Quantum Circuit Simulator
quantumcircuit is open source quantum circuit simulator implemented in javascript. Smoothly runs 20+ qubit simulations in browser or at server (node.js). You can use it in your javascript program to run quantum simulations.
Circuit can be imported from OpenQASM and Quil. You can export circuits to OpenQASM, pyQuil, Quil, Qiskit, Cirq, TensorFlow Quantum, QSharp, and QuEST, so it can be used for conversion between quantum programming languages. Circuit drawing can be exported to SVG vector image.
Live examples
Quantum Programming Studio
Quantum Programming Studio is web based quantum programming IDE and simulator built on top of this package. Circuit can be executed on real quantum computer directly from the UI.
Other live examples

qconvert Online quantum programming language converter
Using in browser
Simply include quantumcircuit.min.js into your html page (available via unpkg CDN https://unpkg.com/quantumcircuit)
<!doctype html>
<html>
<head>
<title>Quantum Circuit Simulator Example</title>
</head>
<body>
<script type="text/javascript" src="https://unpkg.com/quantumcircuit"></script>
<script type="text/javascript">
// Your code here
</script>
</body>
</html>
Using at server with node.js
Add quantumcircuit npm module to your node.js project:
npm install save quantumcircuit
And then import it into your program:
var QuantumCircuit = require("quantumcircuit");
// Your code here
Node.js examples
See /example/nodejs directory.
Using with Jupyter notebook
You need to install ijavascript kernel for Jupyter notebook
You can install quantumcircuit npm module globally and invoke jupyter notebook from any directory:
npm install g quantumcircuit
Or inside new directory do:
npm init
npm install save quantumcircuit
jupyter notebook
Jupyter notebook examples
See /example/jupyter directory.
Getting started
Create circuit
Create instance of QuantumCircuit
class, optionally passing number of qubits (wires) to constructor:
var circuit = new QuantumCircuit(3);
Note: number of qubits is optional argument  circuit will expand automatically if you add gates to nonexisting wires
Add singlequbit gates
Call addGate
method passing gate name, column index and qubit (wire) index:
circuit.addGate(gateName, column, wire);
For example, to add Hadamard gate as a first gate (column 0) at second qubit (wire 1) type:
circuit.addGate("h", 0, 1);
Result is:
Column 0
Wire 0 

Wire 1  H 

Note: if column
is negative integer then gate will be added to the end of the wire
Add multiqubit gates
Call addGate
method passing gate name, column index and array of connected qubits (wires):
circuit.addGate(gateName, column, arrayOfWires);
For example, to add CNOT as a second gate (column 1) controlled by second qubit (wire 1) at third qubit as target (wire 2) do:
circuit.addGate("cx", 1, [1, 2]);
Column 0 Column 1
Wire 0 
Wire 1 o


Wire 2  CX 

Note: if column
is negative integer then gate will be added to the end
Example  Quantum random number generator
var QuantumCircuit = require("quantumcircuit");
//
// 8bit quantum random number generator
//
var quantumRandom = function() {
var circuit = new QuantumCircuit();
for(var i = 0; i < 8; i++) {
//
// add Hadamard gate to the end (1) of ith wire
//
circuit.addGate("h", 1, i);
//
// add measurement gate to ith qubit which will store result
// into classical register "c", into ith classical bit
//
circuit.addMeasure(i, "c", i);
}
// run circuit
circuit.run();
// return value of register "c"
return circuit.getCregValue("c");
};
// Usage  print random number to terminal
console.log(quantumRandom());
Implemented gates
Name  pyQuil  Cirq  Q#  Qubits  Params  Description 

id  I  I  I  1  Single qubit identity gate  
x  X  X  X  1  Pauli X (PI rotation over Xaxis) aka "NOT" gate  
y  Y  Y  Y  1  Pauli Y (PI rotation over Yaxis)  
z  Z  Z  Z  1  Pauli Z (PI rotation over Zaxis)  
h  H  H  H  1  Hadamard gate  
srn  def srn  X**(1/2)  1  Square root of NOT  
srndg  def srndg  X**(1/2)  1  Inverse square root of NOT  
r2  S  S  S  1  PI/2 rotation over Zaxis aka "Phase PI/2"  
r4  T  T  T  1  PI/4 rotation over Zaxis aka "Phase PI/4"  
r8  PHASE(pi/8)  u1(pi/8)  1  PI/8 rotation over Zaxis aka "Phase PI/8"  
rx  RX  rx  Rx  1  theta  Rotation around the Xaxis by given angle 
ry  RY  ry  Ry  1  theta  Rotation around the Yaxis by given angle 
rz  RZ  rz  Rz  1  phi  Rotation around the Zaxis by given angle 
u1  PHASE  def u1  1  lambda  Singlequbit rotation about the Z axis  
u2  def u2  def u2  1  phi, lambda  Singlequbit rotation about the X+Z axis  
u3  def u3  def u3  1  theta, phi, lambda  Generic singlequbit rotation gate with 3 Euler angles  
s  S  S  S  1  PI/2 rotation over Zaxis (synonym for r2 ) 

t  T  T  T  1  PI/4 rotation over Zaxis (synonym for r4 ) 

sdg  PHASE(pi/2)  u1(pi/2)  1  (PI/2) rotation over Zaxis  
tdg  PHASE(pi/4)  u1(pi/4)  1  (PI/4) rotation over Zaxis  
swap  SWAP  SWAP  SWAP  2  Swaps the state of two qubits.  
srswap  def srswap  SWAP**(1/2)  2  Square root of swap  
iswap  ISWAP  ISWAP  2  Swaps the state of two qubits, applying a i phase to q1 when it is in the 1 state and a i phase to q2 when it is in the 0 state  
xy  XY  def xy  2  phi  XY gate  
cx  CNOT  CNOT  CNOT  2  Controlled NOT (CNOT) gate  
cy  def cy  Y  Controlled Y  2  Controlled Y gate (controlled rotation over Yaxis by PI)  
cz  CZ  CZ  Controlled Z  2  Controlled Z gate (controlled rotation over Zaxis by PI)  
ch  def ch  H  Controlled H  2  Controlled Hadamard gate  
csrn  def csrn  X**(1/2)  2  Controlled square root of NOT  
ms  def ms  ms  2  theta  MølmerSørensen gate  
yy  def yy  YY  2  theta  YY gate  
zz  def zz  2  theta  Parametric 2qubit rotation about ZZ  
cr2  CPHASE(pi/2)  cu1(pi/2)  2  Controlled PI/2 rotation over Zaxis  
cr4  CPHASE(pi/4)  cu1(pi/4)  2  Controlled PI/4 rotation over Zaxis  
cr8  CPHASE(pi/8)  cu1(pi/8)  2  Controlled PI/8 rotation over Zaxis  
crx  def crx  rx(theta)  Controlled Rx  2  theta  Controlled rotation around the Xaxis by given angle 
cry  def cry  ry(theta)  Controlled Ry  2  theta  Controlled rotation around the Yaxis by given angle 
crz  def crz  rz(phi)  Controlled Rz  2  phi  Controlled rotation around the Zaxis by given angle 
cu1  CPHASE  def cu1  2  lambda  Controlled rotation about the Z axis  
cu2  def cu2  def cu2  2  phi, lambda  Controlled rotation about the X+Z axis  
cu3  def cu3  def cu3  2  theta, phi, lambda  Controlled rotation gate with 3 Euler angles  
cs  CPHASE(pi/2)  cu1(pi/2)  2  Controlled PI/2 rotation over Zaxis (synonym for cr2 ) 

