1. The document discusses entanglement generation and state transfer in a Heisenberg spin-1/2 chain under an external magnetic field.
2. It analyzes the fidelity and concurrence of the system over time and temperature using the density matrix and Hamiltonian equations for a 2-qubit system.
3. The results show that maximally entangled states are difficult to achieve but desirable for quantum computation applications like quantum teleportation.
Quantum computing is a new method of computing based on quantum mechanics that offers greater computational power than classical computers. Quantum computers use quantum bits or qubits that can exist in superpositions of states allowing massive parallelism. Several approaches like ion traps, quantum dots and NMR have demonstrated quantum computing. However, challenges remain around errors from decoherence and a lack of reliable reading mechanisms. If these obstacles can be overcome, quantum computers may solve problems in artificial intelligence, cybersecurity, drug design and more exponentially faster than classical computers.
This document provides an introduction to quantum computing. It discusses how quantum computers work using quantum bits (qubits) that can exist in superpositions of states unlike classical bits. Qubits can become entangled so that operations on one qubit affect others. Implementing qubits requires isolating quantum systems to avoid decoherence. Challenges include controlling decoherence, but research continues on algorithms, hardware, and bringing theoretical quantum computers to practical use. Quantum computers may solve problems intractable for classical computers.
This document provides an overview of quantum computers. It begins by explaining that quantum physics must be understood first as quantum computers are based on quantum mechanical principles rather than classical physics. It then defines a quantum computer as a machine that performs calculations based on the laws of quantum mechanics. The document goes on to discuss key quantum properties like superposition and entanglement that quantum computers exploit. It also covers qubits, quantum gates, applications, advantages, challenges, and concludes by stating that quantum computers will require a new way of looking at computing.
The document summarizes research on understanding charge transport in low dimensional semiconductor nanostructures embedded in an insulating matrix. Specifically, it examines current-voltage characteristics of germanium nanowire arrays in an alumina matrix as a function of temperature. Key findings include:
1) At room temperature, conduction follows Ohm's law at low voltages and Mott-Gurney's space charge limited current law at higher voltages.
2) With decreasing temperature, conduction transitions from a trap-free regime to an exponentially distributed trap regime.
3) Mobility decreases with decreasing temperature, and activation energy is extracted from an Arrhenius plot, found to be 85 meV at low temperatures and 301 meV
What is Quantum Computing
What is Quantum bits (Qubit)
What is Reversible Logic gates and Logic Circuits
What is Quantum Neuron (Quron)
What are the methods of implementing ANN using Quantum computing
1. The document discusses entanglement generation and state transfer in a Heisenberg spin-1/2 chain under an external magnetic field.
2. It analyzes the fidelity and concurrence of the system over time and temperature using the density matrix and Hamiltonian equations for a 2-qubit system.
3. The results show that maximally entangled states are difficult to achieve but desirable for quantum computation applications like quantum teleportation.
Quantum computing is a new method of computing based on quantum mechanics that offers greater computational power than classical computers. Quantum computers use quantum bits or qubits that can exist in superpositions of states allowing massive parallelism. Several approaches like ion traps, quantum dots and NMR have demonstrated quantum computing. However, challenges remain around errors from decoherence and a lack of reliable reading mechanisms. If these obstacles can be overcome, quantum computers may solve problems in artificial intelligence, cybersecurity, drug design and more exponentially faster than classical computers.
This document provides an introduction to quantum computing. It discusses how quantum computers work using quantum bits (qubits) that can exist in superpositions of states unlike classical bits. Qubits can become entangled so that operations on one qubit affect others. Implementing qubits requires isolating quantum systems to avoid decoherence. Challenges include controlling decoherence, but research continues on algorithms, hardware, and bringing theoretical quantum computers to practical use. Quantum computers may solve problems intractable for classical computers.
