Mher Ghulinyan - FBK-SD
Transcript of Mher Ghulinyan - FBK-SD
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Quantum technologies:Building a Quantum Simulator
Mher GhulinyanFunctional Materials & Photonic Systems
Luciano SerafiniData and Knowledge Management
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This manifesto is a call to launch an ambitious European initiative in quantum technologies, needed to ensure Europe’s leading role in a technological revolution now under way.
Europe needs strategic investment now in order to lead the second quantum revolution. Building upon its scientific excellence, Europe has the opportunity to create a competitive industry for long-term prosperity and security.
http://qurope.eu/manifesto
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Why “quantum”?
Bit vs Qubit
Logic gates
optical C-NOT quantum gate
Reconfigurability of a Q-circuit
Quantum simulators
the project INQUEST
o Hardware – Quantum simulator
o Software – Quantum algorithms
Outline
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Why Quantum and not Classical?
1 0
Classical computation –data unit is bit
Valid output
1 0or
Quantum computation –data unit is qubit
1 0
Valid output
1 0
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Qubit – a two-state quantum-mechanical system
• Polarization of a single photon ( ↑ up or ↓ down)
Superposition of two states:
Probability 0 → a 2 ; 1 → b 2
store much more information than just 1 or 0, because they can exist in any superposition of these values.
Quantum computation –data unit is qubit
1 0
Valid output
1 0
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Why Quantum and not Classical?
Valid output Valid output
1
0
0
1
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Qubit – a two-state quantum-mechanical system
Classical Bit → One out of 2N
possible permutations
A 3-bit register:
Input100
Output011
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CLASSICAL vs QUANTUM computation
By 2040 we will not have the capability to power all of the machines around the globe (Semiconductor Industry Association report).
Industry is focused on finding ways to make computing more energy efficient, but classical computers are limited by the minimum amount of energy it takes them to perform one operation.
This energy limit is named after Rolf Landauer (IBM Research), who in 1961 found that in any computer, each single bit operation must use an absolute minimum amount of energy.0.0178139
@ room temperature it is 18 meV or 2.88 x10-6 fJ
Necessity in turning to radically different ways of computing, such as QUANTUM COMPUTING, to find ways to cut energy use.
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Qubit – a two-state quantum-mechanical system
Classical Bit → One out of 2N
possible permutations
Qubit → All of possible 2N
permutations
Qubits are processed all at the same time!
A 3-bit register:
Input100
Output011
A 3-Qubit register:
Input000001010100110101101111
Output000001010100110101101111
Exponential speedup
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CLASSICAL vs QUANTUM computation
f (a1, a2, …, an) b
a1
a2
an single-valued function on ndiscrete inputs
0 or 1
0 or 1
0 or 1
0 or 1
n-bit Boolean function
• given an arbitrarily large function f, is it possible to identify a universal set of simple functions – called GATEs – that can be used repeatedly in sequence to simulate f on its inputs
• each gate is formed by small number of inputs from a1, …, an
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CLASSICAL vs QUANTUM computation
simulate arbitrary Boolean functions using the AND, OR, and NOT gates only
+ +
the number of NAND (2-bit) gates needed to simulate a function with n inputs scales exponentially in n
a1
a2
Y
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CLASSICAL vs QUANTUM computation