ct  CPHASE(pi/4)  cu1(pi/4)  2  Controlled PI/4 rotation over Zaxis (synonym for cr4 ) 

csdg  CPHASE(pi/2)  cu1(pi/2)  2  Controlled (PI/2) rotation over Zaxis  
ctdg  CPHASE(pi/4)  cu1(pi/4)  2  Controlled (PI/4) rotation over Zaxis  
ccx  CCNOT  CCX  CCNOT  3  Toffoli aka "CCNOT" gate  
cswap  CSWAP  CSWAP  Controlled SWAP  3  Controlled swap aka "Fredkin" gate  
csrswap  def csrswap  SWAP**(1/2)  3  Controlled square root of swap  
reset  RESET  reset  Reset  1  Resets qubit  
measure  MEASURE  measure  M  1  Measures qubit and stores chance (0 or 1) into classical bit 
For more details see gate reference
Run circuit
Simply call run
method.
circuit.run();
Initial state
By default, initial state of each qubit is 0>
. You can pass initial values as array of bool (true
or false
) or integers (0
or 1
). This will set first two qubits to 1>
and evaluate circuit:
circuit.run([1, 1]);
Measurement
Method probabilities()
will return array of probabilities (real numbers between 0 and 1) for each qubit:
console.log(circuit.probabilities());
Method probability(wire)
will return probability (real number between 0 and 1) for given qubit:
console.log(circuit.probability(0));
Method measureAll()
returns array of chances (as integers 0 or 1) for each qubit:
Example:
console.log(circuit.measureAll());
Method measure(wire)
returns chance (as integer 0 or 1) for given qubit:
Example:
console.log(circuit.measure(0));
You can store measurement into classical register. For example, to measure first qubit (wire 0) and store result into classical register named c
as fourth bit (bit 3):
circuit.measure(0, "c", 3);
You can add measure
gate to circuit and then measurement will be done automatically and result will be stored into classical register:
circuit.addGate("measure", 1, 0, { creg: { name: "c", bit: 3 } });
Short form of writing this is addMeasure(wire, creg, cbit)
:
circuit.addMeasure(0, "c", 3);
Note:

Measurement gate will reset qubit to measured value only if there are gates with classical control (gates controlled by classical registers). Otherwise, measurement gate will leave qubit as is  measured value will be written to classical register and qubit will remain unchanged. This "nondestructive" behavior is handy when experimenting. However, it will automatically switches to "destructive" mode when needed (when classical control is present)

If specified classical register doesn't exists  it will be created automatically.
Classical registers
Create register
Classical registers are created automatically if you add measurement gate to the circuit but you can also manually create registers by calling createCreg(name, len)
.
Example: create classical 5bit register named ans
:
circuit.createCreg("ans", 5);
Read register
To get register value as integer, call getCregValue(name)
.
Example:
var value = circuit.getCregValue("ans");
Read all registers as dictionary
var regs = circuit.getCregs();
console.log(regs);
Read all registers as tab delimited CSV string
var tsv = circuit.cregsAsString();
console.log(tsv);
Read single bit
Example: get bit 3 from register named ans
:
console.log(circuit.getCregBit("ans", 3));
Returns integer: 0 or 1
Set single bit
Example: set bit 3 to 1
in register named ans
:
circuit.setCregBit("ans", 3, 1);
Control by classical register
Each quatum gate in the circuit (except "measure" gate) can be controlled by classical register  gate will be executed only if classical register contains specified value. Pass options
object as fourth argument to addGate
method:
Example:
circuit.addGate("x", 1, 0, {
condition: {
creg: "ans",
value: 7
}
});
In this example, "x" gate will execute on qubit 0 only if value of register named "ans" equals 7.
Reset qubit
You can reset qubit to value 0>
or 1>
with resetQubit
method:
circuit.resetQubit(3, 0);
In this example, qubit 3 will be set to 0>
.
Note that all entangled qubits will be changed as well
View/print state vector
You can get state as string with method stateAsString(onlyPossible)
:
var s = circuit.stateAsString(false);
If you want only possible values (only values with probability > 0) then pass true
:
var s = circuit.stateAsString(true);
Or, you can print state to javascript console with method print(onlyPossible)
:
circuit.print(false);
If you want to print only possible values (only values with probability > 0) then pass true
:
var s = circuit.print(true);
Save/Load circuit
You can export circuit to javascript object (format internally used by QuantumCircuit) by calling save
method:
var obj = circuit.save();
// now do something with obj, save to file or whatever...
And load previously saved circuit by calling load
method:
var obj = // ...load object from file or from another circuit or whatever
circuit.load(obj);
Use circuit as a gate in another circuit
You can "compile" any circuit and use it as a gate in another circuit like this:
// export circuit to variable
var obj = someCircuit.save();
// register it as a gate in another circuit
anotherCircuit.registerGate("my_gate", obj);
// use it as a gate in another circuit
// assuming original circuit has three qubits then gate must spread to 3 qubits, in this example: 2, 3, 4)
anotherCircuit.addGate("my_gate", 0, [2, 3, 4]);
Decompose circuit
If your circuit contains user defined gates (created from another circuit), you can decompose it into equivalent circuit containing only basic gates.
If you pass true
as argument to function save
, you'll get decomposed circuit.
Example:
var obj = circuit.save(true);
// now obj contains decomposed circuit. You can load it:
circuit.load(obj);
Export circuit
Export to JavaScript
Circuit can be exported to JavaScript with exportJavaScript(comment, decompose, null, asJupyter)
method:
Example:
var js = circuit.exportJavaScript("Comment to insert at the beginning.\nCan be multiline comment like this one.", false);

comment
 comment to insert at the beginning of the file. 
decompose
 if set totrue
and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set tofalse
then user defined gates will exported as subroutines. 
asJupyter
 when this argument istrue
jupyter notebook (set to useijavascript
kernel) will be returned.
Export to python (Qiskit)
Circuit can be exported to Qiskit with following limitation:

