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quantastica
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Description

Quantum Circuit Simulator implemented in JavaScript

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Quantum Circuit Simulator

quantum-circuit 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

Using in browser

Simply include quantum-circuit.min.js into your html page (available via unpkg CDN https://unpkg.com/quantum-circuit)

    <title>Quantum Circuit Simulator Example</title>



    <script type="text/javascript" src="https://unpkg.com/quantum-circuit"></script>

    <script type="text/javascript">
        // Your code here
    </script>

Using at server with node.js

Add quantum-circuit npm module to your node.js project:

npm install --save quantum-circuit

And then import it into your program:

var QuantumCircuit = require("quantum-circuit");

// 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 quantum-circuit npm module globally and invoke jupyter notebook from any directory:

npm install -g quantum-circuit

Or inside new directory do:

npm init
npm install --save quantum-circuit
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 non-existing wires

Add single-qubit 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 multi-qubit 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("quantum-circuit");

// // 8-bit quantum random number generator //

var quantumRandom = function() {

var circuit = new QuantumCircuit();

for(var i = 0; i &lt; 8; i++) {
    //
    // add Hadamard gate to the end (-1) of i-th wire
    //
    circuit.addGate("h", -1, i);

    //
    // add measurement gate to i-th qubit which will store result 
    // into classical register "c", into i-th 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 X-axis) aka "NOT" gate | | y | Y | Y | Y | 1 | | Pauli Y (PI rotation over Y-axis) | | z | Z | Z | Z | 1 | | Pauli Z (PI rotation over Z-axis) | | 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 Z-axis aka "Phase PI/2" | | r4 | T | T | T | 1 | | PI/4 rotation over Z-axis aka "Phase PI/4" | | r8 | PHASE(pi/8) | u1(pi/8) | | 1 | | PI/8 rotation over Z-axis aka "Phase PI/8" | | rx | RX | rx | Rx | 1 | theta | Rotation around the X-axis by given angle | | ry | RY | ry | Ry | 1 | theta | Rotation around the Y-axis by given angle | | rz | RZ | rz | Rz | 1 | phi | Rotation around the Z-axis by given angle | | u1 | PHASE | def u1 | | 1 | lambda | Single-qubit rotation about the Z axis | | u2 | def u2 | def u2 | | 1 | phi, lambda | Single-qubit rotation about the X+Z axis | | u3 | def u3 | def u3 | | 1 | theta, phi, lambda | Generic single-qubit rotation gate with 3 Euler angles | | s | S | S | S | 1 | | PI/2 rotation over Z-axis (synonym for

r2
) | | t | T | T | T | 1 | | PI/4 rotation over Z-axis (synonym for
r4
) | | sdg | PHASE(-pi/2) | u1(-pi/2) | | 1 | | (-PI/2) rotation over Z-axis | | tdg | PHASE(-pi/4) | u1(-pi/4) | | 1 | | (-PI/4) rotation over Z-axis | | 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 Y-axis by PI) | | cz | CZ | CZ | Controlled Z | 2 | | Controlled Z gate (controlled rotation over Z-axis 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 | Mølmer-Sørensen gate | | yy | def yy | YY | | 2 | theta | YY gate | | zz | def zz | | | 2 | theta | Parametric 2-qubit rotation about ZZ | | cr2 | CPHASE(pi/2) | cu1(pi/2) | | 2 | | Controlled PI/2 rotation over Z-axis | | cr4 | CPHASE(pi/4) | cu1(pi/4) | | 2 | | Controlled PI/4 rotation over Z-axis | | cr8 | CPHASE(pi/8) | cu1(pi/8) | | 2 | | Controlled PI/8 rotation over Z-axis | | crx | def crx | rx(theta) | Controlled Rx | 2 | theta | Controlled rotation around the X-axis by given angle | | cry | def cry | ry(theta) | Controlled Ry | 2 | theta | Controlled rotation around the Y-axis by given angle | | crz | def crz | rz(phi) | Controlled Rz | 2 | phi | Controlled rotation around the Z-axis 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 Z-axis (synonym for
cr2
) | | ct | CPHASE(pi/4) | cu1(pi/4) | | 2 | | Controlled PI/4 rotation over Z-axis (synonym for
cr4
) | | csdg | CPHASE(-pi/2) | cu1(-pi/2) | | 2 | | Controlled (-PI/2) rotation over Z-axis | | ctdg | CPHASE(-pi/4) | cu1(-pi/4) | | 2 | | Controlled (-PI/4) rotation over Z-axis | | 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:

javascript
console.log(circuit.measureAll());

