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| Trap to develop a quantum computer based on single-electron transistors. |
Introduction:
A quantum computer is a device for computation that makes direct use of quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data. Quantum computers are different from traditional computers based on transistors. The basic principle behind quantum computation is that quantum properties can be used to represent data and perform operations on these data.
A theoretical model is the quantum Turing machine, also known as the universal quantum computer. Quantum computers share theoretical similarities with non-deterministic and probabilistic computers, like the ability to be in more than one state simultaneously. The field of quantum computing was first introduced by Richard Feynman in 1982.
Although quantum computing is still in its infancy, experiments have been carried out in which quantum computational operations were executed on a very small number of qubits (quantum bits). Both practical and theoretical research continues, and many national government and military funding agencies support quantum computing research to develop quantum computers for both civilian and national security purposes, such as cryptanalysis.
Large-scale quantum computers could be able to solve certain problems much faster than any classical computer by using the best currently known algorithms, like integer factorization using Shor's algorithm or the simulation of quantum many-body systems. There exist quantum algorithms, such as Simon's algorithm, which run faster than any possible probabilistic classical algorithm.Given unlimited resources, a classical computer can simulate an arbitrary quantum algorithm so quantum computation does not violate the Church–Turing thesis.However, in practice infinite resources are never available and the computational basis of 500 qubits, for example, would already be too large to be represented on a classical computer because it would require 2500 complex values to be stored.Nielsen and Chuang point out that "Trying to store all these complex numbers would not be possible on any conceivable classical computer."
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| The Bloch sphere is a representation of a qubit, the fundamental building block of quantum computers. |
Basis:
A classical computer has a memory made up of bits, where each bit represents either a one or a zero. A quantum computer maintains a sequence of qubits. A single qubit can represent a one, a zero, or, crucially, any quantum superposition of these; moreover, a pair of qubits can be in any quantum superposition of 4 states, and three qubits in any superposition of 8. In general a quantum computer with n qubits can be in an arbitrary superposition of up to 2n different states simultaneously (this compares to a normal computer that can only be in one of these 2n states at any one time). A quantum computer operates by manipulating those qubits with a fixed sequence of quantum logic gates. The sequence of gates to be applied is called a quantum algorithm.
An example of an implementation of qubits for a quantum computer could start with the use of particles with two spin states: "down" and "up" (typically written |{\downarrow}\rangle and |{\uparrow}\rangle, or |0{\rangle} and |1{\rangle}). But in fact any system possessing an observable quantity A which is conserved under time evolution and such that A has at least two discrete and sufficiently spaced consecutive eigenvalues, is a suitable candidate for implementing a qubit. This is true because any such system can be mapped onto an effective spin-1/2 system.
An example of an implementation of qubits for a quantum computer could start with the use of particles with two spin states: "down" and "up" (typically written |{\downarrow}\rangle and |{\uparrow}\rangle, or |0{\rangle} and |1{\rangle}). But in fact any system possessing an observable quantity A which is conserved under time evolution and such that A has at least two discrete and sufficiently spaced consecutive eigenvalues, is a suitable candidate for implementing a qubit. This is true because any such system can be mapped onto an effective spin-1/2 system.
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| World record: Julich supercomputer simulates quantum compute |
Latest Research on Quantum Computers:(Dec 19, 2011)
Quantum computing -- considered the powerhouse of computational tasks --
may have applications in areas outside of pure electronics, according
to a University of Pittsburgh researcher and his collaborators.
Working at the interface of quantum measurement and nanotechnology, Gurudev Dutt, assistant professor in Pitt's Department of Physics and Astronomy in the Kenneth P. Dietrich School of Arts and Sciences, and his colleagues report their findings in a paper published online Dec. 18 in Nature Nanotechnology. The paper documents important progress towards realizing a nanoscale magnetic imager comprising single electrons encased in a diamond crystal.
"Think of this like a typical medical procedure -- a Magnetic Resonance Imaging (MRI) -- but on single molecules or groups of molecules inside cells instead of the entire body. Traditional MRI techniques don't work well with such small volumes, so an instrument must be built to accommodate such high-precision work," says Dutt.
