Classical expressions

qiskit.circuit.classical

This module contains an exploratory representation of runtime operations on classical values during circuit execution.

Currently, only simple expressions on bits and registers that result in a Boolean value are supported, and these are only valid for use in the conditions of QuantumCircuit.if_test() (IfElseOp) and QuantumCircuit.while_loop() (WhileLoopOp), and in the target of QuantumCircuit.switch() (SwitchCaseOp).

Note

This is an exploratory module, and while we will commit to the standard Qiskit deprecation policy within it, please be aware that the module will be deliberately limited in scope at the start, and early versions may not evolve cleanly into the final version. It is possible that various components of this module will be replaced (subject to deprecations) instead of improved into a new form.

The type system and expression tree will be expanded over time, and it is possible that the allowed types of some operations may need to change between versions of Qiskit as the classical processing capabilities develop.

Expressions

qiskit.circuit.classical.expr

The necessary components for building expressions are all exported from the expr namespace within qiskit.circuit.classical, so you can choose whether to use qualified access (for example expr.Value) or import the names you need directly and call them without the prefix.

There are two pathways for constructing expressions. The classes that form the representation of the expression system have constructors that perform zero type checking; it is up to the caller to ensure that they are building valid objects. For a more user-friendly interface to direct construction, there are helper functions associated with most of the classes that do type validation and inference. These are described below, in Construction.

Representation

The expression system is based on tree representation. All nodes in the tree are final (uninheritable) instances of the abstract base class:

Expr

class qiskit.circuit.classical.expr.Expr

Root base class of all nodes in the expression tree. The base case should never be instantiated directly.

This must not be subclassed by users; subclasses form the internal data of the representation of expressions, and it does not make sense to add more outside of Qiskit library code.

All subclasses are responsible for setting their type attribute in their __init__, and should not call the parent initialiser.

These objects are mutable and should not be reused in a different location without a copy.

The entry point from general circuit objects to the expression system is by wrapping the object in a Var node and associating a Type with it.

Var

final class qiskit.circuit.classical.expr.Var(var, type)

A classical variable.

Similarly, literals used in comparison (such as integers) should be lifted to Value nodes with associated types.

Value

final class qiskit.circuit.classical.expr.Value(value, type)

A single scalar value.

The operations traditionally associated with pre-, post- or infix operators in programming are represented by the Unary and Binary nodes as appropriate. These each take an operation type code, which are exposed as enumerations inside each class as Unary.Op and Binary.Op respectively.

Unary

final class qiskit.circuit.classical.expr.Unary(op, operand, type)

A unary expression.

Parameters

op (Unary.Op) – The opcode describing which operation is being done.
operand (Expr) – The operand of the operation.
type (Type) – The resolved type of the result.

Op

class Op(value)

Enumeration of the opcodes for unary operations.

The bitwise negation BIT_NOT takes a single bit or an unsigned integer of known width, and returns a value of the same type.

The logical negation LOGIC_NOT takes an input that is implicitly coerced to a Boolean, and returns a Boolean.

BIT_NOT

Default value: 1

Bitwise negation. ~operand.

LOGIC_NOT

Default value: 2

Logical negation. !operand.

Binary

final class qiskit.circuit.classical.expr.Binary(op, left, right, type)

A binary expression.

Parameters

op (Binary.Op) – The opcode describing which operation is being done.
left (Expr) – The left-hand operand.
right (Expr) – The right-hand operand.
type (Type) – The resolved type of the result.

Op

class Op(value)

Enumeration of the opcodes for binary operations.

The bitwise operations BIT_AND, BIT_OR and BIT_XOR apply to two operands of the same type, which must be a single bit or an unsigned integer of fixed width. The resultant type is the same as the two input types.

The logical operations LOGIC_AND and LOGIC_OR first implicitly coerce their arguments to Booleans, and then apply the logical operation. The resultant type is always Boolean.

The binary mathematical relations EQUAL, NOT_EQUAL, LESS, LESS_EQUAL, GREATER and GREATER_EQUAL take unsigned integers (with an implicit cast to make them the same width), and return a Boolean.

BIT_AND

Default value: 1

Bitwise “and”. lhs & rhs.