Method

measure(wire)
returns chance (as integer 0 or 1) for given qubit:

Example:

javascript
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 5-bit register named

ans
:
javascript
circuit.createCreg("ans", 5);

Read register

To get register value as integer, call

getCregValue(name)
.

Example:

javascript
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:

javascript
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
:
javascript
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
:
javascript
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:

javascript
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:

javascript
var js = circuit.exportJavaScript("Comment to insert at the beginning.\nCan be multi-line comment like this one.", false);
  • comment
    - comment to insert at the beginning of the file.
  • decompose
    - if set to
    true
    and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set to
    false
    then user defined gates will exported as subroutines.
  • asJupyter
    - when this argument is
    true
    jupyter notebook (set to use
    ijavascript
    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 as-is - their definition is not generated. TODO

To export circuit to Qiskit use

exportToQiskit(options, exportAsGateName, circuitReplacement, insideSubmodule)
method :

Example:

javascript
var qiskit = circuit.exportToQiskit({comment:"Comment to insert at the beginning.\nCan be multi-line 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 to true and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set to false 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 is true jupyter notebook will be returned.

  • shots - no. of trials.

  • hybrid - when true exports user defined cost function along with circuit for hybrid Quantum-Classical Algorithms

  • insideSubmodule
    - when
    true
    adds extra indent for alignment
  • exportAsGateName
    - name of the custom gate containing the Qiskit circuit.
  • circuitReplacement
    - when
    true
    exports only gates in the circuit
(Deprecated. Please use
exportToQiskit()
instead)

To export circuit to Qiskit you can also use

exportQiskit(comment, decompose, exportAsGateName, versionStr, providerName, backendName, asJupyter, shots, circuitReplacement, insideSubmodule, hybrid)

Example:

javascript
var qiskit = circuit.exportQiskit("Comment to insert at the beginning.\nCan be multi-line comment as this one.", false, null, null);
  • comment
    - comment to insert at the beginning of the file.
  • decompose
    - if set to
    true
    and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set to
    false
    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 is
    true
    jupyter notebook will be returned.
  • shots
    - no. of trials.
  • hybrid
    - when
    true
    exports user defined cost function along with circuit for hybrid Quantum-Classical Algorithms
  • insideSubmodule
    - when
    true
    adds extra indent for alignment
  • exportAsGateName
    - name of the custom gate containing the Qiskit circuit.
  • circuitReplacement
    - when
    true
    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 as-is - their definition is not generated. TODO

To export circuit to OpenQASM use

exportToQASM(options, exportAsGateName, circuitReplacement, insideSubmodule)
method:

Example:

javascript
var qasm = circuit.exportToQASM({comment:"Comment to insert at the beginning.\nCan be multi-line 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 to true and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set to false then user defined gates will exported as subroutines.

  • compatibilityMode - if set to true exports the circuit in compatible mode

  • insideSubmodule
    - when
    true
    adds extra indent for alignment
  • exportAsGateName
    - name of the custom gate containing the Qiskit circuit.
  • circuitReplacement
    - when
    true
    exports only gates in the circuit
(Deprecated. Please use
exportToQASM()
instead)

To export circuit to OpenQASM you can also use

exportQASM(comment, decompose, exportAsGateName, circuitReplacement, compatibilityMode, insideSubmodule)
method:

