor that can use registers of qubits will in effect be able to perform calculations using all the possible values of the input registers simultaneously. This phenomenon is called quantum parallelism, and is the motivating force behind the research being carried out in quantum computing. Classical bit: Quantum bit: Superposition of 0 and 1 (qubits) A quantum computer performs manipulations on information represented as quantum bits, just as a classical computer performs manipulations on information represented as classical bits. If we consider a register of 3 classical bits, it would be possible to represent the numbers from 0 to 7 at any one time. Specifying general classical state requires three binary numbers Specifying general quantum state of N qubits requires 2N numbers: Quantum Computing And Quantum Computers Slide 11: How does Quantum Computing work ? The qubit is the quantum analogue of the bit, the classical fundamental unit of information. It is a mathematical object with specific properties that can be realized physically in many different ways as an actual physical system. Just as the classical bit has a state (either 0 or 1), a qubit also has a state. Yet contrary to the classical bit, 0 and 1 are but two possible states of the qubit, and any linear combination (superposition) thereof is also physically possible. In general, thus, the physical state of a qubit is the superposition ψ = α 0 + β 1 (where α and β are complex numbers). The state of a qubit can be described as a vector in a two-dimensional Hilbert space, a complex vector space . The special states 0 and 1 are known as the computational basis states, and form an orthonormal basis for this vector space. According to quantum theory, when we try to measure the qubit in this basis in order to determine its state, we get either 0 with probability α ² or 1 with probability β ². Since α ² + β ² = 1 (i.e., the qubit is a unit vector in the aforementioned two-dimensional Hilbert state), we may (ignoring the overall phase factor) effectively write its state as ψ = cos(θ) 0 + eiφsin(θ) 1 , where the numbers θ and φ define a point on the unit three-dimensional sphere, as shown here. This sphere is often called the Bloch sphere, and it provides a useful means to visualize the state of a single qubit. The Qubit Quantum Computing And Quantum Computers Slide 12: Quantum Gates The CNOT gate Classical computational gates are Boolean logic gates that perform manipulations of the information stored in the bits. In quantum computing these gates are represented by matrices, and can be visualized as rotations of the quantum state on the Bloch sphere. As in the case of classical computing, where there exists a universal gate (the combinations of which can be used to compute any computable function), namely, the NAND gate which results from performing an AND gate and then a NOT gate, in quantum computing it was shown (Barenco et al., 1995) that any multiple qubit logic gate may be composed from a quantum CNOT gate (which operates on a multiple qubit by flipping or preserving the target bit given the state of the control bit, an operation analogous to the classical XOR, i.e., the exclusive OR gate) and single qubit gates. One feature of quantum gates that distinguishes them from classical gates is that they are reversible: the inverse of a unitary matrix is also a unitary matrix, and thus a quantum gate can always be inverted by another quantum gate. Quantum Computing And Quantum Computers Slide 13: Quantum circuits are similar to classical computer circuits in that they consist of wires and logical gates. The wires are used to carry the information, while the gates manipulate it (note that the wires do not correspond to physical wires; they may Quantum Circuits correspond to a physical particle, a photon, moving from one location to another in space, or even to time-evolution). Conventionally, the input of the quantum circuit is assumed to be a computational basis state, usually the state consisting of all. The output state of the circuit is then measured in the computational basis, or in any other arbitrary orthonormal basis. The first quantum algorithms (i.e. Deutsch-Jozsa, Simon, Shor and Grover) were constructed in this paradigm. Additional paradigms for quantum computing exist today that differ from the quantum circuit model in many interesting ways. So far, however, they all have been demonstrated to be computationally equivalent to the circuit model, in the sense that any computational problem that can be solved by the circuit model can be solved by these new models with only a polynomial overhead in computational resources. D-WAVE Quantum Processor Quantum Computing And Quantum Computers Slide 14: Quantum Algorithms Algorithm design is a highly complicated task, and in quantum computing it becomes even more complicated due to the attempts to harness quantum mechanical features to reduce the complexity of computational problems and to "speed-up" computation. Before attacking this problem, we should first convince ourselves that quantum computers can be harnessed to perform standard, classical, computation without any "speed-up". In some sense this is obvious, given the belief in the universal character of quantum mechanics, and the observation that any quantum computation that is diagonal in the computational basis, i.e., involves no interference between the qubits, is effectively classical. Yet the demonstration that quantum circuits can be used to simulate classical circuits is not straightforward. Indeed, quantum circuits cannot be used directly to simulate classical computation, but the latter can still be simulated on a quantum computer using an intermediate gate, namely the Toffoli gate. This gate has three input bits and three output bits, two of which are control bits, unaffected by the action of the gate. The third bit is a target bit that is flipped if both control bits are set to 1, and otherwise is left alone. This gate is reversible (its inverse is itself), and can be used to simulate all the elements of the classical irreversible circuit with a reversible one. Consequently, using the quantum version of the Toffoli gate one can simulate, although rather tediously, irreversible classical logic gates with quantum reversible ones. Quantum computers are thus capable of performing any computation which a classical deterministic computer can do. Quantum Computing And Quantum Computers Slide 15: It has been shown in theory that a quantum computer will be able to perform any task that a classical computer can. However, this does not necessarily mean that a quantum computer will outperform a classical computer for all types of task. If we use our classical algorithms on a quantum computer, it will simply perform the calculation in a similar manner to a classical computer. In order for a quantum computer to show its superiority, it needs to use new algorithms which can exploit the phenomenon of quantum parallelism. Quantum Computing And Quantum Computers One of the embarrassments