BIT_OR

Default value: 2

Bitwise “or”. lhs | rhs.

BIT_XOR

Default value: 3

Bitwise “exclusive or”. lhs ^ rhs.

LOGIC_AND

Default value: 4

Logical “and”. lhs && rhs.

LOGIC_OR

Default value: 5

Logical “or”. lhs || rhs.

EQUAL

Default value: 6

Numeric equality. lhs == rhs.

NOT_EQUAL

Default value: 7

Numeric inequality. lhs != rhs.

LESS

Default value: 8

Numeric less than. lhs < rhs.

LESS_EQUAL

Default value: 9

Numeric less than or equal to. lhs <= rhs

GREATER

Default value: 10

Numeric greater than. lhs > rhs.

GREATER_EQUAL

Default value: 11

Numeric greater than or equal to. lhs >= rhs.

When constructing expressions, one must ensure that the types are valid for the operation. Attempts to construct expressions with invalid types will raise a regular Python TypeError.

Expressions in this system are defined to act only on certain sets of types. However, values may be cast to a suitable supertype in order to satisfy the typing requirements. In these cases, a node in the expression tree is used to represent the promotion. In all cases where operations note that they “implicitly cast” or “coerce” their arguments, the expression tree must have this node representing the conversion.

Cast

final class qiskit.circuit.classical.expr.Cast(operand, type, implicit=False)

A cast from one type to another, implied by the use of an expression in a different context.

Construction

Constructing the tree representation directly is verbose and easy to make a mistake with the typing. In many cases, much of the typing can be inferred, scalar values can automatically be promoted to Value instances, and any required promotions can be resolved into suitable Cast nodes.

The functions and methods described in this section are a more user-friendly way to build the expression tree, while staying close to the internal representation. All these functions will automatically lift valid Python scalar values into corresponding Var or Value objects, and will resolve any required implicit casts on your behalf.

lift

qiskit.circuit.classical.expr.lift(value, /, type=None)

Lift the given Python value to a Value or Var.

If an explicit type is given, the typing in the output will reflect that.

Examples

Lifting simple circuit objects to be Var instances:

>>> from qiskit.circuit import Clbit, ClassicalRegister
>>> from qiskit.circuit.classical import expr
>>> expr.lift(Clbit())
Var(<clbit>, Bool())
>>> expr.lift(ClassicalRegister(3, "c"))
Var(ClassicalRegister(3, "c"), Uint(3))

The type of the return value can be influenced, if the given value could be interpreted losslessly as the given type (use cast() to perform a full set of casting operations, include lossy ones):

>>> from qiskit.circuit import ClassicalRegister
>>> from qiskit.circuit.classical import expr, types
>>> expr.lift(ClassicalRegister(3, "c"), types.Uint(5))
Var(ClassicalRegister(3, "c"), Uint(5))
>>> expr.lift(5, types.Uint(4))
Value(5, Uint(4))

Return type

You can manually specify casts in cases where the cast is allowed in explicit form, but may be lossy (such as the cast of a higher precision Uint to a lower precision one).

cast

qiskit.circuit.classical.expr.cast(operand, type, /)

Create an explicit cast from the given value to the given type.

Examples

Add an explicit cast node that explicitly casts a higher precision type to a lower precision one:

>>> from qiskit.circuit.classical import expr, types
>>> value = expr.value(5, types.Uint(32))
>>> expr.cast(value, types.Uint(8))
Cast(Value(5, types.Uint(32)), types.Uint(8), implicit=False)

Return type

There are helper constructor functions for each of the unary operations.

bit_not

qiskit.circuit.classical.expr.bit_not(operand, /)

Create a bitwise ‘not’ expression node from the given value, resolving any implicit casts and lifting the value into a Value node if required.

Examples

Bitwise negation of a ClassicalRegister:

>>> from qiskit.circuit import ClassicalRegister
>>> from qiskit.circuit.classical import expr
>>> expr.bit_not(ClassicalRegister(3, "c"))
Unary(Unary.Op.BIT_NOT, Var(ClassicalRegister(3, 'c'), Uint(3)), Uint(3))

Return type

logic_not

qiskit.circuit.classical.expr.logic_not(operand, /)

Create a logical ‘not’ expression node from the given value, resolving any implicit casts and lifting the value into a Value node if required.

