Extension methods

• encode_ixyz(paulie) - it accelerates the creation of a bit representation for strings composed of I, X, Y, and Z characters. Each character consists of two bits: I – (0,0), X – (1,0), Y – (1,1), Z – (0,1).

• decode_ixyz() - conversion of IXYZ bit values to strings

• count_non_trivially() - count_or(bits_even, bits_odd)

• diagonal_index() - ba2int(bits_odd) if ba2int(bits_even) == 0 else -1

• complex_conjugate() - count_and(bits_odd, bits_even)

• not_identity_mask() - bits_even | bits_odd

• phase(other) - the exponent f in phase = i^f

• commutes_with(other) check for commutativity

This library provides an object type which efficiently represents an array of booleans. pauliebits are sequence types and behave very much like usual lists. Eight bits are represented by one byte in a contiguous block of memory. The user can select between two representations: little-endian and big-endian. All functionality is implemented in C. Methods for accessing the machine representation are provided, including the ability to import and export buffers. This allows creating pauliebits that are mapped to other objects, including memory-mapped files.

Key features

• The bit-endianness can be specified for each pauliebits object, see below.

• Sequence methods: slicing (including slice assignment and deletion), operations +, *, +=, *=, the in operator, len()

• Bitwise operations: ~, &, |, ^, <<, >> (as well as their in-place versions &=, |=, ^=, <<=, >>=).

• Fast methods for encoding and decoding variable bit length prefix codes.

• pauliebits objects support the buffer protocol (both importing and exporting buffers).

• Packing and unpacking to other binary data formats, e.g. numpy.ndarray.

• Pickling and unpickling of pauliebits objects.

• Immutable frozenpauliebits objects which are hashable

• Sequential search

• Type hinting

• Extensive test suite with about 600 unittests

• Utility module pauliebits.util:

  • conversion to and from hexadecimal strings

  • generating random pauliebits

  • pretty printing

  • conversion to and from integers

  • creating Huffman codes

  • compression of sparse pauliebits

  • (de-) serialization

  • various count functions

  • other helpful functions

Installation

Python wheels are are available on PyPI for all major platforms and Python versions. Which means you can simply:

$ pip install pauliebits

Once you have installed the package, you may want to test it:

$ python -c 'import pauliebits; pauliebits.test()'
pauliebits is installed in: /Users/ilan/pauliebits/pauliebits
pauliebits version: 0.0.1
sys.version: 3.14.5 (main, May 20 2026) [Clang 20.1.8]
sys.prefix: /Users/ilan/miniforge
sys.abiflags: ''
sys._is_gil_enabled(): True
pointer size: 64 bit
sizeof(size_t): 8
sizeof(pauliebitsobject): 80
HAVE_BUILTIN_BSWAP64: 1
default bit-endianness: big
machine byte-order: little
Py_GIL_DISABLED: 0
Py_DEBUG: 0
DEBUG: 0
.........................................................................
................................................s........................
......s.........................................................
----------------------------------------------------------------------
Ran 632 tests in 0.191s

OK (skipped=2)

The test() function is part of the API. It will return a unittest.runner.TextTestResult object, such that one can verify that all tests ran successfully by:

import pauliebits
assert pauliebits.test().wasSuccessful()

Usage

As mentioned above, pauliebits objects behave very much like lists, so there is not too much to learn. The biggest difference from list objects (except that pauliebits are obviously homogeneous) is the ability to access the machine representation of the object. When doing so, the bit-endianness is of importance; this issue is explained in detail in the section below. Here, we demonstrate the basic usage of pauliebits objects:

>>> from pauliebits import pauliebits
>>> a = pauliebits()         # create empty pauliebits
>>> a.append(1)
>>> a.extend([1, 0])
>>> a
pauliebits('110')
>>> x = pauliebits(2 ** 20)  # pauliebits of length 1048576 (initialized to 0)
>>> len(x)
1048576
>>> pauliebits('1001 011')   # initialize from string (whitespace is ignored)
pauliebits('1001011')
>>> lst = [1, 0, False, True, True]
>>> a = pauliebits(lst)      # initialize from iterable
>>> a
pauliebits('10011')
>>> a[2]    # indexing a single item will always return an integer
0
>>> a[2:4]  # whereas indexing a slice will always return a pauliebits
pauliebits('01')
>>> a[2:3]  # even when the slice length is just one
pauliebits('0')
>>> a.count(1)
3
>>> a.remove(0)            # removes first occurrence of 0
>>> a
pauliebits('1011')