Example:

javascript
var qasm = circuit.exportQASM("Comment to insert at the beginning.\nCan be multi-line comment as this one.", false);
  • comment
    - comment to insert at the beginning of the file.
  • decompose
    - if set to
    true
    and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set to
    false
    then user defined gates will exported as subroutines.
  • exportAsGateName
    - name of the custom gate containing the Qiskit circuit.
  • circuitReplacement
    - when
    true
    exports only gates in the circuit
  • compatibilityMode
    - if set to
    true
    exports the circuit in compatible mode
  • insideSubmodule
    - when
    true
    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 in
    qelib1.inc
    are supported) TODO
  • barrier
    is ignored. TODO
  • reset
    is ignored. TODO

To import circuit from OpenQASM use

importQASM(input, errorCallback)
method:

Example:

javascript
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:

javascript
var qasm = circuit.exportToPyquil({comment:"Comment to insert at the beginning.\nCan be multi-line 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 to true and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set to false 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 is true (and if lattice is specified) then produced code will run on QVM mimicking running on QPU. Otherwise, produced code will run on QPU.

  • asJupyter - when this argument is true jupyter notebook will be returned.

  • shots - no. of trials.

  • hybrid - when true exports user defined cost function along with circuit for hybrid Quantum-Classical Algorithms

  • exportAsGateName
    - name of the custom gate containing the Pyquil circuit.
(Deprecated. Please use
exportToPyquil()
instead)

To export circuit to Pyquil you can also use

exportPyquil(comment, decompose, exportAsGateName, versionStr, lattice, asQVM, asJupyter, shots, hybrid)
method:

Example:

javascript
var pyquil = circuit.exportPyquil("Comment to insert at the beginning.\nCan be multi-line comment as this one.", false, null, "2.1", "", false);
  • comment
    - comment to insert at the beginning of the file.
  • decompose
    - if set to
    true
    and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set to
    false
    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 is
    true
    (and if
    lattice
    is specified) then produced code will run on QVM mimicking running on QPU. Otherwise, produced code will run on QPU.
  • asJupyter
    - when this argument is
    true
    jupyter notebook will be returned.
  • shots
    - no. of trials.
  • hybrid
    - when
    true
    exports user defined cost function along with circuit for hybrid Quantum-Classical Algorithms

Export to Quil

Circuit can be exported to Quil

To export circuit to Quil use

exportToQuil(options, exportAsGateName)
method:

Example:

javascript
var quil = circuit.exportToQuil({comment:"Comment to insert at the beginning.\nCan be multi-line 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 to true and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set to false 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.
(Deprecated. Please use
exportToQuil()
instead)

To export circuit to Quil you can also use

exportQuil(comment, decompose, exportAsGateName, versionStr)
method:

Example:

javascript
var quil = circuit.exportQuil("Comment to insert at the beginning.\nCan be multi-line comment as this one.", false, null, "2.0");
  • comment
    - comment to insert at the beginning of the file.
  • decompose
    - if set to
    true
    and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set to
    false
    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:

javascript
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 as-is - 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:

javascript
var cirq = circuit.exportToCirq({comment:"Comment to insert at the beginning.\nCan be multi-line 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 to true and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set to false 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 is true jupyter notebook will be returned.

  • shots - no. of trials.

  • exportTfq - if set to true the export function will export circuit to Tensorflow Quantum.

  • exportAsGateName
    - name of the custom gate containing the Cirq circuit.
(Deprecated. Please use
exportToCirq()
instead)

To export circuit to Cirq you can also use

exportCirq(comment, decompose, exportAsGateName, versionStr, asJupyter, shots, exportTfq)
method:

Example:

javascript
var cirq = circuit.exportCirq("Comment to insert at the beginning.\nCan be multi-line comment as this one.", false, null, null, false, null, false);
  • comment
    - comment to insert at the beginning of the file.
  • decompose
    - if set to
    true
    and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set to
    false
    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 is
    true
    jupyter notebook will be returned.
  • shots
    - no. of trials.
  • exportTfq
    - if set to
    true
    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:

javascript
var quest = circuit.exportToQuEST("Comment to insert at the beginning.\nCan be multi-line 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 to
      true
      and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set to
      false
      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
(Deprecated. Please use
exportToQuEST()
instead)