Examples

Logical negation of a ClassicalRegister:

>>> from qiskit.circuit import ClassicalRegister
>>> from qiskit.circuit.classical import expr
>>> expr.logic_not(ClassicalRegister(3, "c"))
Unary(Unary.Op.LOGIC_NOT, Cast(Var(ClassicalRegister(3, 'c'), Uint(3)), Bool(), implicit=True), Bool())

Return type

Similarly, the binary operations and relations have helper functions defined.

bit_and

qiskit.circuit.classical.expr.bit_and(left, right, /)

Create a bitwise ‘and’ expression node from the given value, resolving any implicit casts and lifting the values into Value nodes if required.

Examples

Bitwise ‘and’ of a classical register and an integer literal:

>>> from qiskit.circuit import ClassicalRegister
>>> from qiskit.circuit.classical import expr
>>> expr.bit_and(ClassicalRegister(3, "c"), 0b111)
Binary(Binary.Op.BIT_AND, Var(ClassicalRegister(3, 'c'), Uint(3)), Value(7, Uint(3)), Uint(3))

Return type

bit_or

qiskit.circuit.classical.expr.bit_or(left, right, /)

Create a bitwise ‘or’ expression node from the given value, resolving any implicit casts and lifting the values into Value nodes if required.

Examples

Bitwise ‘or’ of a classical register and an integer literal:

>>> from qiskit.circuit import ClassicalRegister
>>> from qiskit.circuit.classical import expr
>>> expr.bit_or(ClassicalRegister(3, "c"), 0b101)
Binary(Binary.Op.BIT_OR, Var(ClassicalRegister(3, 'c'), Uint(3)), Value(5, Uint(3)), Uint(3))

Return type

bit_xor

qiskit.circuit.classical.expr.bit_xor(left, right, /)

Create a bitwise ‘exclusive or’ expression node from the given value, resolving any implicit casts and lifting the values into Value nodes if required.

Examples

Bitwise ‘exclusive or’ of a classical register and an integer literal:

>>> from qiskit.circuit import ClassicalRegister
>>> from qiskit.circuit.classical import expr
>>> expr.bit_xor(ClassicalRegister(3, "c"), 0b101)
Binary(Binary.Op.BIT_XOR, Var(ClassicalRegister(3, 'c'), Uint(3)), Value(5, Uint(3)), Uint(3))

Return type

logic_and

qiskit.circuit.classical.expr.logic_and(left, right, /)

Create a logical ‘and’ expression node from the given value, resolving any implicit casts and lifting the values into Value nodes if required.

Examples

Logical ‘and’ of two classical bits:

>>> from qiskit.circuit import Clbit
>>> from qiskit.circuit.classical import expr
>>> expr.logical_and(Clbit(), Clbit())
Binary(Binary.Op.LOGIC_AND, Var(<clbit 0>, Bool()), Var(<clbit 1>, Bool()), Bool())

Return type

logic_or

qiskit.circuit.classical.expr.logic_or(left, right, /)

Create a logical ‘or’ expression node from the given value, resolving any implicit casts and lifting the values into Value nodes if required.

Examples

Logical ‘or’ of two classical bits

>>> from qiskit.circuit import Clbit
>>> from qiskit.circuit.classical import expr
>>> expr.logical_and(Clbit(), Clbit())
Binary(Binary.Op.LOGIC_OR, Var(<clbit 0>, Bool()), Var(<clbit 1>, Bool()), Bool())

Return type

equal

qiskit.circuit.classical.expr.equal(left, right, /)

Create an ‘equal’ expression node from the given value, resolving any implicit casts and lifting the values into Value nodes if required.

Examples

Equality between a classical register and an integer:

>>> from qiskit.circuit import ClassicalRegister
>>> from qiskit.circuit.classical import expr
>>> expr.equal(ClassicalRegister(3, "c"), 7)
Binary(Binary.Op.EQUAL, Var(ClassicalRegister(3, "c"), Uint(3)), Value(7, Uint(3)), Uint(3))

Return type

not_equal

qiskit.circuit.classical.expr.not_equal(left, right, /)

Create a ‘not equal’ expression node from the given value, resolving any implicit casts and lifting the values into Value nodes if required.

