Qsimulation V2.0: an Optimized Quantum Simulator

Source code

You can clone the repository quantum and it can run in eclipse or intellij idea, you may need to add j-science libaray.

Qsimulation V2.0 Grammer

Program     --------> Declare { ; Statement }
Declare     --------> Quantum Identifier INT [Explist]
Statement  --------> Operator | Measurement | Show | Alias | IFStatement | Reset
Operator    --------> UnaryOp | BinaryOp | TernaryOp | MultiOp | GateOp | UOp
UnaryOp     --------> X|Y|Z|S|SD|T|TD Argument
BinaryOp    --------> CNOT Argument Argument
TernaryOp    --------> CCNOT Argument Argument Argument
MultiOp    --------> CNOTS [Argument ]
GateOp      --------> Gate[Explist] Argument
UOp         --------> U[Explist] Argument
Measurement--------> Measure [ Argument Identifier ]
Show        --------> Show
Alias       --------> Alias Argument, Argument
IFStatement---------> IF Bool Then Statement { ; Statement } FI
Reset       ---------> Reset
Bool       ----------> [!] Identifier
Argument   ---------> Identifier | Array
Explist    ---------> (Expression {, Expression})
Expression ---------> Factor [+|-|*|/ Expression]
Factor      ---------> [-] INT | Complex | Real

INT := [0-9]+
Real := [0-9]+\.[0-9]*
Complex := \< \-? Real \, \-? Real \>
Identifier := [a-zA-Z]*
Array := [a-zA-Z]*\[INT\]

The list grammer has been used in the QSimulation. We will add some other grammer in the future.

Qsimulation V2.0 statements

Statement	Description
Quantum Identifier INT	Declare a quantum register named identifier with INT qubits.
Quantum Identifier INT Explist	Declare a quantum register named identifier with INT qubits, and initialize the quantum register according to Explist.
X|Y|Z|S|SD|T|TD Argument	single-qubit gate operation.
U[Explist] Argument	Single quantum gate operation with parameters.
CNOT Argument Argument	double-qubits gate operation.
CCNOT Argument Argument Argument	triple-qubits gate operation.
CNOTS [Argument ]	multi-qubits gate operation.
Gate[Explist] Argument	Custom quantum gate operation.
Measure	Global measurement of quantum states.
Measure [Argument Identifier ]	Measurement of sub-states of quantum states.
Show	Show the current state of the quantum register.
Reset	Reset quantum register.
Alias Argument, Argument	Alias an argument as the second argument.
IF Bool Then Statement { ; Statement } FI	Classical judgment statement. Determine whether to execute the corresponding operation according to the measurement results.

Qsimulation V2.0 Structure

How to use

As you can see, the above picture is screenshot of QSimulation.

left pane

The black box area offers some buttons, which represent different functions.

initialization

• button 'Init'：initialization without parameters
• button 'ass': initialization with possibility ampitudes

Unary Gates

built-gate(without parameters)
  X        Y         Z        S      SD          T           TD 
|0 1|   |0  -i|   |1   0|   |1 0|  |1  0|  |1    0     |   |1     0     |
|1 0|   |i   0|   |0  -1|   |0 i|  |- -i|  |0 exp(iπ/4)|   |0 exp(-iπ/4)|

built-gate(with parameters) U(x,y,z)
            |exp(−i(φ+λ)/2)cos(θ/2)  -exp(−i(φ-λ)/2)sin(θ/2)|
U(θ,φ,λ) =  |                                               |
            |exp(i(φ-λ)/2)sin(θ/2)   exp(i(φ+λ)/2)cos(θ/2)  |
and the global phase is exp(i(φ+λ)/2)/cos(θ/2)

Binary Gate

 Now, we only present a binary gate: CNOT, and we will offer some other universal matrix, such as CNOT-S.
        |1 0 0 0|
        |0 1 0 0|
cnot =  |0 0 0 1|
        |0 0 1 0| 
Although we don't present some other binary gate, we can constuct these.For example,
        |1 0 0 0|
        |0 0 1 0|
swap =  |0 1 0 0| 
        |0 0 0 1| 
swap[q1,q2] = cnot[q1,q2]cnot[q2,q1]cnot[q1,q2].  

Measurements

We only support 0-1 measure now, and we will offer some other measurements

Classical control

input: number of executions It means we can test the program some times and QSimulation will offer the final distribution of statistics.

nav

QSimulation presents some functions : import , save , restart, run, circuit, cirnext ,cirback, bloch

• import : you can import the program to the editor
• save : you can save the program
• restart : you can restart the program
• run : you can run the program
• circuit : you can generate the quantum circuit
• cirNext : you can debug the program
• cirBack : you can debug the program
• bloch: it can be simulated in bloch sphere

Example

quantum teleportation

Quantum a 3;
Alias a[0] Alice1;
Alias a[1] Alice2;
Alias a[2] Bob;
H Alice1;
H Alice2;
CNOT Alice2 Bob;
CNOT Alice1 Alice2;
H Alice1;
Measure Alice1,i;
Measure Alice2, j;
if i then Z Bob fi;
if j then X Bob fi

quantum fourier transform

Quantum q 3;
X q[2];
H q[0];
T q[1];
CNOT q[1] q[0];
TD q[0];
CNOT q[1] q[0];
T q[0];
U(0,0,PI/8) q[2];
CNOT q[2] q[0];
U(0,0,-PI/8) q[0];
CNOT q[2] q[0];
U(0,0,PI/8) q[0];
H q[1];
T q[2];
CNOT q[2] q[1];
TD q[1];
CNOT q[2] q[1];
T q[1];
H q[2];
CNOT q[0] q[2];
CNOT q[2] q[0];
CNOT q[0] q[2]

Grover algorithm

Quantum a 4;
H a[0];H a[1];H a[2];X a[3];H a[3];
CNOTS a[0] a[1] a[2] a[3];
H a[0];H a[1];H a[2];X a[0];X a[1];X a[2];H a[2];
CCNOT a[0] a[1] a[2];
X a[0];X a[1];H a[2];H a[0];H a[1];X a[2];H a[2];
CNOTS a[0] a[1] a[2] a[3];
H a[0];H a[1];H a[2];X a[0];X a[1];X a[2];H a[2];
CCNOT a[0] a[1] a[2];
X a[0];X a[1];H a[2];H a[0];H a[1];X a[2];H a[2]

others

In folder examples, there are all the experiments and data of the paper.