To export circuit to QuEST you can also use

exportQuEST(comment, decompose, exportAsGateName, definedFunc)
method:

Example:

javascript
var quest = circuit.exportQuEST("Comment to insert at the beginning.\nCan be multi-line comment as this one.", false, null, null);
  • comment
    - comment to insert at the beginning of the file.
  • decompose
    - if set to
    true
    and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set to
    false
    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:

javascript
var qsharp = circuit.exportQSharp("Comment to insert at the beginning.\nCan be multi-line 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 to
      true
      and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set to
      false
      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 is
      true
      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.
(Deprecated. Please use
exportToQSharp()
instead)

To export circuit to Q# use

exportQSharp(comment, decompose, exportAsGateName, versionStr, asJupyter, circuitName, indentDepth)
method:

Example:

javascript
var qsharp = circuit.exportQSharp("Comment to insert at the beginning.\nCan be multi-line comment as this one.", false, null, null, false, null);
  • comment
    - comment to insert at the beginning of the file.
  • decompose
    - if set to
    true
    and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set to
    false
    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 is
    true
    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:

javascript
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
    - when
    true
    exports only gates in the circuit
(Deprecated. Please use
exportToQobj()
instead)

To export circuit to Qobj you can also use

exportQobj(circuitName, experimentName, numShots, circuitReplacement)

Example:

javascript
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
    - when
    true
    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:

javascript
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:

javascript
var tfq = circuit.exportToTFQ({comment:"Comment to insert at the beginning.\nCan be multi-line 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 to true and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set to false 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 is true jupyter notebook will be returned.

  • shots - no. of trials.

  • exportAsGateName
    - name of the custom gate containing the TFQ circuit.
(Deprecated. Please use
exportToTFQ()
instead)

To export circuit to TFQ you can also use

exportTFQ(comment, decompose, exportAsGateName, versionStr, asJupyter, shots)

Example:

javascript
var tfq = circuit.exportTFQ("Comment to insert at the beginning.\nCan be multi-line comment as this one.", false, null, null);
  • comment
    - comment to insert at the beginning of the file.
  • decompose
    - if set to
    true
    and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set to
    false
    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 is
    true
    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:

javascript
var braket = circuit.exportToBraket({comment:"Comment to insert at the beginning.\nCan be multi-line 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 to true and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set to false 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 is true jupyter notebook will be returned.

  • shots - no. of trials.

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

  • hybrid - when true exports user defined cost function along with circuit for hybrid Quantum-Classical Algorithms

  • exportAsGateName
    - name of the custom gate containing the Braket circuit.
(Deprecated. Please use
exportToBraket()
instead)

To export circuit to Braket you can also use

exportBraket(comment, decompose, exportAsGateName, versionStr, asJupyter, shots, hybrid, indentDepth)

Example:

javascript
var braket = circuit.exportBraket("Comment to insert at the beginning.\nCan be multi-line comment as this one.", false, null, null);
  • comment
    - comment to insert at the beginning of the file.
  • decompose
    - if set to
    true
    and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set to
    false
    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 is
    true
    jupyter notebook will be returned.
  • shots
    - no. of trials.
  • indentDepth
    - The no. of tabs to be put before a Python line of code.
  • hybrid
    - when
    true
    exports user defined cost function along with circuit for hybrid Quantum-Classical Algorithms

Export to python (pyAQASM)

Circuit can be exported to pyAQASM:

To export circuit to pyAQASM use

exportToPyAQASM(options, exportAsGateName)
method :

Example:

javascript
var pyAqasm = circuit.exportToPyAQASM({comment:"Comment to insert at the beginning.\nCan be multi-line 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 to true and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set to false then user defined gates will exported as subroutines.

  • asJupyter - when this argument is true jupyter notebook will be returned.

  • shots - no. of trials.