a1
a2
Y
a1 a2 a1 NAND a2
0 0 1
0 1 1
1 0 1
1 1 0
a1
a2
Y
5 V
0 V
Transistor
Resistance
HARDWARE
NAND logic gate
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CLASSICAL vs QUANTUM computation
a1
a2
Y
a1 a2 a1 NAND a2
0 0 1
0 1 1
1 0 1
1 1 0
a1
a2
Y
5 V
0 V
Transistor
Resistance
HARDWARE
NAND logic gate
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CLASSICAL vs QUANTUM computation
a1
a2
Y
a1 a2 a1 NAND a2
0 0 1
0 1 1
1 0 1
1 1 0
a1
a2
Y
5 V
0 V
Transistor
Resistance
HARDWARE
NAND logic gate
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CLASSICAL vs QUANTUM computation
a1
a2
Y
a1 a2 a1 NAND a2
0 0 1
0 1 1
1 0 1
1 1 0
a1
a2
Y
5 V
0 V
Transistor
Resistance
HARDWARE
NAND logic gate
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CLASSICAL vs QUANTUM computation
a1
a2
Y
XORa1 a2 a1 NAND a2
0 0 1
0 1 1
1 0 1
1 1 0
a1 a2 a1 XOR a2
0 0 0
0 1 1
1 0 1
1 1 0
a1
a2
Y
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CLASSICAL vs QUANTUM computation
XORa1 a2 a1 XOR a2
0 0 0
0 1 1
1 0 1
1 1 0
a1
a2
Input Output
a1 a2 a1 a2
0 0 0 0
0 1 0 1
1 0 1 1
1 1 1 0
a1
a2
a1
a2
CONTROL
TARGET
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CLASSICAL vs QUANTUM computation
Input Output
a1 a2 a1 a2
0 0 0 0
0 1 0 1
1 0 1 1
1 1 1 0
a1
a2
CONTROL
TARGET
If the CONTROL bit is set to 0 it does nothing.
If it is set to 1, the TARGET bit is flipped.
That is, the gate causes the target bit to be correlated to the control bit.
Input Output
CONTROL TARGET CONTROL TARGET
|0> |0> |0> |0>
|0> |1> |0> |1>
|1> |0> |1> |1>
|1> |1> |1> |0>
Here comes the “ENTANGLEMENT”
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QUANTUM ENTANGLEMENT
Alice (A) Bob (B)
50%
50%
50%
50%
Hey, Alice, I’ve measured |1>, so I know you had |0>
Although the outcomes seemed random, they are CORRELATED
Quantum ENTANGLEMENT is a quantum mechanical phenomenon in
which the quantum states of two or more objects have to be described
with reference to each other (CORRELATED), even though the
individual objects may be spatially separated.
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QUANTUM ENTANGLEMENT
Quantum ENTANGLEMENT is a quantum mechanical phenomenon in
which the quantum states of two or more objects have to be described
with reference to each other (CORRELATED), even though the
individual objects may be spatially separated.
V-polarization
H-polarization
E
E
Pump
E = hv
hv + D
hv – D
Polarization Energy
Quantum dot
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The quantum C-NOT gate
Input Output
CONTROL TARGET CONTROL TARGET
|0> |0> |0> |0>
|0> |1> |0> |1>
|1> |0> |1> |1>
|1> |1> |1> |0>
C-NOT (Controlled NOT)
The CNOT gate is the "quantization" of a classical XOR gate.
It is a quantum gate that is an essential component in the construction of a quantum computer. It can be used to entangle and disentangle quantum states.
Any quantum circuit can be simulated to an arbitrary degree of accuracy using a combination of CNOT gates.
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The quantum C-NOT gate
Input Output
CONTROL TARGET CONTROL TARGET
|0> |0> |0> |0>
|0> |1> |0> |1>
|1> |0> |1> |1>
|1> |1> |1> |0>
C-NOT (Controlled NOT)The CNOT gate operates on a quantum register consisting of 2 qubits.
The CNOT gate flips the second qubit (the target qubit) if and only if the first qubit (the control qubit) is |1>
The CNOT gate transforms a 2-qubit state
into
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How to realize physically a C-NOT gate?
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In an optics lab…
Optical fibers or free-space beams
Beam splitters and mirrors
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…or integrate these functions into tiny chips
Sqeesing the area by million times !Volume reduced by 1011 times !
