Quantum Error Correction Had To Overcome Three Important Obstacles: (1) the no-cloning theorem, which states that it is not possible to copy unknown quantum states (2) measuring a quantum system affects its state (3) errors on qubits can be arbitrary rotations in Hilbert space(1), compared with simple bit flips for classical bits. 

1. QUANTUM ERROR CORRECTION
Overcoming Decoherence
By : Professor Lili Saghafi
Annual Quantum
Information Processing
(AQIP) Conference
Jan. 2016
@Lili_PLS

2. QUANTUM COMPUTING
• Quantum device works on qubits instead of bits.
• Logical bits, can be in a “1” or a “0” state.
• A qubit can be a 0, a 1, or a combination of both
simultaneously
• Quantum physics allows for qubits to take on
multiple configurations simultaneously (e.G. An
equally-weighted superposition of 0 and 1), which is
not happening in conventional computing.

3. QUANTUM COMPUTING
• In the 1990s scientists proved that this property
could be used for solving certain tasks, such as
decryption
• Laws of physics dictate the behaviour of qubits
• Decoherence and instability of the behaviour of
qubits are the main problem causing errors

4. QUANTUM COMPUTING
• Qubits can take many physical forms, such as
trapped ions, neutral atoms, photons,
superconducting devices and more.
• In each case, the great advantage is that qubits can
be used to perform certain kinds of operations
exponentially faster than conventional digital
computers
• qubit’s superposition of states is extremely fragile.
• Once the qubit is prepared in the desired condition,
any contact with the environment can destroy that
condition -- a process called “decoherence.”

5. QUANTUM COMPUTER

6. DECOHERENCE
• One of the biggest challenges faced by quantum
computing researchers is called Decoherence
• Decoherence is the tendency of quantum systems
to be disturbed.
• This vulnerability to noise leads to errors, which can
be overcome by quantum error correction.
• Because error correction techniques are themselves
susceptible to noise, it is crucial to develop fault-
tolerant correction.

7. CONTROLLING DECOHERENCE
Diagram by Wayne Witzel of CMTC shows qubit electron (center) surrounded and affected by random nuclear spins of
atoms in the material’s lattice.

8. DECOHERENCE
• It is not that the simple physical contact are the
only threat to the qubit’s condition
• It is in the nature of quantum systems that objects
interfere with, and are affected by, the state of
other objects , whether they are in immediate
contact or not.
• The qubit’s state is “coupled” to its environment
and so it is vulnerable.

9. DECOHERENCE example
• If a qubit is embodied in the “spin” direction of an
electron -- which is in a “coherent” superposition of
both “up” and “down”
• This condition can be degraded by the influence of
the spins of atoms that are quite far away, forcing
the electron to collapse into decoherence.
• This process can happen very rapidly, sometimes
within nanoseconds
• So we need to find ways to sustain the qubit’s
coherent state at least long enough to use it for
information processing

10. POPULAR ALTERNATIVE QUBIT
CANDIDATE, SQUID
• popular alternative qubit candidate: the
superconducting quantum interference device, or
SQUID.
• A SQUID consists of one or more Josephson
junctions (superconducting elements separated by
a very thin insulating layer) arranged in a loop.
• What transpires across the barrier is affected by
exquisitely small changes in quantum conditions.
• In commercial use, SQUIDs are used to detect the
faintest magnetic fields.
• In the lab, they can be configured in various ways to
examine quantum phenomena -- and perhaps to
form the basis for practical qubits.

11. POPULAR ALTERNATIVE QUBIT
CANDIDATE, SQUID
• Different quantum states can be prepared by
cooling the SQUID to 25 milliKelvin (which brings
the SQUID to the lowest-energy or ground state)
and then exposing the device to microwave bursts
at various frequencies.

12. Josephson Junction
• A Josephson Junction is a quantum mechanical
device, which is made of two superconducting
electrodes separated by a barrier (insulating tunnel
barrier, thin normal metal, etc.).

13. QUANTUM COMPUTER

14. QUANTUM COMPUTING CHALLENGE
• Qubits can be built
• Scaling qubits into large networks is possible
• Detecting and correcting errors remains a challenge
• Quantum systems are fundamentally delicate, and
superposition collapse if they are observed.
• Before useful information can be extracted,
computational resources can be compromised and
even destroyed by interactions with the
environment.
• One of these challenges is dealing with encryption.
• Codes considered unbreakable by today’s best
supercomputers could be handled in a matter of
hours by quantum computers.