  • hybrid - when true exports user defined cost function along with circuit for hybrid Quantum-Classical Algorithms

  • exportAsGateName
    - name of the custom gate containing the pyAQASM circuit.
(Deprecated. Please use
exportToPyAQASM()
instead)

To export circuit to pyAQASM you can also use

exportPyAQASM(comment, decompose, exportAsGateName, asJupyter, shots, hybrid)

Example:

javascript
var pyAqasm = circuit.exportPyAQASM("Comment to insert at the beginning.\nCan be multi-line comment as this one.", false, null, null);
  • comment
    - comment to insert at the beginning of the file.
  • decompose
    - if set to
    true
    and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set to
    false
    then user defined gates will exported as subroutines.
  • exportAsGateName
    - name of the custom gate containing the pyAQASM circuit.
  • asJupyter
    - when this argument is
    true
    jupyter notebook will be returned.
  • shots
    - no. of trials.
  • hybrid
    - when
    true
    exports user defined cost function along with circuit for hybrid Quantum-Classical Algorithms

Export to python (AQASM)

Circuit can be exported to AQASM:

To export circuit to AQASM use

exportToAQASM(options, isExportPyAQASM, exportAsGateName, indentDepth)
method :

Example:

javascript
var aqasm = circuit.exportToAQASM({comment:"Comment to insert at the beginning.\nCan be multi-line 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 to true and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set to false then user defined gates will exported as subroutines.

  • asJupyter - when this argument is true jupyter notebook will be returned.

  • shots - no. of trials.

  • hybrid - when true exports user defined cost function along with circuit for hybrid Quantum-Classical Algorithms

  • isExportPyAQASM
    - if
    true
    , 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.
(Deprecated. Please use
exportToAQASM()
instead)

To export circuit to pyAQASM you can also use

exportAQASM(comment, decompose, isExportPyAQASM, exportAsGateName, asJupyter, shots, hybrid, indentDepth)

Example:

javascript
var aqasm = circuit.exportAQASM("Comment to insert at the beginning.\nCan be multi-line comment as this one.", false, null, null);
  • comment
    - comment to insert at the beginning of the file.
  • decompose
    - if set to
    true
    and circuit contains user defined gates then it will be decomposed to basic gates and then exported. If set to
    false
    then user defined gates will exported as subroutines.
  • isExportPyAQASM
    - if
    true
    , 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 is
    true
    jupyter notebook will be returned.
  • shots
    - no. of trials.
  • hybrid
    - when
    true
    exports user defined cost function along with circuit for hybrid Quantum-Classical 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 non-standard. TODO (BTW, do we have standard?)

Example 1

Show circuit in browser:

// Assuming we have 
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 open-source drag-and-drop 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 non-sequentially positioned multi-qubit user-defined 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 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 non-zero probabilities are stored. So, in worst case, size of state map is
    2^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 mid-2015 (Core i7 2.5 GHz, 16GB RAM)

Benchmark 1

Benchmark 2

Benchmark 3

You can find scripts in /benchmark directory.

Gates

id

Single qubit identity gate

Qubits: 1

Matrix: ```javascript [

[1,0],
[0,1]

] ```

Example:

javascript
circuit.appendGate("id", 0);

x

Pauli X (PI rotation over X-axis) aka "NOT" gate

Qubits: 1

Matrix: ```javascript [

[0,1],
[1,0]

] ```

Example:

javascript
circuit.appendGate("x", 0);

y

Pauli Y (PI rotation over Y-axis)

Qubits: 1

Matrix: ```javascript [

[0,"-i"],
["i",0]

] ```

Example:

javascript
circuit.appendGate("y", 0);

z

Pauli Z (PI rotation over Z-axis)

Qubits: 1

Matrix: ```javascript [

[1,0],
[0,-1]

] ```

Example:

javascript
circuit.appendGate("z", 0);

h

Hadamard gate

Qubits: 1

Matrix: ```javascript [

["1 / sqrt(2)","1 / sqrt(2)"],
["1 / sqrt(2)","-1 / sqrt(2)"]