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50 microns
http://www2.optics.rochester.edu/workgroups/cml/opt307/spr07/luke/
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50 microns
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500 nanometers
Waveguide coupler
Waveguide
Waveguide =Optical fiber
Free-beam + mirror
Waveguide coupler = Beam splitter
http://www.photonics.umbc.edu/
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Beam splitter – waveguide coupler
Input 2Input 1
Output 2Output 1
Transfer length L0
Periodic exchange of power between waveguides
L0
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Beam splitter – waveguide coupler
Input 2Input 1
Output 2Output 1
L0 / 2
Periodic exchange of power between waveguides
L0 / 2 3L0 / 2 5L0 / 2
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Beam splitter – waveguide coupler
50/50 splitter Full transfer No transfer
L0 / 2
L0
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An optical C-NOT quantum gate
Nonlinear phase shifter
50/50 splitter
50/50 splitter
requires the control photon to induce a π phase shift on the target photon if the control photon is in the ‘1’ state
O’Brien, Jeremy L., Akira Furusawa, and Jelena Vučković. "Photonic quantum technologies." Nature Photonics 3.12 (2009): 687-695.
0/1
1/0
0/1
1/0
Control
Target
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A linear optical C-NOT quantum gate
0/1
1/0
0/1
1/0
Target 1/2
Ralph, Timothy C., et al. "Linear optical controlled-NOT gate in the
coincidence basis." Physical Review A 65.6 (2002): 062324.
1/2
1/3
1/3
1/3
Control
Auxiliary photon1
Auxiliary photon2
Single Photon Detector
The CNOT operation is applied to the control and target qubits, conditional on a single photon being detected at each detector
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Reconfigurable Quantum circuit
Shadbolt, Peter J., et al. "Generating, manipulating and measuring entanglement and mixture
with a reconfigurable photonic circuit." Nature Photonics 6.1 (2012): 45-49.
C-NOT gate
Phase-shifter Mach Zehnder interferometer
The two qubits are input in the logical zero states of both the control and target (upper waveguides)
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Reconfigurable Quantum circuit
Shadbolt, Peter J., et al. "Generating, manipulating and measuring entanglement and mixture
with a reconfigurable photonic circuit." Nature Photonics 6.1 (2012): 45-49.
C-NOT gate
Phase-shifter Mach Zehnder interferometer
Arbitrary state preparation
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A Quantum simulator
Controllable quantum systems that can be used to mimic other quantum systems.
They have the potential to enable the tackling of problems that are intractable on conventional computers
… the physical world is quantum mechanical, and therefore the proper problem
is the simulation of quantum physics.
Let the computer itself be built of quantum mechanical elements which obey
quantum mechanical laws.
…therefore, I believe it's true that with a suitable class of quantum machines
you could imitate any quantum system, including the physical world.
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Quantum simulators
Supercomputers cannot yet predict if a material composed of few hundred atoms will conduct electricity or behave as a magnet, or if a chemical reaction will take place.
Quantum simulators based on the laws of quantum physics will allow us to overcome the shortcomings of supercomputers and to simulate materials or chemical compounds, as well as to solve equations in other areas, like high-energy physics …
Results of quantum optics experiment for simulating the energy of the hydrogen molecule in the minimal basis set. Plot of the molecular energies of the different electronic states as a function of interatomic distance.
Lanyon, B. P. et al. Towards quantum chemistry on a quantum computer. Nature Chem. 2, 106 (2010)
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Bulky quantum simulators/computers
UCSB superconducting qubit chip
ETH-Z Quantum Optics labIBM Quantum Experience
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Photonic Quantum simulator: ingredients
Qu
antu
m h
ard
war
e
Photon source
State preparator (qubits)
Simulator (Quantum gates)
Detection
Analog drivers
Hardware level Software level
Quantum algorithms
Decision making
Digital co
ntro
l
User interface
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INQUEST - Hybrid integrated photonic-electronic platform for quantum simulations
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INQUEST – the concept
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INQUEST – our vision
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INQUEST – on chip photon source
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