15. QUANTUM ERROR CORRECTION
• Quantum Error Correction Had To Overcome Three
Important Obstacles:
• (1) the no-cloning theorem, which states that it is
not possible to copy unknown quantum states
• (2) measuring a quantum system affects its state
• (3) errors on qubits can be arbitrary rotations in
Hilbert space(1), compared with simple bit flips for
classical bits.
(1) A Hilbert space is an abstractvector space possessing the structure of an inner productthat allows length and angle to
be measured. Furthermore, Hilbert spaces are complete: there are enough limits in the space to allow the techniques of
calculus to be used ( .Wikipedia)

16. QUANTUM ERROR CORRECTION
• Quantum error correction requires many extra
operations and extra qubits .
• It may introduce more errors than are corrected,
because the effect of Decoherence increases
exponentially with the number of entangled (1)
qubits
• in much the same manner that multiple quantum
coherences decay exponentially faster than single
quantum coherences.
• the error rate (probability of error per elementary
operation) is below a certain threshold,
• it is possible to perform arbitrarily long quantum
computations
(1) Entanglement is a term used in quantumtheory to describe the way that particles of energy/matter can become
correlatedto predictably interact with each other regardless of how far apart they are. ( Wikipedia )

17. Error Correction Need
• Applications of quantum computing require
thousands or millions of qubits
• Error correction will be crucial
• In classical computer, we can encode quantum
systems in a way that corrects for errors that
happen like an accidental bit flip where a 1 becomes
0, or vice versa.
• In ion-trapping systems ( charged atomic particles) ,
errors grow fairly rapidly as qubits are added.
• Because quantum systems collapse due to
measurement
https://en.wikipedia.org/wiki/Trapped_ion_quantum_computer

18. Error Correction Need Continue….
• Interrogating the qubits directly and fixing the
broken ones destroys the quantum computation.
• Qubits are stored in stable electronic states of each
ion
• Quantum information can be transferred through
the collective quantized motion of the ions in a
shared trap
• Lasers are applied to induce coupling between the
qubit states (for single qubit operations) or coupling
between the internal qubit states and the external
motional states (for entanglement between qubits).
• The electrodynamic ion trap currently used in
trapped ion quantum computing research was
invented in the 1950s by Wolfgang Paul (who
received the Nobel Prize in 1989 for his work).

19. QUANTUM COMPUTER

20. Solution
• One of the first steps is to construct an extremely
robust physical realization of a qubit.
• trapped atomic ions have quantum staying power.
• Each qubit is stored in the internal energy levels of a
single atomic ion—the same states that are used in
atomic clocks.
• This boast coherence times unmatched in any other
physical system.
• The qubits are manipulated through laser and
microwave radiation to form quantum logic gates
and extended circuits for calculations.

21. Ion trappers
• Ion trappers have become quite adept at controlling
a handful of individual qubits.
• This collaboration has previously proposed and
performed demonstrations that their approach is
scalable and modular, a necessity because many
qubits are needed for useful quantum
computation.
• We need to bring together a large number of
atomic qubits to realize modular “super-qubits”
that can be scaled up while correcting for errors.

22. Modular Super-qubit Or Logical Qubit
•Modular super-qubit or logical qubit begins
to address the problem
• The information stored in a logical qubit
is encoded into specialized quantum
states comprising multiple physical
qubits.
•Now we can have protection that allows for
errors to be detected and corrected, all
without actually knowing the exact details
of the quantum state as a whole.
• Design to achieve the goal of stopping
qubits from degrading through error
correction needs making quantum
computers practically viable

23. Quantum A.I.

25. We Know …..
•“Atomic ion qubits are fundamentally
scalable, because they can be replicated
with virtually identical characteristics: an
isolated ytterbium atom is exactly the same
in Washington, D.C. as it is in Los Angeles,”
Christopher Monroe, professor of physics at
the University of Maryland
•“…ion trapping approach is one of the
leading technologies that can accomplish
this goal,” Jungsang Kim, professor of
electrical and computer engineering,
computer science, and physics at Duke
University,

26. Ytterbium

27. References and Image Credits
• Microsoft partners with Rambus to explore quantum computing
Everything You Need To Know About Quantum Computing
• predictions of where supercomputing is going in 2016
• QUANTUM COMPUTING JOURNAL
• Researchers have discovered a new fundamental property of quantum
mechanics
• Grant Targets Quantum Computing’s Error Control Challenge
• Quantum Computers New Generation of Computers Part 8 Quantum
Error Correction by Prof. Lili Saghafi
• Google's Quantum Computer Appears To Be 100 Million Times Faster
Than A Conventional One
• Quantum Computing at USRA
• https://en.wikipedia.org/wiki/Trapped_ion_quantum_computer
• http://jqi.umd.edu/news/controlling-decoherence
• http://cloudtweaks.com/2016/01/big-data-and-quantum-computers/
• https://www.behance.net/gallery/33138021/Quantum-Computer

28. QUANTUM ERROR
CORRECTION
BY : PROFESSOR LILI SAGHAFI
ANNUAL QUANTUM INFORMATION PROCESSING
(AQIP) CONFERENCE
JAN. 2016
@Lili_PLS