User defined gates are not generated. Instead, circuit is decomposed to basic gates and exported. Effect is the same but code is less readable. TODO

Gates not directly supported by Qiskit are exported asis  their definition is not generated. TODO
To export circuit to Qiskit use exportToQiskit(options, exportAsGateName, circuitReplacement, insideSubmodule)
method :
Example:
var qiskit = circuit.exportToQiskit({comment:"Comment to insert at the beginning.\nCan be multiline comment as this one."}, false, null, null);

options
 consists of parameters for circuit export as follows:
comment
 comment to insert at the beginning of the file. 
decompose
 if set totrue
and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set tofalse
then user defined gates will exported as subroutines. 
versionStr
 Qiskit version. Can be"0.7"
. Exports to latest supported version when empty string is provided. Remember  it is a string. 
providerName
 name of the Qiskit backend simulator provider. 
backendName
 name of the Qiskit backend simulator. 
asJupyter
 when this argument istrue
jupyter notebook will be returned. 
shots
 no. of trials. 
hybrid
 whentrue
exports user defined cost function along with circuit for hybrid QuantumClassical Algorithms


insideSubmodule
 whentrue
adds extra indent for alignment 
exportAsGateName
 name of the custom gate containing the Qiskit circuit. 
circuitReplacement
 whentrue
exports only gates in the circuit
exportToQiskit()
instead)
(Deprecated. Please use To export circuit to Qiskit you can also use exportQiskit(comment, decompose, exportAsGateName, versionStr, providerName, backendName, asJupyter, shots, circuitReplacement, insideSubmodule, hybrid)
Example:
var qiskit = circuit.exportQiskit("Comment to insert at the beginning.\nCan be multiline comment as this one.", false, null, null);

comment
 comment to insert at the beginning of the file. 
decompose
 if set totrue
and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set tofalse
then user defined gates will exported as subroutines. 
versionStr
 Qiskit version. Can be"0.7"
. Exports to latest supported version when empty string is provided. Remember  it is a string. 
providerName
 name of the Qiskit backend simulator provider. 
backendName
 name of the Qiskit backend simulator. 
asJupyter
 when this argument istrue
jupyter notebook will be returned. 
shots
 no. of trials. 
hybrid
 whentrue
exports user defined cost function along with circuit for hybrid QuantumClassical Algorithms 
insideSubmodule
 whentrue
adds extra indent for alignment 
exportAsGateName
 name of the custom gate containing the Qiskit circuit. 
circuitReplacement
 whentrue
exports only gates in the circuit
Export to QASM
Circuit can be exported to OpenQASM with following limitation:
 at the moment, gates not directly supported by QASM and qelib1.inc are exported asis  their definition is not generated. TODO
To export circuit to OpenQASM use exportToQASM(options, exportAsGateName, circuitReplacement, insideSubmodule)
method:
Example:
var qasm = circuit.exportToQASM({comment:"Comment to insert at the beginning.\nCan be multiline comment as this one."}, false);

options
 consists of parameters for circuit export as follows:
comment
 comment to insert at the beginning of the file. 
decompose
 if set totrue
and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set tofalse
then user defined gates will exported as subroutines. 
compatibilityMode
 if set totrue
exports the circuit in compatible mode


insideSubmodule
 whentrue
adds extra indent for alignment 
exportAsGateName
 name of the custom gate containing the Qiskit circuit. 
circuitReplacement
 whentrue
exports only gates in the circuit
exportToQASM()
instead)
(Deprecated. Please use To export circuit to OpenQASM you can also use exportQASM(comment, decompose, exportAsGateName, circuitReplacement, compatibilityMode, insideSubmodule)
method:
Example:
var qasm = circuit.exportQASM("Comment to insert at the beginning.\nCan be multiline comment as this one.", false);

comment
 comment to insert at the beginning of the file. 
decompose
 if set totrue
and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set tofalse
then user defined gates will exported as subroutines. 
exportAsGateName
 name of the custom gate containing the Qiskit circuit. 
circuitReplacement
 whentrue
exports only gates in the circuit 
compatibilityMode
 if set totrue
exports the circuit in compatible mode 
insideSubmodule
 whentrue
adds extra indent for alignment
Import from QASM
Circuit can be imported from OpenQASM with following limitations:

import
directive is ignored (but most of gates defined inqelib1.inc
are supported) TODO 
barrier
is ignored. TODO 
reset
is ignored. TODO
To import circuit from OpenQASM use importQASM(input, errorCallback)
method:
Example:
circuit.importQASM("OPENQASM 2.0;\nimport \"qelib1.inc\";\nqreg q[2];\nh q[0];\ncx q[0],q[1];\n", function(errors) {
console.log(errors);
});

input
is string containing QASM source code. 
errorCallback
(optional) function will be called after parsing with array containing syntax errors.
Export to python (pyQuil)
Circuit can be exported to pyQuil
To export circuit to pyQuil use exportToPyquil(options, exportAsGateName)
method:
Example:
var qasm = circuit.exportToPyquil({comment:"Comment to insert at the beginning.\nCan be multiline comment as this one."}, false);

options
 consists of parameters for circuit export as follows:
comment
 comment to insert at the beginning of the file. 
decompose
 if set totrue
and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set tofalse
then user defined gates will exported as subroutines. 
versionStr
 pyQuil version. Can be"1.9"
,"2.0"
or"2.1"
. Exports to latest supported version when empty string is provided. Remember  it is a string. 
lattice
 You can optionally pass then name of the lattice. 
asQVM
 If this argument istrue
(and iflattice
is specified) then produced code will run on QVM mimicking running on QPU. Otherwise, produced code will run on QPU. 
asJupyter
 when this argument istrue
jupyter notebook will be returned. 
shots
 no. of trials. 
hybrid
 whentrue
exports user defined cost function along with circuit for hybrid QuantumClassical Algorithms


exportAsGateName
 name of the custom gate containing the Pyquil circuit.
exportToPyquil()
instead)
(Deprecated. Please use To export circuit to Pyquil you can also use exportPyquil(comment, decompose, exportAsGateName, versionStr, lattice, asQVM, asJupyter, shots, hybrid)
method:
Example:
var pyquil = circuit.exportPyquil("Comment to insert at the beginning.\nCan be multiline comment as this one.", false, null, "2.1", "", false);

