A data structure to hold a Qram implementation. This provides operations for fetching and storing quantum data from a quantum array, addressed by a quantum integer. One implementation is given by algorithms a8_FetchT, a9_StoreT and a10_FetchStoreT.

A node of the graph (classical circuit type).

A node of the graph (quantum circuit type).

The type of problem specifications for the Triangle Finding Problem. A problem specification consists of:

• an integer n which determines the number N=2ⁿ of nodes of the graph,
• an integer r which determines the size R=2^r of tuples in the Hamming graph,
• a function edge_oracle which inputs two graph nodes and a qubit and flips the qubit if the nodes are connected by an edge and
• additional options, for selecting, e.g., which qRAM implementation should be used.

All three types QIntTF, CIntTF, and IntTF are special cases of a more general type XIntTF x, parameterized by a type x of bits. It is an abstract type, and details of its implementation is not exposed to user-level code.

The type of fixed-length m-qubit quantum integers, regarded modulo 2^m-1.

The type of fixed-length m-bit classical integers, regarded modulo 2^m-1.

The type of fixed-length m-bit integer parameters, regarded modulo 2^m-1. A value of type IntTF may have indeterminate length, similarly to IntM.

Convert an IntTF of length m to an Integer in the range {0, …, 2^m-2}. If the IntTF has indeterminate length, return the original Integer.

Convert an Integer to an IntTF of indeterminate length.

Convert an Integer to an IntTF of length m.

Return the length of an IntTF, or Nothing if indeterminate.

Set the length of an IntTF to m ≥ 0. This operation is only legal if the input (a) has indeterminate length or (b) has determinate length already equal to m. In particular, it cannot be used to change the length from anything other than from indeterminate to determinate.

If both arguments already have determinate lengths, and they do not coincide, throw an error. The String argument is used as an error message in that case.

Try to set the length of an IntTF to that of another XIntTF value (which could be a QIntTF, a CIntTF, or another IntTF). This will fail with an error if both numbers already have determinate lengths that don't coincide. In this case, the string argument is used as an error message. The promotion is done modulo 2^m-1.

Convert an IntTF to human readable form. We show the bit value, i.e., 0 and 2^m-1 are shown as different values.

Convert a QIntTF to a list of qubits. The conversion is little-headian, i.e., the head of the list holds the least significant digit.

Convert a list of qubits to a QIntTF. The conversion is little-headian, i.e., the head of the list holds the least significant digit.

Return a piece of shape data to represent an m-qubit QIntTF. Please note that the data can only be used as shape; it will be undefined at the leaves.

The low-level isomorphism from XInt x to XIntTF x. Note that "isomorphism" is between the underlying raw types, and does not respect the arithmetic operations.

The low-level isomorphism from XIntTF x to XInt x. Note that "isomorphism" is between the underlying raw types, and does not respect the arithmetic operations.

Like xint_of_xinttf, but first try to promote the length of the IntTF to that of the given XIntTF.

Controlled phase flip of -1.

Variant of phaseFlipIf that performs a phase flip unless all controls are in the given state.

qor q c: Applies "not" to q, if any of the control qubits in c is in specified state.

Increment a standard QDInt (i.e. big-endian, mod 2^ℓ).

Decrement a standard QDInt (i.e. big-endian, mod 2^ℓ).

Increment a bit-string, considered as a big-endian integer mod 2^ℓ.

Decrement a bit-string, considered as a big-endian integer mod 2^ℓ.

Increment a bit-string, considered as a little-endian integer mod 2^ℓ.

Decrement a bit-string, considered as a little-endian integer mod 2^ℓ.

The standard “combinations” function “n choose k”.

Replace an IntMap f with the IntMap mapping each key k to (k,f(k)). An auxiliary function for defining mapWithKeyM, etc.

Analogous to mapM, but allows the function to use the key. Particularly useful for mapping in parallel over two (or more) IntMaps assumed to have the same domain.

Analogous to mapM_, but allows the function to use the key.

Analogous to replicate on lists.

Convenient syntax for accessing elements of an IntMap. Left associative, and binds very strongly, like '(!!)'.