2017 10 17_quantum_program_v2

Quantum Programming
A New Approach to Solve Complex Problems
Francisco Gálvez Ramirez
IBM Staff
fjgramirez@es.ibm.com

Introducing myself
Francisco Gálvez
BS in Experimental Physics (UV)
Master in Advanced Physics (UV)
Cloud and Integrated Systems Expert
fjgramirez@es.ibm.com
@fjgramirez
Francisco J. Galvez Ramirez

Agenda
 Why Quantum Computation
 The IBM Quantum Computer
 Quantum Algorithms
 How to Program a Quantum Computer
 Tools for Quantum Computing

Why Quantum Computation ?
“...nature isn't classical, dammit, and if you want to make a simulation
of nature, you'd better make it quantum mechanical...” –
Richard Feynman, Simulating Physics with Computers

A qubit is the quantum concept of a bit.
0 1  It’s not any element or device. It’s a logical concept
that can be implemented on a wide range of
different systems with quantum behaviour
 As a bit, a single qubit can represent two states 0
and 1
But additionally a qubit is able to manage all possible combinations
amont base states 0 and 1
10 βα +
10 βαψ +=
What is a Qubit?

Spin Qubits – Electron or nuclear spins on a solid Substract.
Superconducting Circuits – currents superposition around a superconductor.
Ion’s Traps– Trap ions in electric fields
Photonic Circuits – The qubits are photons driven in in silicon circuits.
Qubit Implementation

 2 BITS
0
1
0 0
0
1
0
1
A 0 0 + B 1 0 + C 0 1 + D 1 1
1 0
0 1
1 1
 2 QUBITS
One state made of a combination
of every possible state of the
system
Quantum Superposition

Quantum Entanglement
1. Preparing an
entangled states.
An entangled stated can be
prepared by applying a common
operation to the system.
2. Measurement
0
1

March - 2016: Quantum Computing in the
Cloud
 IBM scientists have built a quantum processor
that any user can access through the first
quantum computing platform available in the
cloud.
 IBM Quantum Experience, allows users to
execute algorithms and experiments on a real
quantum processor

Marzo-2017: IBM announces IBM Q
IBM Q is the new line of Quantum Computers
IBM announces the building of a quantum computer of 50 qubits and
that will offer services of quantum computation in the cloud

Mayo-2017: First Commercial Quantum
Computer
16 and 17 qubits universal quantum computers
IBM announces a prototype of
17 qubits commercial quantum
computing
IBM has discovered how to
scale quantum architecture
In three years it is planned to
reach 50 qubits

IBM Superconducting Qubits Arquitecture
IBM's new 17-qubit quantum computer.

Coherence Times
• Coherence in IBM today is about
100 microseconds
• There are several initiatives to
improve the coherence times:
• Different materials
• Redesign of geometries
• Cavity Quality
• IR Shielding
• Important progress has been
made in the last decade

The Dilution Refrigerator
 A key piece of the Quantum Computer is the Dilution Refrigerator
Working Temperature 15 mK
Dilution Refrigerator
3
He + 4
He

Quantum Algorithms
• Deusch Algorithm – Determines whether a funcion is balanced or
unbalanced
• Shor Algorithm – Large numbers factorization
• Grover Algoritm – Search in unstructured spaces

Deustch Algorithm
f1:
0 0
1 0
f2:
0 1
1 1
Deustch-Josza Algorithm  Extends Deustch’s
algorithm to n value registers
f3:
0 0
1 1
f4:
0 1
1 0

Shor Algorithm
• Number of steps that a classic computer needs to run in order
to find the prime factors of a number N of x digits
It grows exponencially with x
• The Shor algorithm is made up of two parts:
1. One Classical part - Which focuses on finding the period
of a function
2. A quantum part based on QFT technics
In 2001, IBM and Stanford University, executed for the first time the Shor algorithm in the first quantum computer of 7
qubits developed in Los Álamos.
https://www-03.ibm.com/press/us/en/pressrelease/965.wss

Grover Algorithm
• How many attempts need a data search in an unordered N-
element database to locate a particular element?
An average of N/2 attemps are needed)
http://www.dma.eui.upm.es/MatDis/Seminario4/AlgoritmoGrover.pdf
• A Quantum Computer executing the Grover Algorithm would
run attempsN

How To Program A Quantum Computer?

Quantum Circuits
The Circuit Model
Gates execution time ~ 25 ns
~25 ns~25 ns ~25 ns ... ... ... ... ...
Coherence time 100 ms
measurement

Quantum Operations
X-Gate
Flips a qubit from a 0 to a 1, or vice versa.
Hadamard Gate
Puts a qubit into a superposition of states.
Flips a second qubit only if the first qubit is 1.
Controlled Not Gate
Entanglement
H gate puts the first qubit in a
superposition. CNOT gate both
flips and does not flip the
second qubit.
Assuming the qubits start as 0,
when measured, they will be 11
or 00, but never 10 or 01.