Examples

Inequality between a classical register and an integer:

>>> from qiskit.circuit import ClassicalRegister
>>> from qiskit.circuit.classical import expr
>>> expr.not_equal(ClassicalRegister(3, "c"), 7)
Binary(Binary.Op.NOT_EQUAL, Var(ClassicalRegister(3, "c"), Uint(3)), Value(7, Uint(3)), Uint(3))

Return type

less

qiskit.circuit.classical.expr.less(left, right, /)

Create a ‘less than’ expression node from the given value, resolving any implicit casts and lifting the values into Value nodes if required.

Examples

Query if a classical register is less than an integer:

>>> from qiskit.circuit import ClassicalRegister
>>> from qiskit.circuit.classical import expr
>>> expr.less(ClassicalRegister(3, "c"), 5)
Binary(Binary.Op.LESS, Var(ClassicalRegister(3, "c"), Uint(3)), Value(5, Uint(3)), Uint(3))

Return type

less_equal

qiskit.circuit.classical.expr.less_equal(left, right, /)

Create a ‘less than or equal to’ expression node from the given value, resolving any implicit casts and lifting the values into Value nodes if required.

Examples

Query if a classical register is less than or equal to another:

>>> from qiskit.circuit import ClassicalRegister
>>> from qiskit.circuit.classical import expr
>>> expr.less(ClassicalRegister(3, "a"), ClassicalRegister(3, "b"))
Binary(Binary.Op.LESS_EQUAL, Var(ClassicalRegister(3, "a"), Uint(3)), Var(ClassicalRegister(3, "b"), Uint(3)), Uint(3))

Return type

greater

qiskit.circuit.classical.expr.greater(left, right, /)

Create a ‘greater than’ expression node from the given value, resolving any implicit casts and lifting the values into Value nodes if required.

Examples

Query if a classical register is greater than an integer:

>>> from qiskit.circuit import ClassicalRegister
>>> from qiskit.circuit.classical import expr
>>> expr.less(ClassicalRegister(3, "c"), 5)
Binary(Binary.Op.GREATER, Var(ClassicalRegister(3, "c"), Uint(3)), Value(5, Uint(3)), Uint(3))

Return type

greater_equal

qiskit.circuit.classical.expr.greater_equal(left, right, /)

Create a ‘greater than or equal to’ expression node from the given value, resolving any implicit casts and lifting the values into Value nodes if required.

Examples

Query if a classical register is greater than or equal to another:

>>> from qiskit.circuit import ClassicalRegister
>>> from qiskit.circuit.classical import expr
>>> expr.less(ClassicalRegister(3, "a"), ClassicalRegister(3, "b"))
Binary(Binary.Op.GREATER_EQUAL, Var(ClassicalRegister(3, "a"), Uint(3)), Var(ClassicalRegister(3, "b"), Uint(3)), Uint(3))

Return type

Qiskit’s legacy method for specifying equality conditions for use in conditionals is to use a two-tuple of a Clbit or ClassicalRegister and an integer. This represents an exact equality condition, and there are no ways to specify any other relations. The helper function lift_legacy_condition() converts this legacy format into the new expression syntax.

lift_legacy_condition

qiskit.circuit.classical.expr.lift_legacy_condition(condition, /)

Lift a legacy two-tuple equality condition into a new-style Expr.

Examples

Taking an old-style conditional instruction and getting an Expr from its condition:

from qiskit.circuit import ClassicalRegister
from qiskit.circuit.library import HGate
from qiskit.circuit.classical import expr
 
cr = ClassicalRegister(2)
instr = HGate().c_if(cr, 3)
 
lifted = expr.lift_legacy_condition(instr.condition)

Return type

Working with the expression tree

A typical consumer of the expression tree wants to recursively walk through the tree, potentially statefully, acting on each node differently depending on its type. This is naturally a double-dispatch problem; the logic of ‘what is to be done’ is likely stateful and users should be free to define their own operations, yet each node defines ‘what is being acted on’. We enable this double dispatch by providing a base visitor class for the expression tree.