comment
 comment to insert at the beginning of the file. 
decompose
 if set totrue
and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set tofalse
then user defined gates will exported as subroutines. 
exportAsGateName
 name of the custom gate containing the Pyquil circuit. 
versionStr
 pyQuil version. Can be"1.9"
,"2.0"
or"2.1"
. Exports to latest supported version when empty string is provided. Remember  it is a string. 
lattice
 You can optionally pass then name of the lattice. 
asQVM
 If this argument istrue
(and iflattice
is specified) then produced code will run on QVM mimicking running on QPU. Otherwise, produced code will run on QPU. 
asJupyter
 when this argument istrue
jupyter notebook will be returned. 
shots
 no. of trials. 
hybrid
 whentrue
exports user defined cost function along with circuit for hybrid QuantumClassical Algorithms
Export to Quil
Circuit can be exported to Quil
To export circuit to Quil use exportToQuil(options, exportAsGateName)
method:
Example:
var quil = circuit.exportToQuil({comment:"Comment to insert at the beginning.\nCan be multiline comment as this one."}, false);

options
 consists of parameters for circuit export as follows:
comment
 comment to insert at the beginning of the file. 
decompose
 if set totrue
and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set tofalse
then user defined gates will exported as subroutines. 
versionStr
 pyQuil version. Can be"1.9"
,"2.0"
or"2.1"
. Exports to latest supported version when empty string is provided. Remember  it is a string.


exportAsGateName
 name of the custom gate containing the Pyquil circuit.
exportToQuil()
instead)
(Deprecated. Please use To export circuit to Quil you can also use exportQuil(comment, decompose, exportAsGateName, versionStr)
method:
Example:
var quil = circuit.exportQuil("Comment to insert at the beginning.\nCan be multiline comment as this one.", false, null, "2.0");

comment
 comment to insert at the beginning of the file. 
decompose
 if set totrue
and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set tofalse
then user defined gates will exported as subroutines (DEFCIRCUIT). 
exportAsGateName
 name of the custom gate containing the Quil circuit. 
versionStr
 Quil version. Can be"1.0"
or"2.0"
or empty string. Exports to latest supported version when empty string is provided. Remember  it is a string.
Import from QUIL
Circuit can be imported from Quil:
To import circuit from OpenQASM use importQuil(quil, errorCallback, options, qubitNames, renamedGates, lineOffset)
method:
Example:
circuit.importQuil("H 0\nCNOT 0 1\n", function(errors) {
console.log(errors);
});

quil
is string containing QUIL source code. 
errorCallback
(optional) function will be called after parsing with array containing syntax errors. 
options
(optional) function will be called after parsing with array containing syntax errors. 
qubitNames
(optional) names to be given to the qubits. 
renamedGates
(optional) custom names given to basic commands 
lineOffset
(optional) no. of spaces before a new line
Export to python (Cirq)
Circuit can be exported to Cirq with following limitation:

Gates not directly supported by Cirq are exported asis  their definition is not generated. TODO

Classical control is ignored (comment with warning is generated). TODO
To export circuit to Cirq use exportToCirq(options, exportAsGateName)
method:
Example:
var cirq = circuit.exportToCirq({comment:"Comment to insert at the beginning.\nCan be multiline comment as this one."}, false);

options
 consists of parameters for circuit export as follows:
comment
 comment to insert at the beginning of the file. 
decompose
 if set totrue
and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set tofalse
then user defined gates will exported as subroutines. 
versionStr
 Cirq version. Can be"0.5"
or empty string. Exports to latest supported version when empty string is provided. Remember  it is a string. 
asJupyter
 when this argument istrue
jupyter notebook will be returned. 
shots
 no. of trials. 
exportTfq
 if set totrue
the export function will export circuit to Tensorflow Quantum.


exportAsGateName
 name of the custom gate containing the Cirq circuit.
exportToCirq()
instead)
(Deprecated. Please use To export circuit to Cirq you can also use exportCirq(comment, decompose, exportAsGateName, versionStr, asJupyter, shots, exportTfq)
method:
Example:
var cirq = circuit.exportCirq("Comment to insert at the beginning.\nCan be multiline comment as this one.", false, null, null, false, null, false);

comment
 comment to insert at the beginning of the file. 
decompose
 if set totrue
and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set tofalse
then user defined gates will exported as subroutines. 
exportAsGateName
 name of the custom gate containing the Cirq circuit. 
versionStr
 Cirq version. Can be"0.5"
or empty string. Exports to latest supported version when empty string is provided. Remember  it is a string. 
asJupyter
 when this argument istrue
jupyter notebook will be returned. 
shots
 no. of trials. 
exportTfq
 if set totrue
the export function will export circuit to Tensorflow Quantum.
Export to C/C++ (QuEST)
Circuit can be exported to QuEST
To export circuit to QuEST use exportQuEST(newOptions, exportAsGateName, definedFunc)
method:
Example:
var quest = circuit.exportToQuEST("Comment to insert at the beginning.\nCan be multiline comment as this one.", false);

options
 consists of parameters for circuit export as follows:
comment
 comment to insert at the beginning of the file. 
decompose
 if set totrue
and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set tofalse
then user defined gates will exported as subroutines.


exportAsGateName
 name of the custom gate containing the Cirq circuit. 
definedFunc
 list of gates that must be present in the defined function
exportToQuEST()
instead)
(Deprecated. Please use To export circuit to QuEST you can also use exportQuEST(comment, decompose, exportAsGateName, definedFunc)
method:
Example:
var quest = circuit.exportQuEST("Comment to insert at the beginning.\nCan be multiline comment as this one.", false, null, null);

comment
 comment to insert at the beginning of the file. 
decompose
 if set totrue
and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set tofalse
then user defined gates will exported as subroutines. 
exportAsGateName
 name of the custom gate containing the QuEST circuit. 
definedFunc
 list of gates that must be present in the defined function
Export to Q# (QSharp)
Circuit can be exported to Q#.
To export circuit to Q# use exportQSharp(options, exportAsGateName)
method:
Example:
var qsharp = circuit.exportQSharp("Comment to insert at the beginning.\nCan be multiline comment as this one.", false, null, null, false, null);

options
 consists of parameters for circuit export as follows:
comment
 comment to insert at the beginning of the file. 
decompose
 if set totrue
and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set tofalse
then user defined gates will exported as subroutines. 
versionStr
 QSharp version. Can be"0.1"
or empty string. Exports to latest supported version when empty string is provided. Remember  it is a string. 
asJupyter
 when this argument istrue
jupyter notebook (set to use qsharp kernel) will be returned. 
circuitName
 Name of the circuit that is being exported to QSharp. By default set to"Circuit"

indentDepth
 The no. of tabs to be put before a Python line of code.