] ```

Example:

javascript
circuit.appendGate("h", 0);

srn

Square root of NOT

Qubits: 1

Matrix: ```javascript [

["0.5+0.5i","0.5-0.5i"],
["0.5-0.5i","0.5+0.5i"]

] ```

Example:

javascript
circuit.appendGate("srn", 0);

srndg

Inverse square root of NOT

Qubits: 1

Matrix: ```javascript [

["0.5-0.5i","0.5+0.5i"],
["0.5+0.5i","0.5-0.5i"]

] ```

Example:

javascript
circuit.appendGate("srndg", 0);

r2

PI/2 rotation over Z-axis aka "Phase PI/2"

Qubits: 1

Matrix: ```javascript [

[1,0],
[0,"exp(i * pi / 2)"]

] ```

Example:

javascript
circuit.appendGate("r2", 0);

r4

PI/4 rotation over Z-axis aka "Phase PI/4"

Qubits: 1

Matrix: ```javascript [

[1,0],
[0,"exp(i * pi / 4)"]

] ```

Example:

javascript
circuit.appendGate("r4", 0);

r8

PI/8 rotation over Z-axis aka "Phase PI/8"

Qubits: 1

Matrix: ```javascript [

[1,0],
[0,"exp(i * pi / 8)"]

] ```

Example:

javascript
circuit.appendGate("r8", 0);

rx

Rotation around the X-axis by given angle

Qubits: 1

Parameters:

  • theta

Matrix: ```javascript [

["cos(theta / 2)","-i * sin(theta / 2)"],
["-i * sin(theta / 2)","cos(theta / 2)"]

] ```

Example:

javascript
circuit.appendGate("rx", 0, {
    params: {
        theta: "pi/2"
    }
});

ry

Rotation around the Y-axis by given angle

Qubits: 1

Parameters:

  • theta

Matrix: ```javascript [

["cos(theta / 2)","-1 * sin(theta / 2)"],
["sin(theta / 2)","cos(theta / 2)"]

] ```

Example:

javascript
circuit.appendGate("ry", 0, {
    params: {
        theta: "pi/2"
    }
});

rz

Rotation around the Z-axis by given angle

Qubits: 1

Parameters:

  • phi

Matrix: ```javascript [

["cos(phi / 2) - i * sin(phi / 2)",0],
[0,"cos(phi / 2) + i * sin(phi / 2)"]

] ```

Example:

javascript
circuit.appendGate("rz", 0, {
    params: {
        phi: "pi/2"
    }
});

u1

Single-qubit rotation about the Z axis

Qubits: 1

Parameters:

  • lambda

Matrix: ```javascript [

[1,0],
[0,"exp(i * lambda)"]

] ```

Example:

javascript
circuit.appendGate("u1", 0, {
    params: {
        lambda: "pi/2"
    }
});

u2

Single-qubit rotation about the X+Z axis

Qubits: 1

Parameters:

  • phi
  • lambda

Matrix: ```javascript [

["1 / sqrt(2)","-exp(i * lambda) * 1 / sqrt(2)"],
["exp(i * phi) * 1 / sqrt(2)","exp(i * lambda + i * phi) * 1 / sqrt(2)"]

] ```

Example:

javascript
circuit.appendGate("u2", 0, {
    params: {
        phi: "pi/2",
        lambda: "pi/2"
    }
});

u3

Generic single-qubit rotation gate with 3 Euler angles

Qubits: 1

Parameters:

  • theta
  • phi
  • lambda

Matrix: ```javascript [

["cos(theta/2)","-exp(i * lambda) * sin(theta / 2)"],
["exp(i * phi) * sin(theta / 2)","exp(i * lambda + i * phi) * cos(theta / 2)"]

] ```

Example:

javascript
circuit.appendGate("u3", 0, {
    params: {
        theta: "pi/2",
        phi: "pi/2",
        lambda: "pi/2"
    }
});

s

PI/2 rotation over Z-axis (synonym for

r2
)