ExprVisitor

class qiskit.circuit.classical.expr.ExprVisitor

Base class for visitors to the Expr tree. Subclasses should override whichever of the visit_* methods that they are able to handle, and should be organised such that non-existent methods will never be called.

visit_binary

visit_binary(node, /)

Return type

_T_co

visit_cast

visit_cast(node, /)

Return type

_T_co

visit_generic

visit_generic(node, /)

Return type

_T_co

visit_unary

visit_unary(node, /)

Return type

_T_co

visit_value

visit_value(node, /)

Return type

_T_co

visit_var

visit_var(node, /)

Return type

_T_co

Consumers of the expression tree should subclass the visitor, and override the visit_* methods that they wish to handle. Any non-overridden methods will call visit_generic(), which unless overridden will raise a RuntimeError to ensure that you are aware if new nodes have been added to the expression tree that you are not yet handling.

For the convenience of simple visitors that only need to inspect the variables in an expression and not the general structure, the iterator method iter_vars() is provided.

iter_vars

qiskit.circuit.classical.expr.iter_vars(node)

Get an iterator over the Var nodes referenced at any level in the given Expr.

Examples

Print out the name of each ClassicalRegister encountered:

from qiskit.circuit import ClassicalRegister
from qiskit.circuit.classical import expr
 
cr1 = ClassicalRegister(3, "a")
cr2 = ClassicalRegister(3, "b")
 
for node in expr.iter_vars(expr.bit_and(expr.bit_not(cr1), cr2)):
    if isinstance(node.var, ClassicalRegister):
        print(node.var.name)

Return type

Iterator[Var]

Two expressions can be compared for direct structural equality by using the built-in Python == operator. In general, though, one might want to compare two expressions slightly more semantically, allowing that the Var nodes inside them are bound to different memory-location descriptions between two different circuits. In this case, one can use structurally_equivalent() with two suitable “key” functions to do the comparison.

structurally_equivalent

qiskit.circuit.classical.expr.structurally_equivalent(left, right, left_var_key=None, right_var_key=None)

Do these two expressions have exactly the same tree structure, up to some key function for the Var objects?

In other words, are these two expressions the exact same trees, except we compare the Var.var fields by calling the appropriate *_var_key function on them, and comparing that output for equality. This function does not allow any semantic “equivalences” such as asserting that a == b is equivalent to b == a; the evaluation order of the operands could, in general, cause such a statement to be false (consider hypothetical extern functions that access global state).

There’s no requirements on the key functions, except that their outputs should have general __eq__ methods. If a key function returns None, the variable will be used verbatim instead.

Parameters

left (expr.Expr) – one of the Expr nodes.
right (expr.Expr) – the other Expr node.
left_var_key (Callable[[Any], Any] | None) – a callable whose output should be used when comparing Var.var attributes. If this argument is None or its output is None for a given variable in left, the variable will be used verbatim.
right_var_key (Callable[[Any], Any] | None) – same as left_var_key, but used on the variables in right instead.

Return type

Examples

Comparing two expressions for structural equivalence, with no remapping of the variables. These are different because the different Clbit instances compare differently:

>>> from qiskit.circuit import Clbit
>>> from qiskit.circuit.classical import expr
>>> left_bits = [Clbit(), Clbit()]
>>> right_bits = [Clbit(), Clbit()]
>>> left = expr.logic_and(expr.logic_not(left_bits[0]), left_bits[1])
>>> right = expr.logic_and(expr.logic_not(right_bits[0]), right_bits[1])
>>> expr.structurally_equivalent(left, right)
False

Comparing the same two expressions, but this time using mapping functions that associate the bits with simple indices:

>>> left_key = {var: i for i, var in enumerate(left_bits)}.get
>>> right_key = {var: i for i, var in enumerate(right_bits)}.get
>>> expr.structurally_equivalent(left, right, left_key, right_key)
True

Typing

qiskit.circuit.classical.types

The type system of the expression tree is exposed through this module. This is inherently linked to the expression system in the expr module, as most expressions can only be understood with the context of the types that they act on.

All types inherit from an abstract base class:

Type

class qiskit.circuit.classical.types.Type

Root base class of all nodes in the type tree. The base case should never be instantiated directly.