exportAsGateName
 name of the custom gate containing the QSharp circuit.
exportToQSharp()
instead)
(Deprecated. Please use To export circuit to Q# use exportQSharp(comment, decompose, exportAsGateName, versionStr, asJupyter, circuitName, indentDepth)
method:
Example:
var qsharp = circuit.exportQSharp("Comment to insert at the beginning.\nCan be multiline comment as this one.", false, null, null, false, null);

comment
 comment to insert at the beginning of the file. 
decompose
 if set totrue
and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set tofalse
then user defined gates will exported as subroutines. 
exportAsGateName
 name of the custom gate containing the QSharp circuit. 
versionStr
 QSharp version. Can be"0.1"
or empty string. Exports to latest supported version when empty string is provided. Remember  it is a string. 
asJupyter
 when this argument istrue
jupyter notebook (set to use qsharp kernel) will be returned. 
circuitName
 Name of the circuit that is being exported to QSharp. By default set to"Circuit"

indentDepth
 The no. of tabs to be put before a Python line of code.
Export to Qobj
Circuit can be exported to Qobj:
To export circuit to Qiskit use exportToQobj(options, circuitReplacement)
method :
Example:
var qobj = circuit.exportToQobj({circuitName:"new_circuit"}, false);

options
 consists of parameters for circuit export as follows:
circuitName
 name of the circuit that is being exported to Qobj 
experimentName
 name of the experiment that describes the number of memory slots, qubits, qubit names, classical bit names etc. 
numShots
 no. of trials.


circuitReplacement
 whentrue
exports only gates in the circuit
exportToQobj()
instead)
(Deprecated. Please use To export circuit to Qobj you can also use exportQobj(circuitName, experimentName, numShots, circuitReplacement)
Example:
var qobj = circuit.exportQobj("new_circuit", false);

circuitName
 name of the circuit that is being exported to Qobj 
experimentName
 name of the experiment that describes the number of memory slots, qubits, qubit names, classical bit names etc. 
numShots
 no. of trials. 
circuitReplacement
 whentrue
exports only gates in the circuit
Import from Qobj
Circuit can be imported from Qobj:
To import circuit from OpenQASM use importQobj(qobj, errorCallback)
method:
Example:
circuit.importQobj({"qobj_id":"qobj_WlLkcGHxihyqWGrKEZ","type":"QASM","schema_version":"1.0","experiments":[{"header":{"memory_slots":0,"n_qubits":2,"qreg_sizes":[["q",2]],"qubit_labels":[["q",0],["q",1]],"creg_sizes":[],"clbit_labels":[],"name":"circuit0","description":"text_exp"},"config":{"n_qubits":2,"memory_slots":0},"instructions":[{"name":"x","qubits":[0,1]}]}],"header":{"description":"test_circ"},"config":{"shots":1,"memory_slots":0}}, function(errors) {
console.log(errors);
});

qobj
is string containing Qobj source code. 
errorCallback
(optional) function will be called after parsing with array containing syntax errors.
Export to python (Tensorflow Quantum)
Circuit can be exported to Tensorflow Quantum:
To export circuit to TFQ use exportToTFQ(options, exportAsGateName)
method :
Example:
var tfq = circuit.exportToTFQ({comment:"Comment to insert at the beginning.\nCan be multiline comment as this one."}, false);

options
 consists of parameters for circuit export as follows:
comment
 comment to insert at the beginning of the file. 
decompose
 if set totrue
and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set tofalse
then user defined gates will exported as subroutines. 
versionStr
 TFQ version. Exports to latest supported version when empty string is provided. Remember  it is a string. 
asJupyter
 when this argument istrue
jupyter notebook will be returned. 
shots
 no. of trials.


exportAsGateName
 name of the custom gate containing the TFQ circuit.
exportToTFQ()
instead)
(Deprecated. Please use To export circuit to TFQ you can also use exportTFQ(comment, decompose, exportAsGateName, versionStr, asJupyter, shots)
Example:
var tfq = circuit.exportTFQ("Comment to insert at the beginning.\nCan be multiline comment as this one.", false, null, null);

comment
 comment to insert at the beginning of the file. 
decompose
 if set totrue
and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set tofalse
then user defined gates will exported as subroutines. 
exportAsGateName
 name of the custom gate containing the TFQ circuit. 
versionStr
 TFQ version. Exports to latest supported version when empty string is provided. Remember  it is a string. 
asJupyter
 when this argument istrue
jupyter notebook will be returned. 
shots
 no. of trials.
Export to python (Braket)
Circuit can be exported to Braket:
To export circuit to Braket use exportToBraket(options, exportAsGateName)
method :
Example:
var braket = circuit.exportToBraket({comment:"Comment to insert at the beginning.\nCan be multiline comment as this one."}, false);

options
 consists of parameters for circuit export as follows:
comment
 comment to insert at the beginning of the file. 
decompose
 if set totrue
and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set tofalse
then user defined gates will exported as subroutines. 
versionStr
 Braket version. Exports to latest supported version when empty string is provided. Remember  it is a string. 
asJupyter
 when this argument istrue
jupyter notebook will be returned. 
shots
 no. of trials. 
indentDepth
 The no. of tabs to be put before a Python line of code. 
hybrid
 whentrue
exports user defined cost function along with circuit for hybrid QuantumClassical Algorithms


exportAsGateName
 name of the custom gate containing the Braket circuit.
exportToBraket()
instead)
(Deprecated. Please use To export circuit to Braket you can also use exportBraket(comment, decompose, exportAsGateName, versionStr, asJupyter, shots, hybrid, indentDepth)
Example:
var braket = circuit.exportBraket("Comment to insert at the beginning.\nCan be multiline comment as this one.", false, null, null);

comment
 comment to insert at the beginning of the file. 
decompose
 if set totrue
and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set tofalse
then user defined gates will exported as subroutines. 
exportAsGateName
 name of the custom gate containing the Braket circuit. 
versionStr
 Braket version. Exports to latest supported version when empty string is provided. Remember  it is a string. 
asJupyter
 when this argument istrue
jupyter notebook will be returned. 
shots
 no. of trials. 
indentDepth
 The no. of tabs to be put before a Python line of code. 
hybrid
 whentrue
exports user defined cost function along with circuit for hybrid QuantumClassical Algorithms
Export to python (pyAQASM)
Circuit can be exported to pyAQASM:
To export circuit to pyAQASM use exportToPyAQASM(options, exportAsGateName)
method :
Example:
var pyAqasm = circuit.exportToPyAQASM({comment:"Comment to insert at the beginning.\nCan be multiline comment as this one."}, false);

options
 consists of parameters for circuit export as follows:
comment
 comment to insert at the beginning of the file. 
decompose
 if set totrue
and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set tofalse
then user defined gates will exported as subroutines. 
asJupyter
 when this argument istrue
jupyter notebook will be returned. 
shots
 no. of trials. 
hybrid
 whentrue
exports user defined cost function along with circuit for hybrid QuantumClassical Algorithms