This document provides an overview of quantum computers. It begins by explaining that quantum physics must be understood first as quantum computers are based on quantum mechanical principles rather than classical physics. It then defines a quantum computer as a machine that performs calculations based on the laws of quantum mechanics. The document goes on to discuss key quantum properties like superposition and entanglement that quantum computers exploit. It also covers qubits, quantum gates, applications, advantages, challenges, and concludes by stating that quantum computers will require a new way of looking at computing.
The document summarizes research on understanding charge transport in low dimensional semiconductor nanostructures embedded in an insulating matrix. Specifically, it examines current-voltage characteristics of germanium nanowire arrays in an alumina matrix as a function of temperature. Key findings include:
1) At room temperature, conduction follows Ohm's law at low voltages and Mott-Gurney's space charge limited current law at higher voltages.
2) With decreasing temperature, conduction transitions from a trap-free regime to an exponentially distributed trap regime.
3) Mobility decreases with decreasing temperature, and activation energy is extracted from an Arrhenius plot, found to be 85 meV at low temperatures and 301 meV
What is Quantum Computing
What is Quantum bits (Qubit)
What is Reversible Logic gates and Logic Circuits
What is Quantum Neuron (Quron)
What are the methods of implementing ANN using Quantum computing
A silicon based nuclear spin quantum computerGabriel O'Brien
This document describes a proposed scheme for building a quantum computer using the nuclear spins of phosphorus donor atoms embedded in silicon. Key points:
- Information would be encoded in the nuclear spins of phosphorus atoms acting as quantum bits (qubits).
- Logical operations on the qubits would be performed by manipulating the hyperfine interaction between electron and nuclear spins using electric fields from nearby gates.
- Measurements of the nuclear spin states could be made by transferring spin polarization to electrons and detecting the effect on electron orbital wavefunctions using capacitance measurements.
- Silicon is proposed as the host semiconductor because it contains only spin-0 isotopes, isolating the phosphorus donor nuclear spins from decoherence caused by host
On the atomic scale matter obeys the rules of quantum mechanics, which are quite different from the classical rules that determine the properties of conventional logic gates. So if computers are to become smaller in the future, new, quantum technology must replace or supplement for this.
This document provides an overview of quantum computing. It discusses how quantum computing works using quantum bits that can exist in superposition allowing both 1s and 0s to be represented simultaneously. Several methods for demonstrating quantum computing are described, including nuclear magnetic resonance, ion traps, quantum dots, and optical techniques. Quantum computing provides advantages like faster processing speeds and an exponential increase in storage capacity. Challenges that must be overcome include error correction and fighting decoherence. The document outlines desirable features for an ideal quantum computing system.
This lecture provides an overview of electromagnetic fields and Maxwell's equations. It introduces key concepts including electric and magnetic fields, Maxwell's equations in integral and differential form, electromagnetic boundary conditions, and electromagnetic fields in materials. Maxwell's equations are the fundamental laws of classical electromagnetics and govern all electromagnetic phenomena. The lecture also discusses phasor representation for time-harmonic fields.
This document summarizes a simulation of two electrons in silicon under an externally applied potential. The simulation models the electron wavefunctions in two dimensions using a Schrodinger-Poisson solver. It calculates the quadrupole interaction between electrons through iterative calculations of the electron wavefunctions and their electrostatic interactions. Results show the quadrupole coupling increases with more prolate wavefunctions and is sufficient for use in quantum logic gates at realistic scales. Future work could provide more accurate results at higher resolution or extend the simulation to three dimensions.
This document contains a sample physics exam for Class XII with 30 questions covering topics such as electromagnetism, optics, modern physics, and semiconductor devices. The exam is 3 hours long and contains short answer and long answer questions worth varying point values. An introduction provides instructions on the number and type of questions, and lists important physical constants that may be needed.