Quantum Operations
 It is a basic circuit that acts on one or several qubits
 It is equivalent to logical gates in digital circuits
Quantum Gates
1. Quantum Gates are Reversible
2. Matematically are represented by unitary matrices.
3. The qubits upon they act keep their quantum nature.






−
=
11
11
2
1












=
0100
1000
0010
0001
=
Hadamard Gate
C-NOT Gate






=
01
10
X - Gate

NOT Gate
 Transforms the state in
the state and viceversa
 It means a rotation of π
radians around X axis
0
1
Change of state
One Qubit Quantum Gates

Hadamard Gate
 It transforms any of the base
states or in a
combination of both
 It means a rotation of π/2
radians around X axis and Z
axis
Superposition of base states
0 1
It cannot be meassured on Z axis, but we can use an H gate to change the basis

The Z Gate Cambio de Fase - π
 It runs a rotation of π radians
around Z axis

The S Gate Phase Shift: – π/2
 It run a rotation of π/2
radians around Z axis

The S Gate
Phase Shift: – π/4
 It runs a rotation of π/4
radians around Z axis

Two Qubit Quantum Gates
The CNOT Gate
Flips the target qubit, depending on the state
of the control qubit

Gates with more than two qubits
The Toffoli Gate
Flips the target qubit, depending on the state
of two control qubits
control 1
control 2
target

User Defined Gates
( ) ( ) ( )λλλ zRUu == ,0,0:11
2
3
( ) ( ) ( ) 





−





+==
2
2
2
,,2:,2
π
λπ
π
φλφπλφ zxz RRRUu
( ) ( ) ( ) ( ) ( ) ( ) ( )λππθππφλφθλφθ zxzxz RRRRRUu 223,,:,,3 ++==

User Defined Control Gates
1
1
if(q0==1) U1 q1;
if(q0==1 and q1==1) U1 q2;

Quantum Operations
Quantum Gates Set

Quantum Operations
The Bloch Sphere
 Standard Basis is not enough to specify a quantum State.
 We need to specify a phase as well.
 Bloch Sphere depicts the amplitudes and the phase of
one state.
1
2
0
2
cos 





+





=
θθ
ψ φ
senei
 There’s a one-to-one correspondence between pure qubits
states and the points on the surface on a unit sphere
2
C 3
R

Quantum Operations
The Qsphere
Qsphere shows states of more than 1 qubit
For 1 qubit  2 points
For 2 qubit  3 points
for n qubit  (n+1) points
 Each line from the center is possible outcome
 Allows to distinguish classical states from entangled states
• A classical state will have a single line pointing in one direction
• A superposition of two basis states will have two lines pointing in two directions of half
weight.

Tools for Quantum Programming
IBM Quantum Experience
Visual interface, Drag and Drop for 5 qubits
QISKit OpenQASM
Asembler Language for representing Quantum
Circuits
QISKit API
Python API to create and execute Quantum Circuits

Tools For Quantum Programming
IBM Quantum Experience QX2, QX4

IBM Quantum Experience
https://quantumexperience.ng.bluemix.net/qx

Quantum Circutis
IBM QX Composer

The Circuit Model
Quantum Circutis

Creating Scores
 Graphical Interface used to create programs for the quantum processor
 It allows to create quantum circuits using a logical gates library and well defined points of
measurement

Running Scores
 Bar Chart
• 0’s & 1’s combination in the bottom means the measured Qubit state.
• The height of the bar represents how often that particular state occurs

IBM Quantum Experience QX2, QX4
Grover Algorithm

1 2 3 4 ... ... N=2nω
Programming the Grover Algorithm – (I)
 A list of N item and there’s one item with a unique property that we wish to locate
 A classical computation needs to check on average of this boxes2N
 On a quantum computer, using the Grover’s algorithm it can be done in aprox. stepsN
1 2 3 4
Lets do it for N = 4

Programming the Grover Algorithm – (II)
∑
−
=
=
1
0
1 N
x
x
N
s
 At the beginning we have a uniform superposition
amplitu
de
0ψ
N
1
Items1 2 3 4
00 01 10 11

Programming the Grover Algorithm – (III)
 We need a function such that: for the marked state:1)( =xf ω
 In that way we build the “oracle” matrix: fU
( ) xxU xf
f
)(
1−=
 Applying the oracle reflection: If is an unmarked item, the oracle does nothing, otherwise:x
ωω −=fU
amplitu
de
0ψ
N
1
Items
1 2 3 4
00 01 10 11

Rotates 90º (on the basis )
Superposition  Changes to the basis
Superposition  Back to the basis  only qubit #2
Change state of qubit #2 (based on #1)
−+ ,
−+ ,
1,0

