Cheatsheet¶

Working with qubits¶

A number of methods exist for helping setup and create qubits for use in QCEngine programs. In many commands qubits from either the whole QPU or a QInt object (introduced below) can be specified using either hexadecimal, binary, or decimal notation. For example, 0x4, 0b001 and 4 would all specify the third of three qubits (having a weight of \(2^2=4\)). Multiple qubits can be selected using JavaScript’s bitwise OR operation between hexadecimal or binary values (for example, 0x2|0x4, 0b010|0b001 and 3 all specify the second two of three qubits (having weights \(2^1=2\) and \(2^2=4\)).

qc.reset(num_qubits)

Reset the QPU and initialize it with num_qubits qubits.
Example: qc.reset(4)

qc.write(val, qubit)

Write the integer value val in binary to the qubit at location qubit. If no qubit argument is passed, then write the value using all qubits in the QPU if called as a method on qc or in the QInt if called as a method on a qint object.
Example: qc.write(2)

qint.new(num_qubits, qint_label)

Create a QInt with the first num_qubits free in the QPU and label it with the string qint_label in circuit diagrams. QInt’s provide a way to group qubits together and act on them in these groups.
Example: var myqint = qint.new(2, 'myqint')

qc.discard()

Remvoves a specified qubit from the QPU. Can be used as a method on the qc object or a QInt object. If called without an argument then discards all qubits associated with the parent object.
Example: qc.discard(0x2);

qint.bits()

qint.peekProbability(value)

Returns the probability of observing the specified value if the parent QInt were to have all of its qubits measured. Note that although qint.peekProbability() can be useful for debugging QPU programs, a real QPU could not implement this function directly as in general it is not possible to determine the amplitudes (and therefore probabilities) of a QPU register’s possible configurations. Take care not to rely on it for any critical component of your QPU programs.
Example: myqint.peekProbability(2)

qint.numBits()

Returns an integer specifying the number of qubits contained within a QInt object.
Example: myqint.numBits()

qint.reverseBits(qubits)

When called with no argument, reverses the ordering of all qubits in a QInt (so that first becomes last, second becomes second from last, etc…). The argument qubits can be used to specify a subset of qubits to be reversed.
Example: myqint.reverseBits(0x1|0x2|0x4)

Single-qubit operations¶

Most single-qubit operations can either be performed as methods of the qc object or of a qint object. In either case, a specific qubit for the operation to act on can be specified using hexadecimal, or if no specific qubit is specified, the single-qubit operation is applied separately to all qubits in the object. When used as a qc method, qubit specifications are relative to all qubits from the whole QPU. For qint methods, qubit specifications are relative only to qubits in the qint.

qc.not(qubit)

Applies the NOT operation to a qubit specified by qubit. This flips the \(|0\rangle\) and |1\rangle values. Can also be applied to a qint as myqint.not(qubit). Example: qc.not(0x2)

qc.had(qubit) (alias qc.hadamard(qubit))

Applies the Hadamard operation (HAD) to qubit, creating an equal superposition when acted on \(|0\rangle\), and an equal superposition with a relative phase of \(180^{\circ}\) when acted on \(|1\rangle\). Can also be acted on a qint as myqint.had(qubit). When called without a specific qubit address, acts HAD operations on all qubits in the parent object.
Example: qc.had(0x2)

qc.phase(angle, qubit)

Applies the single-qubit PHASE operation to a qubit, which applies a rotation to the relative phase of a qubit. Takes two arguments angle (first argument) and qubit (second argument). The angle argument is the rotation angle to apply (in circle notation, the angle through which the \(|1\rangle\) circle is rotated). This is equivalent to a ROTZ operation. The qubit argument references one or more qubits to apply the operation to. Can also be acted on a qint as myqint.phase(angle qubit).
Example: qc.phase(45, 0x4)

qc.read(qubit)

Applies the READ operation to a qubit specified with qubit, producing a conventional 0 or 1 outcome with probabilities determined by the qubits state amplitudes. Following qc.read(qubit), any superposition within the qubit is destroyed. The 0/1 result of qc.read(qubit) can be assigned to a JavaScript variable for future use. Can also be acted on a qint as myqint.read(qubit). Example: var result = qc.read(0x8)

qc.rootnot(qubit)

Applies the square root of the NOT operation to a qubit, such that applying the operation twice is equivalent to qc.not(qubit). Can also be acted on a qint as myqint.rootnot(qubit).
Example: qc.rootnot(qubit)

qc.roty(angle, qubit)

Applies a rotation around the \(y\) axis of the Bloch sphere. Takes two arguments angle (first argument) and qubit (second argument). The angle argument is the rotation angle to apply, and qubit is the qubit to apply the rotation to. Can also be applied to a qint as myqint.roty(angle, qubit). Example: qc.roty(45, 0x4)

Multi-qubit operations¶

Many single-qubit operations can be used as multi-qubit operations simply by passing an additional argument specifying an additional condition qubit, whose value determines whether or not the operation is applied to the previously specified target qubit. In many cases, when called as methods on a qint object, single qubit operations can also be conditioned by passing a qubit argument. The qint that the operation is called on will then be the target qubit for the operation, whilst the other qubit(s) passed as the argument to this method will be the condition qubit(s). For example, qc.phase(angle, qubit) is a single-qubit operation, but qc.phase(angle, target_qubit, condition_qubit) and myqint.phase(angle, condition_qubit) are both multi-qubit operations performing a conditional phase.