The document discusses various mechanisms of charge carrier transport in semiconductors including drift and diffusion. It defines carrier drift as the movement of electrons and holes under the influence of an applied electric field. Carrier mobility is introduced as a material property that determines how fast carriers drift in response to an electric field. Diffusion is defined as the movement of carriers from areas of high concentration to low concentration due to random thermal motion. The Einstein relation links diffusion and mobility through the carrier temperature. Total current in a semiconductor is the sum of drift and diffusion currents.
Quantum Computation for Predicting Electron and Phonon Properties of SolidsKAMAL CHOUDHARY
This document outlines a workflow for using quantum computing to simulate electron and phonon properties of solids. It discusses the motivation for using quantum bits to simulate quantum systems more easily. It provides background on band theory of solids, quantum algorithms like VQE and circuit models. The workflow is then applied to calculate properties of aluminum metal and over 1000 other materials using classical and quantum solvers. Future opportunities and challenges are also discussed.
The Quantum computing has become a buzzword now a days, however it has not been the favorite of the researchers until recent times.
Let's follow about
What's Quantum Computing?
It's Evolution
Primary Focus
Future
The document discusses the Superconducting Quantum Interference Device (SQUID), which uses the Josephson junction effect to achieve extremely sensitive magnetic flux-to-voltage conversion. SQUIDs can be used to precisely measure small magnetic fields and currents. The document outlines how SQUIDs work and their applications in measuring DC and AC magnetic fields. It also describes temperature control systems, reciprocating sample options (RSO), and considerations for optimizing RSO measurements.
This document presents a new method for analyzing transient voltage distributions in transformer windings. It models the electric, magnetic, and current fields as equivalent circuits consisting of interconnected electric and magnetic networks.
The electric network models the voltage distribution within each winding section using resistances and emfs derived from the geometry. The magnetic network models the flux paths using reluctances, which is then converted to an equivalent inductance network. Capacitances model the electric fields within and between sections.
The electric, magnetic, and capacitance networks are coupled through ideal transformers to form a single overall mathematical model without mutual inductances. The model can analyze transient voltages inside the windings resulting from any applied terminal overvoltage waveform. An example application
This document summarizes the current state of semiconductor qubits for quantum applications. It discusses different types of semiconductor qubits including charge qubits in gate-controlled quantum dots, spin qubits in quantum dots, dopants, and color centers. For each type of qubit, it evaluates their potential for applications in quantum sensing, simulation, computation, and communication. Overall, the review finds that semiconductor qubits show promise for diverse applications depending on their specific material properties and degrees of freedom, such as charge, spin, or photon interfaces.
This document discusses using WiTricity technology to wirelessly power sensor nodes in wireless sensor networks (WSNs). WiTricity uses electromagnetic resonance to transfer energy between two coils from up to 3 meters away. The document proposes using WiTricity to overcome the power constraints of WSNs by continuously charging sensor nodes. It examines requirements for integrating WiTricity into WSNs, including techniques for multi-hop wireless energy transfer. It also discusses hardware needs of immortal sensor nodes and proposes charging protocols for flat and clustered WSN topologies. The document concludes that WiTricity has the potential to free WSNs from cables and batteries by allowing wireless energy transfer.
osama-quantum-computing and its uses and applicationsRachitdas2
This document provides an overview of quantum computing. It begins with introductions to quantum mechanics and the basic concept of a quantum computer. Qubits can represent superpositions of states allowing quantum computers to perform massive parallelism. Data is represented using qubit states and operations involve entanglement. Measurement causes superpositions to collapse probabilistically. While quantum mechanics is strange, quantum computing may enable solving problems like factoring exponentially faster than classical computers. The document questions the Church-Turing thesis in light of quantum computing's ability.
Josephson junctions are superconductor-insulator-superconductor devices that exhibit the Josephson effect. This allows a superconducting current to tunnel through the insulating barrier while maintaining a fixed phase relationship between the superconductors. This quantum coherence effect can be used to create superconducting qubits by trapping quantum states in potential wells created by Josephson junction circuits. However, challenges include intrinsic decoherence from coupling to the environment and fabrication variations, as well as noise-induced transitions between states. Current research focuses on identifying and reducing sources of decoherence to improve qubit performance and manipulation.