However, a significant challenge arose for researchers working on the problem of building such an instrument: How does one measure a magnetic field accurately using the resonance of the single electrons within the diamond crystal? Resonance is defined as an object's tendency to oscillate with higher energy at a particular frequency, and occurs naturally all around us: for example, with musical instruments, children on swings, and pendulum clocks. Dutt says that resonances are particularly powerful because they allow physicists to make sensitive measurements of quantities like force, mass, and electric and magnetic fields. "But they also restrict the maximum field that one can measure accurately."
In magnetic imaging, this means that physicists can only detect a narrow range of fields from molecules near the sensor's resonant frequency, making the imaging process more difficult.
"It can be done," says Dutt, "but it requires very sophisticated image processing and other techniques to understand what one is imaging. Essentially, one must use software to fix the limitations of hardware, and the scans take longer and are harder to interpret."
Dutt -- working with postdoctoral researcher Ummal Momeen and PhD student Naufer Nusran (A&S'08 G), both in Pitt's Department of Physics and Astronomy -- has used quantum computing methods to circumvent the hardware limitation to view the entire magnetic field. By extending the field, the Pitt researchers have improved the ratio between maximum detectable field strength and field precision by a factor of 10 compared to the standard technique used previously. This puts them one step closer toward a future nanoscale MRI instrument that could study properties of molecules, materials, and cells in a noninvasive way, displaying where atoms are located without destroying them; current methods employed for this kind of study inevitably destroy the samples.
"This would have an immediate impact on our understanding of these molecules, materials, or living cells and potentially allow us to create better technologies," says Dutt.
These are only the initial results, says Dutt, and he expects further improvements to be made with additional research: "Our work shows that quantum computing methods reach beyond pure electronic technologies and can solve problems that, earlier, seemed to be fundamental roadblocks to making progress with high-precision measurements."
"Think of this like a typical medical procedure -- a Magnetic Resonance Imaging (MRI) -- but on single molecules or groups of molecules inside cells instead of the entire body. Traditional MRI techniques don't work well with such small volumes, so an instrument must be built to accommodate such high-precision work," says Dutt.
However, a significant challenge arose for researchers working on the problem of building such an instrument: How does one measure a magnetic field accurately using the resonance of the single electrons within the diamond crystal? Resonance is defined as an object's tendency to oscillate with higher energy at a particular frequency, and occurs naturally all around us: for example, with musical instruments, children on swings, and pendulum clocks. Dutt says that resonances are particularly powerful because they allow physicists to make sensitive measurements of quantities like force, mass, and electric and magnetic fields. "But they also restrict the maximum field that one can measure accurately."
In magnetic imaging, this means that physicists can only detect a narrow range of fields from molecules near the sensor's resonant frequency, making the imaging process more difficult.
"It can be done," says Dutt, "but it requires very sophisticated image processing and other techniques to understand what one is imaging. Essentially, one must use software to fix the limitations of hardware, and the scans take longer and are harder to interpret."
Dutt -- working with postdoctoral researcher Ummal Momeen and PhD student Naufer Nusran (A&S'08 G), both in Pitt's Department of Physics and Astronomy -- has used quantum computing methods to circumvent the hardware limitation to view the entire magnetic field. By extending the field, the Pitt researchers have improved the ratio between maximum detectable field strength and field precision by a factor of 10 compared to the standard technique used previously. This puts them one step closer toward a future nanoscale MRI instrument that could study properties of molecules, materials, and cells in a noninvasive way, displaying where atoms are located without destroying them; current methods employed for this kind of study inevitably destroy the samples.
"This would have an immediate impact on our understanding of these molecules, materials, or living cells and potentially allow us to create better technologies," says Dutt.
These are only the initial results, says Dutt, and he expects further improvements to be made with additional research: "Our work shows that quantum computing methods reach beyond pure electronic technologies and can solve problems that, earlier, seemed to be fundamental roadblocks to making progress with high-precision measurements."
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