qc.cnot(target_qubit, condition_qubit)

Applies the CNOT operation between two qubits. Takes two arguments target_qubit and condition_qubit. The second argument (condition_qubit) specifies the qubit whose value will determine whether or not a NOT operation is applied to the target_qubit specified in the first argument. Example: qc.cnot(0x4, 0x2)

qc.exchange(qubits)

Exchanges a number of qubits specified by the qubits argument. The qubits to be exchanged can be specified in binary, hexadecimal or decimal. For example, the middle two of four qubits can be exchanged using either qc.exchange(0b0110), qc.exchange(0x2|0x4) or qc.exchange(6). Can also be applied to a qint as myqint.exchange(qubits). Example: qc.exchange(0x2|0x4)

qc.phase(angle, control_qubit, target_qubit)

Applies a PHASE operation with angle angle on the qubit specified by the target_qubit argument dependent on the value of the qubit specified by the control_qubit argument. Note that this is the same method as the single qubit qc.phase(angle, qubit), only called with an additional target_qubit argument. Can also be applied to a qint as myqint.phase(angle, control_qubit, target_qubit). Example: qc.phase(45, 0x2, 0x4)

qc.swap(qubits)

Swaps the qubits specified by the qubits argument. Can also be applied to a qint as myqint.swap(qubits). Example: qc.swap(0x2|0x4)

qc.swap(target_qubits, control_qubit)

This alternative signature for the qc.swap() method allows the qubits specified by the target_qubits first parameter to be swapped conditional on the value of the control_qubit specified in the second parameter. Can also be applied to a qint as myqint.swap(target_qubits, control_qubit). Example: qc.swap(0x2|0x4, 0x8)

Primitives¶

This section contains a reference for commands that perform either full-blown primitives (such as the Quantum Fourier Transform), or smaller components of primitives (such as basic arithmetic functions).

qc.QFT(qubits)

Applies the Quantum Fourier Transform (QFT) circuit to all qubits specified by the qubits parameter. Can also be applied to a qint as myqint.QFT(qubits). Example: qc.QFT(0b1110)

qc.invQFT(qubits)

Applies the inverse Quantum Fourier Transform circuit to all qubits specified by the qubits parameter. Can also be applied to a qint as myqint.invQFT(qubits). Example: qc.invQFT(0b1110)

qc.Grover(qubits)

Applies a Grover iteration to the qubits specified in the qubits parameter. In Programming Quantum Computers this is referred to as the MIRROR operation (see page 108). Can also be applied to a qint as myqint.Grover(qubits). Example: qc.Grover(0x2|0x4|0x8)

qc.phase_est(q_in, q_out, cont_u)

Applies the phase estimation primitive. Takes two qint objects for its input arguments q_in and q_out. The first argument q_in should reference a qint object containing the state for which the corresponding eigenphase is desired (this can either be an eigenstate or a superposition of eigenstates). The second argument q_out should provide a qint object (with qubits initialized in the \(|0\rangle\) state) that will be used to return a binary representation of the eigenphase. The number of qubits in q_out determines the precision with which the eigenphase can be returned. The qc.phase_est() method also takes a third argument cont_u, which should be a reference to a JavaScript function that returns a controlled implementation of the operation whose eigenphases are to be determined. Can also be applied to a qint as myqint.phase_est(q_in, q_out, cont_u). Example: qc.phase_est(my_input_qint, my_output_qint, cont_u_fn) .. See code example 8.1

qc.amplitude_encode(vector, myqint)

Applies the amplitude encoding algorithm for representing a JavaScript array of values (specified in the first parameter, vector) in the amplitudes of the qubits contained in a qint object (specified in the second parameter, myqint). Note that vectors passed to this method should be normalized in order to be faithfully represented in state amplitudes. Example: qc.amplitude_encode([2,3,4,1], myqint) .. See example 9.3

Formatting commands¶

qc.print(qint)

This command can be used to print values to the QCEngine UI output window. One common usage would be to print the output of a qc.read() operation as shown in the below example. Note consecutive calls to qc.print() will not automatically occur on new lines in the output window. You can force new lines yourself using qc.print("\n"). Example: qc.print(qc.read(0x2))

qc.label(label)

Can be used to produce ‘code labels’ which group operations together in the circuit diagram shown in the QCEngine UI circuit window under a label specified by a string passed to the label parameter. A call to qc.label(label) specifies the point in the code where the code label with name label should begin. A second empty call to the method, qc.label("") declares where the labelled section of the circuit should end. Example: qc.label("My label name")

qc.nop()

Used to insert space in the QCEngine UI circuit window. Useful for spacing out operations in the circuit diagram to increase readability. Example: qc.nop()

qc_options.color_by_phase=bool

Setting this attribute of the qc_options object to true will color the filled areas in the circle notation shown in the QCEngine UI circle window according to their relative rotations. This increases visibility in differences in phases in the circle notation for QPUs containing large numbers of qubits. Note that the same effect can be achieved using the buttons in the circle window header. Example: qc_options.color_by_phase=true

qc_options.book_render=bool

Setting this attribute of the qc_options object to true will use bold needles with small circles at their tips to represent the relative rotations of circles in the QCEngine UI circle window. This increases visibility in differences in phases in the circle notation for QPUs containing large numbers of qubits. Note that the same effect can be achieved using the buttons in the circle window header. Example: qc_options.book_render=true

qc.panel_chart.widgets

qc.clearOutput()

qc.disableAnimation()

qc.disableRecording()