quantum technologies in the 21 century eugene demler harvard university
Post on 21-Dec-2015
216 views
TRANSCRIPT
3
Moore‘s law
From Gordon Moore “No exponential if forever”
faster = smaller
Every 18 months computer power doubles
Suppress quantum
Our alternatives:Exploit quantum
H = E
“Quantum Technology is a radical departure in technology, more fundamentally different from current technology than the digital computer is from the abacus”.
William D. Phillips,1997 Physics Nobel Laureate
“When we get to the very, very small world – say circuits of seven atoms - we have a lot of new things that would happen that represent completely new opportunities for design. Atoms on a small scale behave like nothing on a large scale, for they satisfy the laws of quantum mechanics…”
“There's Plenty of Room at the Bottom”(1959)
Richard Feynman
Quantum Computers
Exponential speed up of number factoring Shor (1994)
Quadratic speed up in database search Grover (1996)
Highlights
Bits and QubitsA quantum bit (qubit) is the quantum mechanical generalization of a classical bit, a two-level system such as a spin, thepolarization of a photon, or ring currents in a superconductor.
0, 1
Classical bit
Physical realization via a charged/uncharged capacitor
0 V
1 V
Q QQuantum objects are waves and can be
in states of superpositionQubit
spin ring-currentphoton
polarization
Classical & quantum gatesThe combination of the classicalgates allows us to construct all manipulations on classical bits.
Is there a set of universal quantum gates ?How does such a set look like ?
Manipulation of a quantum bit is much richer than of a classical bit. We can perform rotations around the x -, y -, and z - axis
Two-qubit gate gate:XOR (CNOT)
Includes entangling gates
Quantum registers
= a0 [000] + a1[001] + a2 [010] + a3 [011] a4 [100] + a5[101] + a6 [110] + a7 [111]
Parallel quantum information processing
Quantum computing = smart computing
Example: need to find the tallest wooden block
Traditional computing: measure every block and compare them.
Smart computing: bring blocks together and check which of them stands out.Requires new types ofoperations!
Example: Deutsch’s algorithm (1985)We are given a 1-bit function f(x): one bit in, one bit out.
→ Is f(x) constant or balanced?
x f(x)0 01 0
x f(x)0 11 0
x f(x)0 11 1
x f(x)0 01 1
f(x) = 0 f(x) = xf(x) = xf(x) = 1
constant balanced
classically, require 2 queries to determinewhether f(x) is constant or balanced
Quantum computers use “massive quantum parallelism” to speed up computations
[0] + [1] x → x y → yf(x)[0] [1]
[0][0]
[0][1]
+[1][0]
[1][1]
[0][f(0)f(0)]
+[1][f(1)f(1)]
single (quantum) query
NOT measure
[01][0] if f(x) constant
[01][01] if f(x) balanced
NOT[0][0] if f(x) constant
[1][01] if f(x) balanced
Quantum computing = smart computing
Quantum Factoring P. Shor (1994)
Second example
15 = 3 5 38647884621009387621432325631 = ? ?
Quantum Factoring
A quantum computer can factor numbers exponentially faster than classical computers
Look for a joint property of all 2N inputse.g.: the periodicity of a function
f(x) = sin(2x/p) p = period
P. Shor (1994)
f(x) = ax (Mod N) r = period (a = constant)
s
O s
2
G s
0x
Whose phone number is 458-0223 ?
Grover’s search algorithmUnsorted database search
Grover algorithm sees all entries at once,marks the right answer and amplifies it.Geometrical interpretation: state vector rotates towards the answer every iteration
Number of steps O(N1/2) vs O(N)
Candidate QubitsA cross-disciplinary race
NMR
ions
Quantumdots
Photons in opticalcavities Atoms in cavities
Superconductingcharge and flux based
Trapped Atomic Ions
Yb+ crystal
~5 m
8 qubitsRecord holders in the numbers of q-bitsand complexity of operations8-qbits in 2006
Elements of a successful quantum computer
Existence of coherent qubit systemIsolation from environment for sufficient time
Universal set of gates. Reproduce all operations
InitializationBegin calculations from well defined initial state
ReadoutAbility to access and read qubits
ScalabilityNecessary to increase the number of bits without fundamental change in strategy
Your name
Other QC designs:
Nitrogen + Vacancyimpurity in diamond
Fluorescence of an array of single impurities in diamond
Most recent QC designs: NV Centers in Diamond Room temperature quantum computing M. Lukin (Harvard)
Other QC designs:Most recent QC designs: Topological QCA. Kitaev (2003) Landau Institute/Caltech
=5/2 state is a quantum topological statewhich allows topological quantum computations
Microsoft Q Station is fully devoted to topological QC Cost: about 20 million in the last 5 years
Quantum Technologies beyond quantum computing
Quantum computers with thousands of bits,which can be used to factorize large numbersare still several years away.