Superposition  qubit # 2 back to the basis
Rotates 90º (on the basis )
−+ ,
−+ ,

Programming the Grover Algorithm
 We now apply an additional reflection about the state .
 In the bra-ket notation this reflection is written as:
 This transformation maps the state to:
 and completes the transformation:
s
12 −= ssUs
'tsU ψ
tfst UU ψψ =+1
sU
amplitu
de
0ψ
Items
1 2 3 4
00 01 10 11

Programming the Grover Algorithm – (IV)

Programming the Grover Algorithm – (V)

Programming the Grover Algorithm – (VI)

Programming the Grover Algorithm – (VII)

Programming the Grover Algorithm – (VIII)

Programming the Grover Algorithm – (IX)

Programming the Grover Algorithm – (X)
 Getting the right oracle function :
For element
For element
For element
For element
10
11
fU
00
01

Programming the Grover Algorithm – Results
 The most probable state is |00>

QISKit OpenQASM

QISKit OpenQASM
What is OpenQASM?
An intermediate representation for Quantun Circuits
Hardware Agnostic
OPENQASM, or “Quantum Assembly Language,” is a simple
text representation that describes generic quantum circuits.
OpenQASM submit batch jobs via HTTP API/PYTHON wrapper.

QISKit API
Architecture
User Program *.py KISQit SDK
KISQit API Cient
Internet
Simulators QX2 QX4 QX16
User Program *.qasm

OpenQASM
Language Statements
IBMQASM 2.0;
qreg name[size];
creg name[size];
include "filename";
gate name(params) qargs { body }
opaque name(params) qargs;
U(theta,phi,lambda) qubit|qreg;
CX qubit|qreg,qubit|qreg;
measure qubit|qreg -> bit|creg;
reset qubit|qreg;
gatename(params) qargs;
if(creg==int) qop;
barrier qargs;

QISKit OpenQASM
Predefined Gates
// These are the predefined gates
U(theta,phi,lambda) qubit|qreg;
CX qubit|qreg,qubit|qreg;
New Gate Definition
// This is the definition
gate name(params) qargs
{
body
}
// This is an example
gate g a
{
U(0,0,0) a;
}
gate crz(theta) a,b
{
U(0,0,theta/2) a;
CX a,b;
U(0,0,-theta/2) b;
CX a,b;
U(0,0,theta/2) b;
}
crz(pi/2) q[0],q[1];

QISKit OpenQASM
Example: Quantum Fourier Transform// quantum Fourier
transform
IBMQASM 2.0;
include "qelib1.inc";
qreg q[4];
creg c[4];
x q[0];
x q[2];
barrier q;
h q[0];
cu1(pi/2) q[1],q[0];
h q[1];
cu1(pi/4) q[2],q[0];
cu1(pi/2) q[2],q[1];
h q[2];
cu1(pi/8) q[3],q[0];
cu1(pi/4) q[3],q[1];
cu1(pi/2) q[3],q[2];
h q[3];
measure q -> c;
 The quantum Fourier transform demonstrates parameter
passing to gate subroutines.
 This circuit applies the QFT to the state
and measures in the computational basis.
=3210 qqqq 0101

QISKit Python SDK

QISKit API
What is QISKit API?
 Access to IBM’s Quantum Experience using a Python interface.
 This interface allows working with quantum circuits and executing multiple
circuits in an efficient batch of experiments.

QISKit API
QISKit SDK Installation
1.Using pip python tool
• Install Anaconda (with Python3)
• Run Anaconda command line
• Execute pip install qiskit
1.Cloning github project
• Install Anaconda (with Python3)
• Clone github project:
git clone https://github.com/QISKit/qiskit-sdk-py
• Activate environment:
> activate QISKitenv
• Change to directory: qiskit-sdk-py and execute
.make env

QISKit API
Managing Packages with Anaconda
http://corochann.com/setup-python-environment-1395.html

QISKit API
Basic program elements:
The Quantum Program
QuantumProgram()
The Circuit
.create_circuit()
The Quantum Register
.create_quantum_registers()
The Classical Register
.create_classical_registers()

QISKit API
The Circuit
First, create the circuit
circuit = Q_program.get_circuit(“Circuit")
The Registers
 Quantum Registers
q2 = Q_program.create_quantum_registers("q2", 2)
 Classical Registers
c2 = Q_program.create_classical_registers("c2", 2)

QISKit API
The Gates
Adding Gates to the circuit

QISKit API
Extracting QASM code

QISKit API
Creating an entangled Bell state
1.Create Quantum Registers
q2 = Q_program.create_quantum_registers("q2", 2)
1.Create Classical Registers
c2 = Q_program.create_classical_registers("c2", 2)

2017 10 17_quantum_program_v2

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