Qubits: 1

Matrix: ```javascript [

[1,0],
[0,"exp(i * pi / 2)"]

] ```

Example:

javascript
circuit.appendGate("s", 0);

t

PI/4 rotation over Z-axis (synonym for

r4
)

Qubits: 1

Matrix: ```javascript [

[1,0],
[0,"exp(i * pi / 4)"]

] ```

Example:

javascript
circuit.appendGate("t", 0);

sdg

(-PI/2) rotation over Z-axis

Qubits: 1

Matrix: ```javascript [

[1,0],
[0,"exp(-i * pi / 2)"]

] ```

Example:

javascript
circuit.appendGate("sdg", 0);

tdg

(-PI/4) rotation over Z-axis

Qubits: 1

Matrix: ```javascript [

[1,0],
[0,"exp(-i * pi / 4)"]

] ```

Example:

javascript
circuit.appendGate("tdg", 0);

swap

Swaps the state of two qubits.

Qubits: 2

Matrix: ```javascript [

[1,0,0,0],
[0,0,1,0],
[0,1,0,0],
[0,0,0,1]

] ```

Example:

javascript
circuit.appendGate("swap", [0, 1]);

srswap

Square root of swap

Qubits: 2

Matrix: ```javascript [

[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:

javascript
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: ```javascript [

[1,0,0,0],
[0,0,"0+i",0],
[0,"0+i",0,0],
[0,0,0,1]

] ```

Example:

javascript
circuit.appendGate("iswap", [0, 1]);

xy

XY gate

Qubits: 2

Parameters:

  • phi

Matrix: ```javascript [

[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:

javascript
circuit.appendGate("xy", [0, 1], {
    params: {
        phi: "pi/2"
    }
});

cx

Controlled NOT (CNOT) gate

Qubits: 2

Matrix: ```javascript [

[1,0,0,0],
[0,1,0,0],
[0,0,0,1],
[0,0,1,0]

] ```

Example:

javascript
circuit.appendGate("cx", [0, 1]);

cy

Controlled Y gate (controlled rotation over Y-axis by PI)

Qubits: 2

Matrix: ```javascript [

[1,0,0,0],
[0,1,0,0],
[0,0,0,"-i"],
[0,0,"i",0]

] ```

Example:

javascript
circuit.appendGate("cy", [0, 1]);

cz

Controlled Z gate (controlled rotation over Z-axis by PI)

Qubits: 2

Matrix: ```javascript [

[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[0,0,0,-1]

] ```

Example:

javascript
circuit.appendGate("cz", [0, 1]);

ch

Controlled Hadamard gate

Qubits: 2

Matrix: ```javascript [

[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:

javascript
circuit.appendGate("ch", [0, 1]);

csrn

Controlled square root of NOT

Qubits: 2

Matrix: ```javascript [

[1,0,0,0],
[0,1,0,0],
[0,0,"0.5+0.5i","0.5-0.5i"],
[0,0,"0.5-0.5i","0.5+0.5i"]

] ```

Example:

javascript
circuit.appendGate("csrn", [0, 1]);

ms

Mølmer-Sørensen gate

Qubits: 2

Parameters:

  • theta

Matrix: ```javascript [

["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:

javascript
circuit.appendGate("ms", [0, 1], {
    params: {
        theta: "pi/2"
    }
});

yy

YY gate

Qubits: 2

Parameters:

  • theta

Matrix: ```javascript [

["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:

javascript
circuit.appendGate("yy", [0, 1], {
    params: {
        theta: "pi/2"
    }
});

zz

Parametric 2-qubit rotation about ZZ

Qubits: 2

Parameters:

  • theta

Matrix: ```javascript [

["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:

javascript
circuit.appendGate("zz", [0, 1], {
    params: {
        theta: "pi/2"
    }
});

cr2

Controlled PI/2 rotation over Z-axis

Qubits: 2

Matrix: ```javascript [

[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[0,0,0,"exp(i * pi / 2)"]