Already now quantum technology has important applications
World’s most precise clocks
The new aluminum clock would neither gain nor lose one second in about 3.7 billion years
It employs the logical processing used for atoms storing data in experimental quantum computing
Compact versions of super-precise atomic clocks can be the basis for navigational systems of the future. They may eliminate the need for human drivers
NIST’s “quantum logic clock” based on Al ionsis world’s most precise clock
Accuracy of GPS is determined by the precision of clocks. Current accuracy of the order of meters.Needed centimeters.
Quantum sensing and imaging
Nitrogen vacancy colorCenter in diamond combined with quantum information processing can be used for ultrahigh resolutionmagnetometry
Potential applications forreal-time, non-invasive imagingin medecine
Needed for the world soccer Cup in Russia in 2018?
Critical communication link in the 2010 World Soccer Cup used quantum technology
Solving fundamental problems with quantum technologyOpen challenges in physical sciences
Understand and design quantum materialsone of the biggest challenges in Physics in the 21 century
High temperature superconductivity (electricity)
Magnetism (data storage)
10-20% of electric power is lost in transmission. This problem can be solved by creating lossless transmission lines from high temperature superconductors
Why we can not solve these problems with conventional computers
Example: Electrons on a lattice. SSystem underlying many solid state and materials problems.Magnets, High Temperature Superconductors, Spintronics, …
Modeling: from airplanes to wind-tunnels
Quantum simulations: understanding high Tc superconductors using artificial quantum systems
International Centers for Quantum Sciences and Technology
Harvard-MIT CenterFor Ultracold Atoms,Boston USA
Institute for Quantum Optics andQuantum Information of the Austrian Academy of Sciences,Innsbruck, Austria
The Institute for Photonic SciencesBarcelona, Spain
Max Planck Institute of Quantum OpticsMunchen, Germany
Needed: Quantum Center in RussiaInternational, interdisciplinary Center of excellence focused on exploring a new area of quantum science & technologyKey component: a new model of research institute based in Russian Federation (RF)Goals: obtain fundamental understanding of complex quantum systems & their control, train new generation of scientists & engineers, develop quantum processing technologies, including•Ultra-fast information processors•Absolutely secure communication systems•High precision navigational and time-keeping systems•All-optical energy efficient communication/processing • Novel quantum materials with properties designed on demand• Novel energy harvesting technologies • Ultra-sensitive quantum biomedical diagnostic technologies
34
The first solid-state transistor(Bardeen, Brattain & Shockley, 1947)The first solid state transistorBardeen, Brattain & Shockley, 1947
Albert Einstein (1879-1955) Erwin Schrödinger (1887-1961)Werner Heisenberg (1901-1976)
Quantum Mechanics: A 20th century revolution in physics
Quantum objects are waves and can be in states of superposition.
CAT CAT
10
…BAD NEWS!decoherence
Decoherence: A peculiarly quantum form of noise that has no classical analog. Decoherence destroys quantum superpositions and is the most important and ubiquitous form of noise in quantum computers
2. Rule #1 holds as long as you don’t look!
[1][0]
[0] & [1]
or
1. Quantum objects are waves and can be in states of superposition.
“qubit”: [0] & [1]
1. Individual atoms and photonsion trapsatoms in optical latticescavity-QED
2. SuperconductorsCooper-pair boxes (charge qubits)rf-SQUIDS (flux qubits)
3. Semiconductorsquantum dots
4. Other condensed-matterelectrons floating on liquid heliumsingle phosphorus atoms in silicon
scales
works
Quantum Computer Physical Implementations
1981. First idea: Feynman q. simulator
1995. Shor’s algorithm; Cirac-Zoller gate
2000. Diverse approaches
2002. 2-qubit gates
2006. Quantum byte (trapped ions)
2008. Error correction threshold reached
Start of q. comp
(Trapped ions, neutral atoms, cavity QED, semiconductor, superconducting, linear optics,impurity spins, single molecular cluster, NMR,...)
2015 (?). Few qubit quantum processorsQ. simulators
timeline forquantum computationtimeline forquantum computation
Current status• Small-scale (<100 km) quantum networks
realized, early commercialization efforts• Challenges: speed, distances
Albert Einstein (1879-1955) Erwin Schrödinger (1887-1961)Werner Heisenberg (1901-1976)
Quantum Mechanics: A 20th century revolution in physics
Quantum objects are waves and can be in states of superposition.
1. Individual atoms and photonsion trapsatoms in optical latticescavity-QED
2. SuperconductorsCooper-pair boxes (charge qubits)rf-SQUIDS (flux qubits)
3. Semiconductorsquantum dots
4. Other condensed-matterelectrons floating on liquid heliumsingle phosphorus atoms in silicon
scales
works
Quantum Computer Physical Implementations