exportAsGateName
 name of the custom gate containing the pyAQASM circuit.
exportToPyAQASM()
instead)
(Deprecated. Please use To export circuit to pyAQASM you can also use exportPyAQASM(comment, decompose, exportAsGateName, asJupyter, shots, hybrid)
Example:
var pyAqasm = circuit.exportPyAQASM("Comment to insert at the beginning.\nCan be multiline comment as this one.", false, null, null);

comment
 comment to insert at the beginning of the file. 
decompose
 if set totrue
and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set tofalse
then user defined gates will exported as subroutines. 
exportAsGateName
 name of the custom gate containing the pyAQASM circuit. 
asJupyter
 when this argument istrue
jupyter notebook will be returned. 
shots
 no. of trials. 
hybrid
 whentrue
exports user defined cost function along with circuit for hybrid QuantumClassical Algorithms
Export to python (AQASM)
Circuit can be exported to AQASM:
To export circuit to AQASM use exportToAQASM(options, isExportPyAQASM, exportAsGateName, indentDepth)
method :
Example:
var aqasm = circuit.exportToAQASM({comment:"Comment to insert at the beginning.\nCan be multiline comment as this one."}, false);

options
 consists of parameters for circuit export as follows:
comment
 comment to insert at the beginning of the file. 
decompose
 if set totrue
and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set tofalse
then user defined gates will exported as subroutines. 
asJupyter
 when this argument istrue
jupyter notebook will be returned. 
shots
 no. of trials. 
hybrid
 whentrue
exports user defined cost function along with circuit for hybrid QuantumClassical Algorithms


isExportPyAQASM
 iftrue
, this function will be used to export to pyAQASM instead of AQASM. 
exportAsGateName
 name of the custom gate containing the AQASM circuit. 
indentDepth
 The no. of tabs to be put before a Python line of code.
exportToAQASM()
instead)
(Deprecated. Please use To export circuit to pyAQASM you can also use exportAQASM(comment, decompose, isExportPyAQASM, exportAsGateName, asJupyter, shots, hybrid, indentDepth)
Example:
var aqasm = circuit.exportAQASM("Comment to insert at the beginning.\nCan be multiline comment as this one.", false, null, null);

comment
 comment to insert at the beginning of the file. 
decompose
 if set totrue
and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set tofalse
then user defined gates will exported as subroutines. 
isExportPyAQASM
 iftrue
, this function will be used to export to pyAQASM instead of AQASM. 
exportAsGateName
 name of the custom gate containing the AQASM circuit. 
asJupyter
 when this argument istrue
jupyter notebook will be returned. 
shots
 no. of trials. 
hybrid
 whentrue
exports user defined cost function along with circuit for hybrid QuantumClassical Algorithms 
indentDepth
 The no. of tabs to be put before a Python line of code.
Export to SVG
Vector .svg
image of circuit can be created with exportSVG(embedded)
function with following limitations:
 Gate symbols are nonstandard. TODO (BTW, do we have standard?)
Example 1
Show circuit in browser:
// Assuming we have <div id="drawing"></div> somewhere in HTML
var container = document.getElementById("drawing");
// SVG is returned as string
var svg = circuit.exportSVG(true);
// add SVG into container
container.innerHTML = svg;
Example 2
Generate standalone SVG image at server with node.js:
// export as standalone SVG
var svg = circuit.exportSVG(false);
// do something with svg string (e.g. save to file)
...
// Or, export as embedded SVG for use in browser
svg = circuit.exportSVG(true);
// do something with svg string (e.g. serve via HTTP)
...
Export to Quirk
Circuit can be exported to popular opensource draganddrop quantum circuit simulator Quirk with following limitations:

Quirk doesn't support more than 16 qubits.

Quirk can possibly incorrectly interpret circuit if we have multiple controlled gates in the same column.

Quirk doesn't support nonsequentially positioned multiqubit userdefined gates (for example gate on wires [3, 0, 1]) so it's best to export decomposed circuit.
Example:
var quirkData = circuit.exportQuirk(true);
var quirkURL = "http://algassert.com/quirk#circuit=" + JSON.stringify(quirkData);
// Now do something with quirkURL. Assuming this code runs in browser and we have <a id="quirk"></a> somewhere, you can:
var quirkLink = document.getElementById("quirk");
quirkLink.setAttr("href", quirkLink);
About simulator algorithm
Memory usage: up to 2 * (2^numQubits) * sizeOfComplexNumber