Josephson junctions are superconductor-insulator-superconductor devices that exhibit the Josephson effect. This allows a superconducting current to tunnel through the insulating barrier while maintaining a fixed phase relationship between the superconductors. This quantum phase coherence enables Josephson junctions to be used as qubits and quantum circuits. Common Josephson junction devices include Cooper pair boxes, flux qubits, and current-biased junctions that utilize quantized energy levels as qubit states. While Josephson junctions show promise for scalable quantum computing, challenges include intrinsic decoherence, noise from the environment, unwanted transitions, and measurement crosstalk between qubits. Current research aims to better understand and mitigate sources of decoherence while improving qubit control
SINGLE ELECTRON TRANSISTOR: APPLICATIONS & PROBLEMSVLSICS Design
1) Single electron transistors (SETs) function by controlling the transfer of individual electrons between small conducting islands. They exhibit quantum properties like Coulomb blockade and oscillations that enable applications.
2) SETs consist of a small conducting island coupled to source and drain leads by tunnel junctions. Current flows when the applied voltage exceeds the threshold voltage needed to overcome Coulomb blockade.
3) Potential SET applications include ultrasensitive electrometry, quantum dot spectroscopy, standards for current and temperature, and detection of terahertz radiation. Challenges include fabricating small enough islands and addressing issues like background charge.
Single Electron Transistor: Applications & Problems VLSICS Design
1) Single electron transistors (SETs) function by controlling the transfer of individual electrons between small conducting islands. SETs exhibit quantum properties like Coulomb blockade and oscillations that enable applications in electronics.
2) SETs consist of a small conducting island coupled to source and drain leads by tunnel junctions. Current flows when the applied voltage exceeds the threshold voltage needed to overcome Coulomb blockade.
3) Potential SET applications include ultrasensitive electrometry, quantum dot spectroscopy, standards for current and temperature, and detection of terahertz radiation. However, challenges remain for room temperature operation and linking SETs into larger circuits.
Wireless power transmission from solar power satelliteSaquib Maqsood
In the near future due to extensive use of energy, limited supply of resources and the pollution in environment from present resources e.g. (wood, coal, fossil fuel) etc, alternative sources of energy and new ways to generate energy which are efficient, cost effective and produce minimum losses are of great concern. Wireless electricity (Power) transmission (WET) has become a focal point as research point of view and nowadays lies at top 10 future hot burning technologies that are under research these days. This paper presents the concept of transmitting power wirelessly to reduce transmission and distribution losses. The wired distribution losses are 70 - 75% efficient. We cannot imagine the world without electric power which is efficient, cost effective and produce minimum losses is of great concern.This paper tells us the benefits of using WET technology specially by using Solar based Power satellites (SBPS) and also focuses that how we make electric system cost effective, optimized and well organized. Solar Power Satellite (SPS) is an energy system which collects solar energy in space and transmits it to the ground. It has been believed as a promising infrastructure to resolve global environmental and energy problems for human beings. Microwave power transmission has been investigated and demonstrated for more than 40 years, but still requires further research regarding high-efficiency power conversion and high-accuracy beam control for SPS application. Moreover, attempts are made to highlight future issues so as to index some emerging solutions.
A quantum computer uses quantum mechanics phenomena like superposition and entanglement to perform computations. In a quantum computer, a qubit can represent a 0 and 1 simultaneously using superposition. This allows quantum computers to evaluate functions on all possible inputs at once. Measurement causes the superposition to collapse to a single value. Quantum computers may be able to solve certain problems like factoring exponentially faster than classical computers due to these quantum effects. However, building large-scale, reliable quantum computers remains a significant technical challenge.