] ```

Example:

javascript
circuit.appendGate("cr2", [0, 1]);

cr4

Controlled PI/4 rotation over Z-axis

Qubits: 2

Matrix: ```javascript [

[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[0,0,0,"exp(i * pi / 4)"]

] ```

Example:

javascript
circuit.appendGate("cr4", [0, 1]);

cr8

Controlled PI/8 rotation over Z-axis

Qubits: 2

Matrix: ```javascript [

[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[0,0,0,"exp(i * pi / 8)"]

] ```

Example:

javascript
circuit.appendGate("cr8", [0, 1]);

crx

Controlled rotation around the X-axis by given angle

Qubits: 2

Parameters:

  • theta

Matrix: ```javascript [

[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:

javascript
circuit.appendGate("crx", [0, 1], {
    params: {
        theta: "pi/2"
    }
});

cry

Controlled rotation around the Y-axis by given angle

Qubits: 2

Parameters:

  • theta

Matrix: ```javascript [

[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:

javascript
circuit.appendGate("cry", [0, 1], {
    params: {
        theta: "pi/2"
    }
});

crz

Controlled rotation around the Z-axis by given angle

Qubits: 2

Parameters:

  • phi

Matrix: ```javascript [

[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:

javascript
circuit.appendGate("crz", [0, 1], {
    params: {
        phi: "pi/2"
    }
});

cu1

Controlled rotation about the Z axis

Qubits: 2

Parameters:

  • lambda

Matrix: ```javascript [

[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[0,0,0,"exp(i * lambda)"]

] ```

Example:

javascript
circuit.appendGate("cu1", [0, 1], {
    params: {
        lambda: "pi/2"
    }
});

cu2

Controlled rotation about the X+Z axis

Qubits: 2

Parameters:

  • phi
  • lambda

Matrix: ```javascript [

[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:

javascript
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: ```javascript [

[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:

javascript
circuit.appendGate("cu3", [0, 1], {
    params: {
        theta: "pi/2",
        phi: "pi/2",
        lambda: "pi/2"
    }
});

cs

Controlled PI/2 rotation over Z-axis (synonym for

cr2
)

Qubits: 2

Matrix: ```javascript [

[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[0,0,0,"exp(i * pi / 2)"]

] ```

Example:

javascript
circuit.appendGate("cs", [0, 1]);

ct

Controlled PI/4 rotation over Z-axis (synonym for

cr4
)

Qubits: 2

Matrix: ```javascript [

[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[0,0,0,"exp(i * pi / 4)"]

] ```

Example:

javascript
circuit.appendGate("ct", [0, 1]);

csdg

Controlled (-PI/2) rotation over Z-axis

Qubits: 2

Matrix: ```javascript [

[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[0,0,0,"exp(-i * pi / 2)"]

] ```

Example:

javascript
circuit.appendGate("csdg", [0, 1]);

ctdg

Controlled (-PI/4) rotation over Z-axis

Qubits: 2

Matrix: ```javascript [

[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[0,0,0,"exp(-i * pi / 4)"]

] ```

Example:

javascript
circuit.appendGate("ctdg", [0, 1]);

ccx

Toffoli aka "CCNOT" gate

Qubits: 3

Matrix: ```javascript [

[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:

javascript
circuit.appendGate("ccx", [0, 1, 2]);

cswap

Controlled swap aka "Fredkin" gate

Qubits: 3

Matrix: ```javascript [

[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:

javascript
circuit.appendGate("cswap", [0, 1, 2]);

csrswap

Controlled square root of swap

Qubits: 3

Matrix: ```javascript [

[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:

javascript
circuit.appendGate("csrswap", [0, 1, 2]);

reset

Resets qubit

Qubits: 1

Example:

javascript
circuit.appendGate("reset", 0);

measure

Measures qubit and stores chance (0 or 1) into classical bit

Qubits: 1

Example:

javascript
circuit.appendGate("measure", 0, {
    creg: {
        name: "c",
        bit: 3
    }
});

Or:

javascript
circuit.addMeasure(0, "c", 3);

API docs

To be written...

License

MIT

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