Naive implementation stores entire state vector in an array of size
2^numQubits
. We are storing state in a "map", and only amplitudes with nonzero probabilities are stored. So, in worst case, size of state map is2^n
, but it's less most of the time because we don't store zeroes. 
Naive implementation creates transformation matrix and multiplies it with state vector. We are not creating and not storing entire transformation matrix in memory. Instead, elements of transformation matrix are calculated one by one and state is multiplied and stored in new state map on the fly. This way, memory usage is minimal (in worst case we have two
2^n
state vectors at a time). 
Algorithm is parallelizable so it could use GPU, but GPU support is not implemented yet (work in progress).
Benchmark
Performance is measured on MacBook Pro MJLT2 mid2015 (Core i7 2.5 GHz, 16GB RAM)
You can find scripts in /benchmark directory.
Gates
id
Single qubit identity gate
Qubits: 1
Matrix:
[
[1,0],
[0,1]
]
Example:
circuit.appendGate("id", 0);
x
Pauli X (PI rotation over Xaxis) aka "NOT" gate
Qubits: 1
Matrix:
[
[0,1],
[1,0]
]
Example:
circuit.appendGate("x", 0);
y
Pauli Y (PI rotation over Yaxis)
Qubits: 1
Matrix:
[
[0,"i"],
["i",0]
]
Example:
circuit.appendGate("y", 0);
z
Pauli Z (PI rotation over Zaxis)
Qubits: 1
Matrix:
[
[1,0],
[0,1]
]
Example:
circuit.appendGate("z", 0);
h
Hadamard gate
Qubits: 1
Matrix:
[
["1 / sqrt(2)","1 / sqrt(2)"],
["1 / sqrt(2)","1 / sqrt(2)"]
]
Example:
circuit.appendGate("h", 0);
srn
Square root of NOT
Qubits: 1
Matrix:
[
["0.5+0.5i","0.50.5i"],
["0.50.5i","0.5+0.5i"]
]
Example:
circuit.appendGate("srn", 0);
srndg
Inverse square root of NOT
Qubits: 1
Matrix:
[
["0.50.5i","0.5+0.5i"],
["0.5+0.5i","0.50.5i"]
]
Example:
circuit.appendGate("srndg", 0);
r2
PI/2 rotation over Zaxis aka "Phase PI/2"
Qubits: 1
Matrix:
[
[1,0],
[0,"exp(i * pi / 2)"]
]
Example:
circuit.appendGate("r2", 0);
r4
PI/4 rotation over Zaxis aka "Phase PI/4"
Qubits: 1
Matrix:
[
[1,0],
[0,"exp(i * pi / 4)"]
]
Example:
circuit.appendGate("r4", 0);
r8
PI/8 rotation over Zaxis aka "Phase PI/8"
Qubits: 1
Matrix:
[
[1,0],
[0,"exp(i * pi / 8)"]
]
Example:
circuit.appendGate("r8", 0);
rx
Rotation around the Xaxis by given angle
Qubits: 1
Parameters:
 theta
Matrix:
[
["cos(theta / 2)","i * sin(theta / 2)"],
["i * sin(theta / 2)","cos(theta / 2)"]
]
Example:
circuit.appendGate("rx", 0, {
params: {
theta: "pi/2"
}
});
ry
Rotation around the Yaxis by given angle
Qubits: 1
Parameters:
 theta
Matrix:
[
["cos(theta / 2)","1 * sin(theta / 2)"],
["sin(theta / 2)","cos(theta / 2)"]
]
Example:
circuit.appendGate("ry", 0, {
params: {
theta: "pi/2"
}
});
rz
Rotation around the Zaxis by given angle
Qubits: 1
Parameters:
 phi
Matrix:
[
["cos(phi / 2)  i * sin(phi / 2)",0],
[0,"cos(phi / 2) + i * sin(phi / 2)"]
]
Example:
circuit.appendGate("rz", 0, {
params: {
phi: "pi/2"
}
});
u1
Singlequbit rotation about the Z axis
Qubits: 1
Parameters:
 lambda
Matrix:
[
[1,0],
[0,"exp(i * lambda)"]
]
Example:
circuit.appendGate("u1", 0, {
params: {
lambda: "pi/2"
}
});
u2
Singlequbit rotation about the X+Z axis
Qubits: 1
Parameters:
 phi
 lambda
Matrix:
[
["1 / sqrt(2)","exp(i * lambda) * 1 / sqrt(2)"],
["exp(i * phi) * 1 / sqrt(2)","exp(i * lambda + i * phi) * 1 / sqrt(2)"]
]
Example:
circuit.appendGate("u2", 0, {
params: {
phi: "pi/2",
lambda: "pi/2"
}
});
u3
Generic singlequbit rotation gate with 3 Euler angles
Qubits: 1
Parameters:
 theta
 phi
 lambda
Matrix:
[
["cos(theta/2)","exp(i * lambda) * sin(theta / 2)"],
["exp(i * phi) * sin(theta / 2)","exp(i * lambda + i * phi) * cos(theta / 2)"]
]
Example:
circuit.appendGate("u3", 0, {
params: {
theta: "pi/2",
phi: "pi/2",
lambda: "pi/2"
}
});
s
PI/2 rotation over Zaxis (synonym for r2
)
Qubits: 1
Matrix:
[
[1,0],
[0,"exp(i * pi / 2)"]
]
Example:
circuit.appendGate("s", 0);
t
PI/4 rotation over Zaxis (synonym for r4
)
Qubits: 1
Matrix:
[
[1,0],
[0,"exp(i * pi / 4)"]
]
Example:
circuit.appendGate("t", 0);
sdg
(PI/2) rotation over Zaxis
Qubits: 1
Matrix:
[
[1,0],
[0,"exp(i * pi / 2)"]
]
Example:
circuit.appendGate("sdg", 0);
tdg
(PI/4) rotation over Zaxis
Qubits: 1
Matrix:
[
[1,0],
[0,"exp(i * pi / 4)"]
]
Example:
circuit.appendGate("tdg", 0);
swap
Swaps the state of two qubits.
Qubits: 2
Matrix:
[
[1,0,0,0],
[0,0,1,0],
[0,1,0,0],
[0,0,0,1]
]
Example:
circuit.appendGate("swap", [0, 1]);
srswap
Square root of swap
Qubits: 2
Matrix:
[
[1,0,0,0],
[0,"0.5 * (1 + i)","0.5 * (1  i)",0],
[0,"0.5 * (1  i)","0.5 * (1 + i)",0],
[0,0,0,1]
]
Example:
circuit.appendGate("srswap", [0, 1]);
iswap
Swaps the state of two qubits, applying a i phase to q1 when it is in the 1 state and a i phase to q2 when it is in the 0 state
Qubits: 2
Matrix:
[
[1,0,0,0],
[0,0,"0+i",0],
[0,"0+i",0,0],
[0,0,0,1]
]
Example:
circuit.appendGate("iswap", [0, 1]);
xy
XY gate
Qubits: 2
Parameters:
 phi
Matrix:
[
[1,0,0,0],
[0,"cos(phi / 2)","i * sin(phi / 2)",0],
[0,"i * sin(phi / 2)","cos(phi / 2)",0],
[0,0,0,1]
]
Example:
circuit.appendGate("xy", [0, 1], {
params: {
phi: "pi/2"
}
});
cx
Controlled NOT (CNOT) gate
Qubits: 2
Matrix:
[
[1,0,0,0],
[0,1,0,0],
[0,0,0,1],
[0,0,1,0]
]
Example:
circuit.appendGate("cx", [0, 1]);
cy
Controlled Y gate (controlled rotation over Yaxis by PI)
Qubits: 2
Matrix:
[
[1,0,0,0],
[0,1,0,0],
[0,0,0,"i"],
[0,0,"i",0]
]
Example:
circuit.appendGate("cy", [0, 1]);
cz
Controlled Z gate (controlled rotation over Zaxis by PI)
Qubits: 2
Matrix:
[
[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[0,0,0,1]
