Quantum Computing

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Quantum Computing

• Prepared by Vishal Garg
• CSE 5th Semester
• www.linkedin.com/in/vishalgarg4

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What is Quantum Computing?

• Quantum computing is the computer technology
  based on the principles of quantum theory, which
  explains the nature and behaviour of energy and
  matter on the quantum (atomic and subatomic)
  level.
• Quantum computing is essentially harnessing and
  exploiting the amazing laws of quantum mechanics
  to process information.

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What Is Quantum?

• A classical binary bit is always in one of two
  states0 or 1while a quantum bit or qubit exists
  in both of its possible states at once, a
  condition known as a superposition.
• An operation on a qubit thus exploits its quantum
  weirdness by allowing many computations to be
  performed in parallel.
• A two-qubit system would perform the operation
  on 4 values, a three-qubit system on 8 and so
  forth.

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What Is Quantum?
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What Is Quantum?

• Rather than performing each calculation in turn
  on the current single state of its bits, as a
  classical computer does, a quantum computer's
  sequence of qubits can be in every possible
  combination of 1s and 0s at once.
• This allows the computer to test every possible
  solution simultaneously and to perform certain
  complex calculations exponentially faster than a
  classical computer.
• One curious feature of a qubit is that measuring
  it causes it to "collapse" into a single
  classical known state0 or 1 againand lose its
  quantum properties.

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What Is Quantum?

• Many quantum algorithms are non-deterministic
  they find many different solutions in parallel,
  only one of which can be measured, so they
  provide the correct solution with only a certain
  known probability.
• Running the calculation several times will
  increase the chances of finding the correct
  answer but also may reduce quantum computing's
  speed advantage.

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History of Quantum Computing

• Quantum computing tends to trace its roots back
  to a 1959 speech by Richard P. Feynman in which
  he spoke about the idea of exploiting quantum
  effects to create more powerful computers.
• This speech is also generally considered the
  starting point of nanotechnology.
• In 1984, David Deutsch was at a computation
  theory conference and began to wonder about the
  possibility of designing a computer that was
  based exclusively on quantum rules, then
  published his breakthrough paper a few months
  later.
• With this, the race began to exploit his idea.

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History of Quantum Computing

• In 1994, ATT's Peter Shor devised an algorithm
  that could use only 6 qubits to perform some
  basic factorizations ... more cubits the more
  complex the numbers requiring factorization
  became, of course.
• The first, a 2-qubit quantum computer in 1998,
  could perform trivial calculations before losing
  decoherence after a few nanoseconds.
• In 2000, teams successfully built both a 4-qubit
  and a 7-qubit quantum computer.
• Research on the subject is still very active,
  although some physicists and engineers express
  concerns over the difficulties involved in
  upscaling these experiments to full-scale
  computing systems.

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How a Quantum Computer Would Work?

• A quantum computer, would store information as
  either a 1, 0, or a quantum superposition of the
  two states. Such a "quantum bit," called a qubit,
  allows for far greater flexibility than the
  binary system.
• Specifically, a quantum computer would be able to
  perform calculations on a far greater order of
  magnitude than traditional computers ... a
  concept which has serious concerns and
  applications in the realm of cryptography
  encryption.
• Some fear that a successful practical quantum
  computer would devastate the world's financial
  system by ripping through their computer security
  encryptions, which are based on factoring large
  numbers that literally cannot be cracked by
  traditional computers within the life span of the
  universe.
• A quantum computer, on the other hand, could
  factor the numbers in a reasonable period of time.

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How a Quantum Computer Would Work?

• If the qubit is in a superposition of the 1 state
  and the 0 state, and it performed an calculation
  with another qubit in the same superposition,
  then one calculation actually obtains 4 results
  a 1/1 result, a 1/0 result, a 0/1 result, and a
  0/0 result.
• This is a result of the mathematics applied to a
  quantum system when in a state of decoherence,
  which lasts while it is in a superposition of
  states until it collapses down into one state.
• The ability of a quantum computer to perform
  multiple computations simultaneously (or in
  parallel, in computer terms) is called quantum
  parallelism).

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How a Quantum Computer Would Work?

• if there are n qubits in the supercomputer, then
  it will have 2n different states.
• So experimentally, it can hold more information
  as compared to regular digital bits thereby
  increasing the speed of the system exponentially.
• The qubits are dynamic and are only the
  probabilistic superposition of all of their
  states.
• So, the accurate measurement is difficult and
  requires complex algorithms such as Shors
  algorithm

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Superposition and Entanglement?