A silicon based nuclear spin quantum computerGabriel O'Brien
This document describes a proposed scheme for building a quantum computer using the nuclear spins of phosphorus donor atoms embedded in silicon. Key points:
- Information would be encoded in the nuclear spins of phosphorus atoms acting as quantum bits (qubits).
- Logical operations on the qubits would be performed by manipulating the hyperfine interaction between electron and nuclear spins using electric fields from nearby gates.
- Measurements of the nuclear spin states could be made by transferring spin polarization to electrons and detecting the effect on electron orbital wavefunctions using capacitance measurements.
- Silicon is proposed as the host semiconductor because it contains only spin-0 isotopes, isolating the phosphorus donor nuclear spins from decoherence caused by host
On the atomic scale matter obeys the rules of quantum mechanics, which are quite different from the classical rules that determine the properties of conventional logic gates. So if computers are to become smaller in the future, new, quantum technology must replace or supplement for this.
This document provides an overview of quantum computing. It discusses how quantum computing works using quantum bits that can exist in superposition allowing both 1s and 0s to be represented simultaneously. Several methods for demonstrating quantum computing are described, including nuclear magnetic resonance, ion traps, quantum dots, and optical techniques. Quantum computing provides advantages like faster processing speeds and an exponential increase in storage capacity. Challenges that must be overcome include error correction and fighting decoherence. The document outlines desirable features for an ideal quantum computing system.
This lecture provides an overview of electromagnetic fields and Maxwell's equations. It introduces key concepts including electric and magnetic fields, Maxwell's equations in integral and differential form, electromagnetic boundary conditions, and electromagnetic fields in materials. Maxwell's equations are the fundamental laws of classical electromagnetics and govern all electromagnetic phenomena. The lecture also discusses phasor representation for time-harmonic fields.
This document summarizes a simulation of two electrons in silicon under an externally applied potential. The simulation models the electron wavefunctions in two dimensions using a Schrodinger-Poisson solver. It calculates the quadrupole interaction between electrons through iterative calculations of the electron wavefunctions and their electrostatic interactions. Results show the quadrupole coupling increases with more prolate wavefunctions and is sufficient for use in quantum logic gates at realistic scales. Future work could provide more accurate results at higher resolution or extend the simulation to three dimensions.
This document contains a sample physics exam for Class XII with 30 questions covering topics such as electromagnetism, optics, modern physics, and semiconductor devices. The exam is 3 hours long and contains short answer and long answer questions worth varying point values. An introduction provides instructions on the number and type of questions, and lists important physical constants that may be needed.
The document discusses various mechanisms of charge carrier transport in semiconductors including drift and diffusion. It defines carrier drift as the movement of electrons and holes under the influence of an applied electric field. Carrier mobility is introduced as a material property that determines how fast carriers drift in response to an electric field. Diffusion is defined as the movement of carriers from areas of high concentration to low concentration due to random thermal motion. The Einstein relation links diffusion and mobility through the carrier temperature. Total current in a semiconductor is the sum of drift and diffusion currents.
Quantum Computation for Predicting Electron and Phonon Properties of SolidsKAMAL CHOUDHARY
This document outlines a workflow for using quantum computing to simulate electron and phonon properties of solids. It discusses the motivation for using quantum bits to simulate quantum systems more easily. It provides background on band theory of solids, quantum algorithms like VQE and circuit models. The workflow is then applied to calculate properties of aluminum metal and over 1000 other materials using classical and quantum solvers. Future opportunities and challenges are also discussed.
The Quantum computing has become a buzzword now a days, however it has not been the favorite of the researchers until recent times.
Let's follow about
What's Quantum Computing?
It's Evolution
Primary Focus
Future
The document discusses the Superconducting Quantum Interference Device (SQUID), which uses the Josephson junction effect to achieve extremely sensitive magnetic flux-to-voltage conversion. SQUIDs can be used to precisely measure small magnetic fields and currents. The document outlines how SQUIDs work and their applications in measuring DC and AC magnetic fields. It also describes temperature control systems, reciprocating sample options (RSO), and considerations for optimizing RSO measurements.