]
Example:
circuit.appendGate("cz", [0, 1]);
ch
Controlled Hadamard gate
Qubits: 2
Matrix:
[
[1,0,0,0],
[0,1,0,0],
[0,0,"1 / sqrt(2)","1 / sqrt(2)"],
[0,0,"1 / sqrt(2)","1 / sqrt(2)"]
]
Example:
circuit.appendGate("ch", [0, 1]);
csrn
Controlled square root of NOT
Qubits: 2
Matrix:
[
[1,0,0,0],
[0,1,0,0],
[0,0,"0.5+0.5i","0.50.5i"],
[0,0,"0.50.5i","0.5+0.5i"]
]
Example:
circuit.appendGate("csrn", [0, 1]);
ms
MølmerSørensen gate
Qubits: 2
Parameters:
 theta
Matrix:
[
["cos(theta)",0,0,"i*sin(theta)"],
[0,"cos(theta)","i*sin(theta)",0],
[0,"i*sin(theta)","cos(theta)",0],
["i*sin(theta)",0,0,"cos(theta)"]
]
Example:
circuit.appendGate("ms", [0, 1], {
params: {
theta: "pi/2"
}
});
yy
YY gate
Qubits: 2
Parameters:
 theta
Matrix:
[
["cos(theta)",0,0,"i*sin(theta)"],
[0,"cos(theta)","i*sin(theta)",0],
[0,"i*sin(theta)","cos(theta)",0],
["i*sin(theta)",0,0,"cos(theta)"]
]
Example:
circuit.appendGate("yy", [0, 1], {
params: {
theta: "pi/2"
}
});
zz
Parametric 2qubit rotation about ZZ
Qubits: 2
Parameters:
 theta
Matrix:
[
["exp(i * theta / 2)",0,0,0],
[0,"exp(i * theta / 2)",0,0],
[0,0,"exp(i * theta / 2)",0],
[0,0,0,"exp(i * theta / 2)"]
]
Example:
circuit.appendGate("zz", [0, 1], {
params: {
theta: "pi/2"
}
});
cr2
Controlled PI/2 rotation over Zaxis
Qubits: 2
Matrix:
[
[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[0,0,0,"exp(i * pi / 2)"]
]
Example:
circuit.appendGate("cr2", [0, 1]);
cr4
Controlled PI/4 rotation over Zaxis
Qubits: 2
Matrix:
[
[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[0,0,0,"exp(i * pi / 4)"]
]
Example:
circuit.appendGate("cr4", [0, 1]);
cr8
Controlled PI/8 rotation over Zaxis
Qubits: 2
Matrix:
[
[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[0,0,0,"exp(i * pi / 8)"]
]
Example:
circuit.appendGate("cr8", [0, 1]);
crx
Controlled rotation around the Xaxis by given angle
Qubits: 2
Parameters:
 theta
Matrix:
[
[1,0,0,0],
[0,1,0,0],
[0,0,"cos(theta / 2)","i * sin(theta / 2)"],
[0,0,"i * sin(theta / 2)","cos(theta / 2)"]
]
Example:
circuit.appendGate("crx", [0, 1], {
params: {
theta: "pi/2"
}
});
cry
Controlled rotation around the Yaxis by given angle
Qubits: 2
Parameters:
 theta
Matrix:
[
[1,0,0,0],
[0,1,0,0],
[0,0,"cos(theta / 2)","1 * sin(theta / 2)"],
[0,0,"sin(theta / 2)","cos(theta / 2)"]
]
Example:
circuit.appendGate("cry", [0, 1], {
params: {
theta: "pi/2"
}
});
crz
Controlled rotation around the Zaxis by given angle
Qubits: 2
Parameters:
 phi
Matrix:
[
[1,0,0,0],
[0,1,0,0],
[0,0,"cos(phi / 2)  i * sin(phi / 2)",0],
[0,0,0,"cos(phi / 2) + i * sin(phi / 2)"]
]
Example:
circuit.appendGate("crz", [0, 1], {
params: {
phi: "pi/2"
}
});
cu1
Controlled rotation about the Z axis
Qubits: 2
Parameters:
 lambda
Matrix:
[
[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[0,0,0,"exp(i * lambda)"]
]
Example:
circuit.appendGate("cu1", [0, 1], {
params: {
lambda: "pi/2"
}
});
cu2
Controlled rotation about the X+Z axis
Qubits: 2
Parameters:
 phi
 lambda
Matrix:
[
[1,0,0,0],
[0,1,0,0],
[0,0,"1 / sqrt(2)","exp(i * lambda) * 1 / sqrt(2)"],
[0,0,"exp(i * phi) * 1 / sqrt(2)","exp(i * lambda + i * phi) * 1 / sqrt(2)"]
]
Example:
circuit.appendGate("cu2", [0, 1], {
params: {
phi: "pi/2",
lambda: "pi/2"
}
});
cu3
Controlled rotation gate with 3 Euler angles
Qubits: 2
Parameters:
 theta
 phi
 lambda
Matrix:
[
[1,0,0,0],
[0,1,0,0],
[0,0,"cos(theta/2)","exp(i * lambda) * sin(theta / 2)"],
[0,0,"exp(i * phi) * sin(theta / 2)","exp(i * lambda + i * phi) * cos(theta / 2)"]
]
Example:
circuit.appendGate("cu3", [0, 1], {
params: {
theta: "pi/2",
phi: "pi/2",
lambda: "pi/2"
}
});
cs
Controlled PI/2 rotation over Zaxis (synonym for cr2
)
Qubits: 2
Matrix:
[
[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[0,0,0,"exp(i * pi / 2)"]
]
Example:
circuit.appendGate("cs", [0, 1]);
ct
Controlled PI/4 rotation over Zaxis (synonym for cr4
)
Qubits: 2
Matrix:
[
[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[0,0,0,"exp(i * pi / 4)"]
]
Example:
circuit.appendGate("ct", [0, 1]);
csdg
Controlled (PI/2) rotation over Zaxis
Qubits: 2
Matrix:
[
[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[0,0,0,"exp(i * pi / 2)"]
]
Example:
circuit.appendGate("csdg", [0, 1]);
ctdg
Controlled (PI/4) rotation over Zaxis
Qubits: 2
Matrix:
[
[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[0,0,0,"exp(i * pi / 4)"]
]
Example:
circuit.appendGate("ctdg", [0, 1]);
ccx
Toffoli aka "CCNOT" gate
Qubits: 3
Matrix:
[
[1,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0],
[0,0,0,1,0,0,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,0,1],
[0,0,0,0,0,0,1,0]
]
Example:
circuit.appendGate("ccx", [0, 1, 2]);
cswap
Controlled swap aka "Fredkin" gate
Qubits: 3
Matrix:
[
[1,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0],
[0,0,0,1,0,0,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,0,1]
]
Example:
circuit.appendGate("cswap", [0, 1, 2]);
csrswap
Controlled square root of swap
Qubits: 3
Matrix:
[
[1,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0],
[0,0,0,1,0,0,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,"0.5 * (1 + i)","0.5 * (1  i)",0],
[0,0,0,0,0,"0.5 * (1  i)","0.5 * (1 + i)",0],
[0,0,0,0,0,0,0,1]
]
Example:
circuit.appendGate("csrswap", [0, 1, 2]);
reset
Resets qubit
Qubits: 1
Example:
circuit.appendGate("reset", 0);
measure
Measures qubit and stores chance (0 or 1) into classical bit
Qubits: 1
Example:
circuit.appendGate("measure", 0, {
creg: {
name: "c",
bit: 3
}
});
Or:
circuit.addMeasure(0, "c", 3);
API docs
To be written...