• Superposition is essentially the ability of a
  quantum system to be in multiple states at the
  same time that is, something can be here and
  there, or up and down at the same time.
• Entanglement is an extremely strong correlation
  that exists between quantum particles so
  strong, in fact, that two or more quantum
  particles can be inextricably linked in perfect
  unison, even if separated by great distances.
• The particles are so intrinsically connected,
  they can be said to dance in instantaneous,
  perfect unison, even when placed at opposite ends
  of the universe.
• This seemingly impossible connection inspired
  Einstein to describe entanglement as spooky
  action at a distance.

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What can a quantum computer do that a classical
computer cant?

• Factoring large numbers, for starters.
• Multiplying two large numbers is easy for any
  computer.
• But calculating the factors of a very large (say,
  500-digit) number, on the other hand, is
  considered impossible for any classical computer.
• In 1994, a mathematician from the Massachusetts
  Institute of Technology (MIT) Peter Shor, who was
  working at ATT at the time, unveiled that if a
  fully working quantum computer was available, it
  could factor large numbers easily.

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I dont want to factor very large numbers

• In fact, the difficulty of factoring big numbers
  is the basis for much of our present day
  cryptography.
• RSA encryption, the method used to encrypt your
  credit card number when youre shopping online,
  relies completely on the factoring problem.
• Since factoring is very hard, no eavesdropper
  will be able to access your credit card number
  and your bank account is safe.
• Unless, that is, somebody has built a quantum
  computer and is running Peter Shor's algorithm!

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So a quantum computer will be able to hack into
my private data?

• Dont worry classical cryptography is not
  completely jeopardized.
• This is where quantum mechanics comes in very
  handy once again
• Quantum Key Distribution (QKD) allows for
  the distribution of completely random keys at
  a distance.

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How can quantum mechanics create these
ultra-secret keys?

• Quantum key distribution relies on another
  interesting property of quantum mechanics any
  attempt to observe or measure a quantum system
  will disturb it.
• Photons have a unique measurable property called
  polarization.

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What is required to build a quantum computer?

• We need qubits that behave the way we want them
  to.
• These qubits could be made of photons, atoms,
  electrons, molecules or perhaps something else.
• Scientists at IQC are researching a large array
  of them as potential bases for quantum computers.
  
• But qubits are notoriously tricky to manipulate,
  since any disturbance causes them to fall out of
  their quantum state (or decohere).

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What is required to build a quantum computer?

• The field of quantum error correction examines
  how to stave off decoherence and combat other
  errors.
• Every day, researchers at IQC and around the
  world are discovering new ways to make qubits
  cooperate.

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Challenges To Quantum Computing

• Decoherence
• One of the biggest challenges is to remove
  quantum decoherence.
• Decoherence in a laymans language could be
  understood as the loss of information to the
  environment. The decoherence of the qubits occurs
  when the system interacts with the surrounding in
  a thermodynamically irreversible manner.
• So, the system needs to be carefully isolated.
  Freezing the qubits is one of the ways to prevent
  decoherence.

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Challenges To Quantum Computing

• Interference
• During the computation phase of a quantum
  calculation, the slightest disturbance in a
  quantum system (say a stray photon or wave of EM
  radiation) causes the quantum computation to
  collapse, a process known as de-coherence.
• A quantum computer must be totally isolated from
  all external interference during the computation
  phase.
• Some success has been achieved with the use of
  qubits in intense magnetic fields, with the use
  of ions.

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Challenges To Quantum Computing

• Error correction
• Because truly isolating a quantum system has
  proven so difficult, error correction systems for
  quantum computations have been developed.
• Qubits are not digital bits of data, thus they
  cannot use conventional (and very effective)
  error correction, such as the triple redundant
  method.
• Given the nature of quantum computing, error
  correction is ultra critical - even a single
  error in a calculation can cause the validity of
  the entire computation to collapse.

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Challenges To Quantum Computing

• Output observance
• Closely related to the above two, retrieving
  output data after a quantum calculation is
  complete risks corrupting the data.
• In an example of a quantum computer with 500
  qubits, we have a 1 in 2500 chance of observing
  the right output if we quantify the output.
• Thus, what is needed is a method to ensure that,
  as soon as all calculations are made and the act
  of observation takes place, the observed value
  will correspond to the correct answer.
• How can this be done? It has been achieved by
  Grover with his database search algorithm, that
  relies on the special "wave" shape of the
  probability curve inherent in quantum computers,
  that ensures, once all calculations are done, the
  act of measurement will see the quantum state
  decohere into the correct answer.

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If Its So Complex, Why Is Everyone After Quantum
Computing?

• A fully functional quantum computer would require
  around a million atoms. And right now, we are at
  a mere thousand.
• But, what would happen if we reach that limit or
  even its half?
• Genome sequencing or Tracking weather patterns
• Second, the modern day encryption systems are
  entirely based on the limitations of the regular
  computers.
• Quantum computing wont be of changing your lives
  in day to day operations, but a quantum
  communication network would definitely provide a
  better and secure network.

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