This document presents a new method for analyzing transient voltage distributions in transformer windings. It models the electric, magnetic, and current fields as equivalent circuits consisting of interconnected electric and magnetic networks.
The electric network models the voltage distribution within each winding section using resistances and emfs derived from the geometry. The magnetic network models the flux paths using reluctances, which is then converted to an equivalent inductance network. Capacitances model the electric fields within and between sections.
The electric, magnetic, and capacitance networks are coupled through ideal transformers to form a single overall mathematical model without mutual inductances. The model can analyze transient voltages inside the windings resulting from any applied terminal overvoltage waveform. An example application
This document summarizes the current state of semiconductor qubits for quantum applications. It discusses different types of semiconductor qubits including charge qubits in gate-controlled quantum dots, spin qubits in quantum dots, dopants, and color centers. For each type of qubit, it evaluates their potential for applications in quantum sensing, simulation, computation, and communication. Overall, the review finds that semiconductor qubits show promise for diverse applications depending on their specific material properties and degrees of freedom, such as charge, spin, or photon interfaces.
This document discusses using WiTricity technology to wirelessly power sensor nodes in wireless sensor networks (WSNs). WiTricity uses electromagnetic resonance to transfer energy between two coils from up to 3 meters away. The document proposes using WiTricity to overcome the power constraints of WSNs by continuously charging sensor nodes. It examines requirements for integrating WiTricity into WSNs, including techniques for multi-hop wireless energy transfer. It also discusses hardware needs of immortal sensor nodes and proposes charging protocols for flat and clustered WSN topologies. The document concludes that WiTricity has the potential to free WSNs from cables and batteries by allowing wireless energy transfer.
osama-quantum-computing and its uses and applicationsRachitdas2
This document provides an overview of quantum computing. It begins with introductions to quantum mechanics and the basic concept of a quantum computer. Qubits can represent superpositions of states allowing quantum computers to perform massive parallelism. Data is represented using qubit states and operations involve entanglement. Measurement causes superpositions to collapse probabilistically. While quantum mechanics is strange, quantum computing may enable solving problems like factoring exponentially faster than classical computers. The document questions the Church-Turing thesis in light of quantum computing's ability.
Josephson junctions are superconductor-insulator-superconductor devices that exhibit the Josephson effect. This allows a superconducting current to tunnel through the insulating barrier while maintaining a fixed phase relationship between the superconductors. This quantum coherence effect can be used to create superconducting qubits by trapping quantum states in potential wells created by Josephson junction circuits. However, challenges include intrinsic decoherence from coupling to the environment and fabrication variations, as well as noise-induced transitions between states. Current research focuses on identifying and reducing sources of decoherence to improve qubit performance and manipulation.
Josephson junctions are superconductor-insulator-superconductor devices that exhibit the Josephson effect. This allows a superconducting current to tunnel through the insulating barrier while maintaining a fixed phase relationship between the superconductors. This quantum phase coherence enables Josephson junctions to be used as qubits and quantum circuits. Common Josephson junction devices include Cooper pair boxes, flux qubits, and current-biased junctions that utilize quantized energy levels as qubit states. While Josephson junctions show promise for scalable quantum computing, challenges include intrinsic decoherence, noise from the environment, unwanted transitions, and measurement crosstalk between qubits. Current research aims to better understand and mitigate sources of decoherence while improving qubit control
SINGLE ELECTRON TRANSISTOR: APPLICATIONS & PROBLEMSVLSICS Design
1) Single electron transistors (SETs) function by controlling the transfer of individual electrons between small conducting islands. They exhibit quantum properties like Coulomb blockade and oscillations that enable applications.
