Quantum technologies:Building a Quantum Simulator

Mher GhulinyanFunctional Materials & Photonic Systems

Luciano SerafiniData and Knowledge Management

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

M. Ghulinyan

M. Ghulinyan

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

M. Ghulinyan

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

M. Ghulinyan

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

M. Ghulinyan

Why Quantum and not Classical?

Valid output Valid output

1

0

0

1

M. Ghulinyan

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.

M. Ghulinyan

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

M. Ghulinyan

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

M. Ghulinyan

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

M. Ghulinyan

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

M. Ghulinyan

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

M. Ghulinyan

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

M. Ghulinyan

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

M. Ghulinyan

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

M. Ghulinyan

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

M. Ghulinyan

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”

M. Ghulinyan

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.

M. Ghulinyan

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

M. Ghulinyan

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.

M. Ghulinyan

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

M. Ghulinyan

How to realize physically a C-NOT gate?

M. Ghulinyan

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/

M. Ghulinyan

50 microns

M. Ghulinyan

500 nanometers

Waveguide coupler

Waveguide

Waveguide =Optical fiber

Free-beam + mirror

Waveguide coupler = Beam splitter

http://www.photonics.umbc.edu/

M. Ghulinyan

Beam splitter – waveguide coupler

Input 2Input 1

Output 2Output 1

Transfer length L0

Periodic exchange of power between waveguides

L0

M. Ghulinyan

Beam splitter – waveguide coupler

Input 2Input 1

Output 2Output 1

L0 / 2

Periodic exchange of power between waveguides

L0 / 2 3L0 / 2 5L0 / 2

M. Ghulinyan

Beam splitter – waveguide coupler

50/50 splitter Full transfer No transfer

L0 / 2

L0

M. Ghulinyan

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

M. Ghulinyan

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

M. Ghulinyan

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)

M. Ghulinyan

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

M. Ghulinyan

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.

M. Ghulinyan

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)

M. Ghulinyan

Bulky quantum simulators/computers

Google

UCSB superconducting qubit chip

ETH-Z Quantum Optics labIBM Quantum Experience

M. Ghulinyan

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

M. Ghulinyan

INQUEST - Hybrid integrated photonic-electronic platform for quantum simulations

M. Ghulinyan

INQUEST – the concept

M. Ghulinyan

INQUEST – our vision

M. Ghulinyan

INQUEST – on chip photon source

M. Ghulinyan

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