of quantum computing is the fact that, so far, only one algorithm has been discovered, namely Shor's, for which a quantum computer is significantly faster than any known classical one. It is almost certain that one of the reasons for this scarcity of quantum algorithms is related to the lack of our understanding of what makes a quantum computer quantum. Shor’s algorithm Slide 16: Projected benefits of Quantum Computing This new conceptualization of computing power will result in three main benefits : Increase in computing power Advances in security Artificial Intelligence The sci-fi concept of teleportation. Each of these opportunities can overcome the limitations of the current computational concept. Quantum Computation : increase in computing power Utilizing quantum parallelism, quantum computers will well serve the purpose of performing difficult mathematical calculations that are impossible using semiconductor computers. Quantum Cryptology : advances in security The expected capabilities of quantum computation promise great improvements in the world of cryptography. Ironically the same technology also poses current cryptography techniques a world of problems. The ability to break the RSA coding system will render almost all current channels of communication insecure. Quantum Computing And Quantum Computers Slide 17: The theories of quantum computation suggest that every physical object, even the universe, is in some sense a quantum computer. Ultimately this suggests that computers will be capable of simulating conscious rational thought, maybe the quantum computer will be the key to achieving true artificial intelligence. Artificial Intelligence Teleportation Teleportation is the capability to make an object or a person disintegrate in one place while a perfect replica appears in another. In physics, teleportation has never been taken seriously because of the uncertainty principle. According to the uncertainty principle, the duplicating process will disturb or destroy the original objects; the more an object is duplicated, the more it is destroyed. The detail information regarding how the duplication is made and how the original object is destroyed is unknown. Therefore, it will reach a point where one cannot extract enough information from the original to make a perfect replica. However, scientists at IBM and elsewhere have discovered a way to make a perfect replica using a distinctive feature of quantum mechanics called EPR (Einstein-Podolsky-Rosen) effect. Quantum computing provides at least a theoretical basis for teleportation. Quantum Computing And Quantum Computers Slide 18: Projected Risks\Disadvantages of Quantum Computing Conceptually, it is believed that with quantum technology we will be able to build microscopic machines such as a nanoassembler, a virtually universal constructor that will not just take materials apart and rebuild them atom by atom but also replicate itself. The bad news is that these HAL-like computing brains with capabilities exceeding those of humans, could redesign and replicate themselves at no cost, other than the loss of human dominance. It sounds as terrifying as those scenarios in a science fiction film : TERMINATOR. Quantum Computing And Quantum Computers Slide 19: Today’s Quantum Computers The technology needed to build a quantum computer is currently beyond our reach. This is due to the fact that the coherent state, fundamental to a quantum computers operation, is destroyed as soon as it is measurably affected by its environment. Attempts at combating this problem have had little success, but the hunt for a practical solution continues. Key technical challenge: prevent decoherence, or unwanted interaction with environment Approaches: NMR, ion trap, quantum dot, Josephson junction, optical… Larger computations will require quantum error-correcting codes The most advanced quantum computers have not gone beyond manipulating more than 16 qubits, meaning that they are a far cry from practical application. Several key advancements have been made in quantum computing in the last few years. 1998 Los Alamos and MIT researchers managed to spread a single qubit across three nuclear spins in each molecule of a liquid solution of alanine (an amino acid used to analyze quantum state decay) or trichloroethylene (a chlorinated hydrocarbon used for quantum error correction) molecules. After that, there were several QCs developed from 3 to 12 qubits till 2006 by the scientists of different countries. 2007 Canadian startup company D-Wave demonstrated a 16-qubit quantum computer. The computer solved a Sudoku puzzle and other pattern matching problems. The company claims it will produce practical systems by 2008. Skeptics believe practical quantum computers are still decades away, that the system D-Wave has created isn't scalable. Quantum computers must have at least several dozen qubits to be able to solve real-world problems, and thus serve as a viable computing method. Quantum Computing And Quantum Computers Slide 20: Quantum Computing And Quantum Computers What comes after Quantum Computing ? Once scientists can use atoms to complete complex computations, the day when a computer will be the size of 1 atom. These new machines can be deployed in ways that are not available today. For example, a nanomachine can be built and programmed to enter human cells to fight diseases or even resuscitate those who have just died. Yet, this approach will not be available until scientists can manipulate atoms using the quantum physics approaches of entanglement and superposition. In addition to smaller machines, scientists also claim that computers can now be stored in carbon-based beings, within DNA. Scientists have long known that DNA could store information. But only when Charles Bennett, in 1973, drew attention to the computational capability that is responsible for processing genetic information in DNA did researchers begin to recognize the potential of a biological computer. However, DNA computing is based on the foundation of quantum computing : ability to manipulate atoms. DNA molecule Slide 21: Although the future of quantum computing looks promising, we have only just taken our first steps to actually realizing a quantum computer. There are many hurdles which need to be overcome before we can begin to appreciate the benefits they may deliver. Researchers around the world are racing to be the first to achieve a practical system, a task which some scientists think is futile.. In comparison the progress in quantum communications has been somewhat more fruitful. Companies like BT have actually achieved working Conclusions Quantum Computing And Quantum Computers systems that are able to use quantum effects to detect eavesdropping on a channel. Whether or not such systems will prove practical remains to be seen. Can we really build a useful quantum computer? Who knows; in a quantum world, anything is possible! Slide 22: Quantum Computing And Quantum Computers

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