2) SETs consist of a small conducting island coupled to source and drain leads by tunnel junctions. Current flows when the applied voltage exceeds the threshold voltage needed to overcome Coulomb blockade.
3) Potential SET applications include ultrasensitive electrometry, quantum dot spectroscopy, standards for current and temperature, and detection of terahertz radiation. Challenges include fabricating small enough islands and addressing issues like background charge.
Single Electron Transistor: Applications & Problems VLSICS Design
1) Single electron transistors (SETs) function by controlling the transfer of individual electrons between small conducting islands. SETs exhibit quantum properties like Coulomb blockade and oscillations that enable applications in electronics.
2) SETs consist of a small conducting island coupled to source and drain leads by tunnel junctions. Current flows when the applied voltage exceeds the threshold voltage needed to overcome Coulomb blockade.
3) Potential SET applications include ultrasensitive electrometry, quantum dot spectroscopy, standards for current and temperature, and detection of terahertz radiation. However, challenges remain for room temperature operation and linking SETs into larger circuits.
Wireless power transmission from solar power satelliteSaquib Maqsood
In the near future due to extensive use of energy, limited supply of resources and the pollution in environment from present resources e.g. (wood, coal, fossil fuel) etc, alternative sources of energy and new ways to generate energy which are efficient, cost effective and produce minimum losses are of great concern. Wireless electricity (Power) transmission (WET) has become a focal point as research point of view and nowadays lies at top 10 future hot burning technologies that are under research these days. This paper presents the concept of transmitting power wirelessly to reduce transmission and distribution losses. The wired distribution losses are 70 - 75% efficient. We cannot imagine the world without electric power which is efficient, cost effective and produce minimum losses is of great concern.This paper tells us the benefits of using WET technology specially by using Solar based Power satellites (SBPS) and also focuses that how we make electric system cost effective, optimized and well organized. Solar Power Satellite (SPS) is an energy system which collects solar energy in space and transmits it to the ground. It has been believed as a promising infrastructure to resolve global environmental and energy problems for human beings. Microwave power transmission has been investigated and demonstrated for more than 40 years, but still requires further research regarding high-efficiency power conversion and high-accuracy beam control for SPS application. Moreover, attempts are made to highlight future issues so as to index some emerging solutions.
A quantum computer uses quantum mechanics phenomena like superposition and entanglement to perform computations. In a quantum computer, a qubit can represent a 0 and 1 simultaneously using superposition. This allows quantum computers to evaluate functions on all possible inputs at once. Measurement causes the superposition to collapse to a single value. Quantum computers may be able to solve certain problems like factoring exponentially faster than classical computers due to these quantum effects. However, building large-scale, reliable quantum computers remains a significant technical challenge.
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Luo_SC_mc_butorqwertyuiomabsvsbsbsjC.ppt
1. UNIVERSITY OF NOTRE DAME
Xiangning Luo
EE 698A
Department of Electrical Engineering, University of Notre Dame
Superconducting Devices for Quantum
Computation
2. UNIVERSITY OF NOTRE DAME
Outline of Presentation
Introduction to quantum computation
Superconducting qubit devices
Josephson charge qubit
Qubits based on the flux degree of freedom
3. UNIVERSITY OF NOTRE DAME
Quantum Computation
Classical Computation:
Classical logic bit: “0” and “1”
Quantum Computation:
Quantum bit, “Qubit”, can be manipulated using the rules of quantum physics
Orthogonal quantum states |0> , |1> and their superposition |Ψ> = c0|0> + c1|1>
A Quantum state of M bits is a superposition of 2M states.
The quantum computation is a parallel computation in which all 2M basis
vectors are acted upon at the same time.
If one wanted to simulate a quantum computer using a classical
computer one would need to multiply together 2M dimensional unitary
matrices, to simulate each step.
A quantum computer can factorize a 250-digit number in seconds while
an ordinary computer will take 800 000 years!
