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# Quantum Computers

## by kathan on May 15, 2008

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## Quantum ComputersPresentation Transcript

• Introduction To Quantum Computers
• According to Moore’s law : The no. of transistors on a microprocessor continues to double every 18 months, The year 2020-30 will find the ckts on a microprocessor measured on an atomic scale.
• Processor being affected by the strange rules of Quantum Mechanics.
• In 1981, Richard Feynman led the way by producing an abstract model of how, in principle, a quantum system could be used to perform computations.
• i.e. Quantum Computer
• Turing Machine Vs Quantum Computers
• In 1930, Alan Turing developed classical theories of computing.
• A tape of unlimited length is divided into little squares. Each squares can either hold a symbol (0 or 1) or be left blank. A read write device reads the symbols & blanks, which gives the machines its instruction to execute a certain program.
• In 1981, Paul Benioff first applied quantum theory to computers.
• In quantum Turing machine, the difference is that – the tape exists in a quantum state, as does the read write head. The symbols on the tape can be 0 or 1 or a “Superposition” of 0 & 1.
• Bit Vs Qubit
• Consider a Classical computer that operates on a 3-bit register. At any given time, bits are in a definite state- 101.
• In a Quantum Computer, the qubits can be in a superposition of all the classically allowed states. In fact, the register is described by a wavefunction :
• where the coefficients α, β, γ,... are complex numbers whose amplitudes squared are the probabilities to measure the qubits in each state. Consequently, | γ | 2 is the probability to measure the register in the state 010.
• For n=300, the no. of states turns out to be ~10 90 , more than no. of atoms in known Universe…
• Power of Quantum Computers
• As a Quantum Computer can contain multiple states simultaneously, it has the potential to be millions of times powerful than today’s most powerful supercomputers.
• In 1985, David Deustch published a theoretical paper in which these idea of parallelism was given.
• A 30 qubit quantum computer could equal the processing power of a conventional computer that could run at 10teraflops . Whereas typical PC’s run at speeds measured in Gigaflops.
• QCs can be used for running quantum mechanical simulations. Feynman observed that there was no known algorithm for simulating quantum system on classical computer & suggested the study of the use of Quantum Computers for this purpose. E.g. some modern simulations those are taking IBM’s Blue Gene Supercomputer years, would take a Q.C. only a matter of seconds.
• Entanglement
• If you look at the subatomic particles, you could disturb them, and thereby change their value. But in Quantum Physics, if you apply external force to 2-atoms, they become ENTANGLED and the second atom can take on the properties according to the first one.
• It helps scientists to know the value of qubits without actually looking at them.
• Quantum Decoherence
• Major problems- to keep the components of the computer in a coherent state as the slightest interaction with external world would cause the system to decohere.
• It causes Unitary character ( Invertibility ) of quantum computational steps to be violated.
• Its Range is nano seconds- seconds at low temperature.
• Error Rate = Operating time / Decoherence time
• Required error rate = 10 -4 .
• Thus, each gate must be able to perform its task 10,000 times faster than the decoherence time of the system.
• Electron on right dot Electron on left dot Charge Electron localization Singly-charged quantum dot pair Current No current Current Superconducting flux qubit Josephson junction Charged capacitor Uncharged capacitor Charge Superconducting charge qubit Josephson junction Down Up Spin Atomic spin Optical lattices Down Up Spin Nuclear spin addressed through NMR Nucleus One electron No electron Charge Electron number Down Up Spin Electronic spin Electrons Phase-squeezed state Amplitude-squeezed state Quadrature Squeezed light Coherent state of light Late Early Time of arrival Time-bin encoding Single photon state Vacuum Photon number Photon number Vertical Horizontal Polarization of light Polarization encoding Single photon ( Fock states ) &quot;1&quot; &quot;0&quot; Information support Name Physical support
• Today's Quantum Computer
• In August 2000, researchers at IBM-Almaden Research Center developed what they claimed was the most advanced quantum computer developed to date. The 5-qubit quantum computer was designed to allow the nuclei of five fluorine atoms to interact with each other as qubits, be programmed by radio frequency pulses and be detected by nuclear magnetic resonance (NMR) instruments similar to those used in hospitals (see How Magnetic Resonance Imaging Works for details). Led by Dr. Isaac Chuang, the IBM team was able to solve in one step a mathematical problem that would take conventional computers repeated cycles. The problem, called order-finding, involves finding the period of a particular function, a typical aspect of many mathematical problems involved in cryptography.
• In March 2000, scientists at Los Alamos National Laboratory announced the development of a 7-qubit quantum computer within a single drop of liquid. The quantum computer uses NMR to manipulate particles in the atomic nuclei of molecules of trans-crotonic acid, a simple fluid consisting of molecules made up of six hydrogen and four carbon atoms. The NMR is used to apply electromagnetic pulses, which force the particles to line up. These particles in positions parallel or counter to the magnetic field allow the quantum computer to mimic the information-encoding of bits in digital computers.
• In 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 or trichloroethylene molecules. Spreading out the qubit made it harder to corrupt, allowing researchers to use entanglement to study interactions between states as an indirect method for analyzing the quantum information.
•
• David DiVincenzo, of IBM, listed the following requirements for a practical quantum computer:
• scalable physically to increase the number of qubits
• qubits can be initialized to arbitrary values
• quantum gates faster than decoherence time
• Turing-complete gate set
• qubits can be read easily
• To summarize the problem from the perspective of an engineer, one needs to solve the challenge of building a system which is isolated from everything except the measurement and manipulation mechanism. Furthermore, one needs to be able to turn off the coupling of the qubits to the measurement so as to not decohere the qubits while performing operations on them.
Challenges
•