This must not be subclassed by users; subclasses form the internal data of the representation of expressions, and it does not make sense to add more outside of Qiskit library code.

Types should be considered immutable objects, and you must not mutate them. It is permissible to reuse a Type that you take from another object without copying it, and generally this will be the best approach for performance. Type objects are designed to be small amounts of data, and it’s best to point to the same instance of the data where possible rather than heap-allocating a new version of the same thing. Where possible, the class constructors will return singleton instances to facilitate this.

The two different types available are for Booleans (corresponding to Clbit and the literals True and False), and unsigned integers (corresponding to ClassicalRegister and Python integers).

Bool

final class qiskit.circuit.classical.types.Bool

The Boolean type. This has exactly two values: True and False.

Uint

final class qiskit.circuit.classical.types.Uint(width)

An unsigned integer of fixed bit width.

Note that Uint defines a family of types parametrised by their width; it is not one single type, which may be slightly different to the ‘classical’ programming languages you are used to.

There are some functions on these types exposed here as well. These are mostly expected to be used only in manipulations of the expression tree; users who are building expressions using the user-facing construction interface should not need to use these.

The type system is equipped with a partial ordering, where $a < b$ is interpreted as “ $a$ is a strict subtype of $b$ ”. Note that the partial ordering is a subset of the directed graph that describes the allowed explicit casting operations between types. The partial ordering defines when one type may be lossless directly interpreted as another.

The low-level interface to querying the subtyping relationship is the order() function.

order

qiskit.circuit.classical.types.order(left, right, /)

Get the ordering relationship between the two types as an enumeration value.

Examples

Compare two Uint types of different widths:

>>> from qiskit.circuit.classical import types
>>> types.order(types.Uint(8), types.Uint(16))
Ordering.LESS

Compare two types that have no ordering between them:

>>> types.order(types.Uint(8), types.Bool())
Ordering.NONE

Return type

The return value is an enumeration Ordering that describes what, if any, subtyping relationship exists between the two types.

Ordering

class qiskit.circuit.classical.types.Ordering(value)

Enumeration listing the possible relations between two types. Types only have a partial ordering, so it’s possible for two types to have no sub-typing relationship.

Note that the sub-/supertyping relationship is not the same as whether a type can be explicitly cast from one to another.

Some helper methods are then defined in terms of this low-level order() primitive:

is_subtype

qiskit.circuit.classical.types.is_subtype(left, right, /, strict=False)

Does the relation $\text{left} \le \text{right}$ hold? If there is no ordering relation between the two types, then this returns False. If strict, then the equality is also forbidden.

Examples

Check if one type is a subclass of another:

>>> from qiskit.circuit.classical import types
>>> types.is_subtype(types.Uint(8), types.Uint(16))
True

Check if one type is a strict subclass of another:

>>> types.is_subtype(types.Bool(), types.Bool())
True
>>> types.is_subtype(types.Bool(), types.Bool(), strict=True)
False

Return type

is_supertype

qiskit.circuit.classical.types.is_supertype(left, right, /, strict=False)

Does the relation $\text{left} \ge \text{right}$ hold? If there is no ordering relation between the two types, then this returns False. If strict, then the equality is also forbidden.

Examples

Check if one type is a superclass of another:

>>> from qiskit.circuit.classical import types
>>> types.is_supertype(types.Uint(8), types.Uint(16))
False

Check if one type is a strict superclass of another:

>>> types.is_supertype(types.Bool(), types.Bool())
True
>>> types.is_supertype(types.Bool(), types.Bool(), strict=True)
False

Return type

greater

qiskit.circuit.classical.types.greater(left, right, /)

Get the greater of the two types, assuming that there is an ordering relation between them. Technically, this is a slightly restricted version of the concept of the ‘meet’ of the two types in that the return value must be one of the inputs. In practice in the type system there is no concept of a ‘sum’ type, so the ‘meet’ exists if and only if there is an ordering between the two types, and is equal to the greater of the two types.

Returns

The greater of the two types.

Raises

TypeError – if there is no ordering relation between the two types.

Return type

Examples

Find the greater of two Uint types:

>>> from qiskit.circuit.classical import types
>>> types.greater(types.Uint(8), types.Uint(16))
types.Uint(16)

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