4. UNIVERSITY OF NOTRE DAME
Quantum Computation
|Ψ(0)>
Preparation:
The initial preparation of the state defines a
wave function at time t0=0.
|Ψ(1)>
….
|Ψ(n)>
P(Ф)=|<Ф|Ψ(n)>|2
U(t1,t0)
U(t2,t1)
U(tn,tn-1)
0
1
n
State evolution:
Evolved by a sequence of unitary operations
Measurement:
Quantum measurement is projective.
Collapsed by measurement of the state
5. UNIVERSITY OF NOTRE DAME
Quantum Logic Gates
Question: How to implement a general unitary operator?
Answer: Introduce a complete set of logic gates.
Any possible operation on an qubit register can be represented in
terms of a suitable sequence of actions of such elementary logic gates
It is proved that an arbitrary 2x2 unitary matrix may be decomposed as
U =
2
/
2
/
2
/
2
/
0
0
2
cos
2
sin
2
sin
2
cos
0
0
i
i
i
i
i
e
e
e
e
e
where α,β,ν, and δ are real-valued.
6. UNIVERSITY OF NOTRE DAME
Superconducting Qubit Devices
Any quantum mechanically coherent system could be used to
implement the ideas of quantum computation.
- single photons
- nuclear spins
- trapped ions
- superconductors
Advantage of solid state implementations
Possibility of a scalable implementation of the qubits
Superconducting devices
The minimum levels of decoherence among solid state
implementations.
A promising implementation of qubit.
two kinds of qubit devices either based on charge or flux degrees of
freedom.
8. UNIVERSITY OF NOTRE DAME
The Cooper Pair Box Qubit
System Hamiltonian
A sudden square pulse is applied to the gate Vg
The square gate pulse lasts for some time ∆t
Vg returns to zero
The probability that the state does not return to the ground state
Energy state of n Cooper pair
Tunneling term
12. UNIVERSITY OF NOTRE DAME
The superconducting Flux Qubit
I. Chiorescu et al., Science 299, 1869 (2003).
Coherent time evolution between two quantum states was observed.
Flux qubit consists of 3 Josephson junctions arranged in a superconducting loop.
Two states carrying opposite persistent currents are used to represent |0> and |1>.
External flux near half Φ0=h/2e is applied.
A SQIUD is attached directly.
MW line provides microwave current bursts inducing oscillating magnetic fields.
Current line provides the measuring pulse and voltage line allows the readout of the
switching pulse.
Φ=h/4e
clockwise anticlockwise
symmetric superposition
antisymmetric superposition
13. UNIVERSITY OF NOTRE DAME
The superconducting Flux Qubit
I. Chiorescu et al., Science 299, 1869 (2003).
Qubit energy separation is adjusted by
changing the external flux.
Resonant absorption peaks/dips are
observed.
Dots are measured peak/dip positions
obtained by varying frequency of MW
pulse.
The continuous line is a numerical fit
giving an energy gap ∆ = 3.4 GHz in
agreement of numerical simulations.
Measurements of two energy levels of qubit
14. UNIVERSITY OF NOTRE DAME
The superconducting Flux Qubit
I. Chiorescu et al., Science 299, 1869 (2003).
Different MW pulse sequences are used to
induce coherent quantum dynamics of the
qubit in the time domain.
Rabi oscillations - when the MW frequency
equals the energy difference of the qubit,
the qubit oscillates between the ground
state and the excited state.
Resonant MW pulse of variable length with
frequency F = E10 is applied.
The pulse length defines the relative
occupancy of the ground state and the
excited state.
The switching probability is obtained by
repeating the whole sequence of
reequilibration, microwave control pulses,
and readout typically 5000 times.
MW F = 6.6GHz
MW power 0dbm, -6dbm, and -12dbm
Linear dependence of the Rabi
frequency on the MW amplitude, a key
signature of the Rabi process.
Decay times up to ~150 ns results in
hundreds of coherent oscillations.
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