Like lists, pauliebits objects support slice assignment and deletion:

>>> a = pauliebits(50)
>>> a.setall(0)            # set all elements in a to 0
>>> a[11:37:3] = 9 * pauliebits('1')
>>> a
pauliebits('00000000000100100100100100100100100100000000000000')
>>> del a[12::3]
>>> a
pauliebits('0000000000010101010101010101000000000')
>>> a[-6:] = pauliebits('10011')
>>> a
pauliebits('000000000001010101010101010100010011')
>>> a += pauliebits('000111')
>>> a[9:]
pauliebits('001010101010101010100010011000111')

In addition, slices can be assigned to booleans, which is easier (and faster) than assigning to a pauliebits in which all values are the same:

>>> a = 20 * pauliebits('0')
>>> a[1:15:3] = True
>>> a
pauliebits('01001001001001000000')

This is easier and faster than:

>>> a = 20 * pauliebits('0')
>>> a[1:15:3] = 5 * pauliebits('1')
>>> a
pauliebits('01001001001001000000')

Note that in the latter we have to create a temporary pauliebits whose length must be known or calculated. Another example of assigning slices to Booleans, is setting ranges:

>>> a = pauliebits(30)
>>> a[:] = 0         # set all elements to 0 - equivalent to a.setall(0)
>>> a[10:25] = 1     # set elements in range(10, 25) to 1
>>> a
pauliebits('000000000011111111111111100000')

As of pauliebits version 2.8, indices may also be lists of arbitrary indices (like in NumPy), or pauliebits that are treated as masks, see pauliebits indexing.

Bitwise operators

pauliebits objects support the bitwise operators ~, &, |, ^, <<, >> (as well as their in-place versions &=, |=, ^=, <<=, >>=). The behavior is very much what one would expect:

>>> a = pauliebits('101110001')
>>> ~a  # invert
pauliebits('010001110')
>>> b = pauliebits('111001011')
>>> a ^ b  # bitwise XOR
pauliebits('010111010')
>>> a &= b  # inplace AND
>>> a
pauliebits('101000001')
>>> a <<= 2  # in-place left-shift by 2
>>> a
pauliebits('100000100')
>>> b >> 1  # return b right-shifted by 1
pauliebits('011100101')

The C language does not specify the behavior of negative shifts and of left shifts larger or equal than the width of the promoted left operand. The exact behavior is compiler/machine specific. This Python pauliebits library specifies the behavior as follows:

• the length of the pauliebits is never changed by any shift operation

• blanks are filled by 0

• negative shifts raise ValueError

• shifts larger or equal to the length of the pauliebits result in pauliebits with all values 0

It is worth noting that (regardless of bit-endianness) the pauliebits left shift (<<) always shifts towards lower indices, and the right shift (>>) always shifts towards higher indices.

Bit-endianness

For many purposes the bit-endianness is not of any relevance to the end user and can be regarded as an implementation detail of pauliebits objects. However, there are use cases when the bit-endianness becomes important. These use cases involve explicitly reading and writing the pauliebits buffer using .tobytes(), .frombytes(), .tofile() or .fromfile(), importing and exporting buffers. Also, a number of utility functions in pauliebits.util will return different results depending on bit-endianness, such as ba2hex() or ba2int. To better understand this topic, please read bit-endianness.

Buffer protocol

pauliebits objects support the buffer protocol. They can both export their own buffer, as well as import another object’s buffer. To learn more about this topic, please read buffer protocol. There is also an example that shows how to memory-map a file to a pauliebits: mmapped-file.py

Variable bit length prefix codes

The .encode() method takes a dictionary mapping symbols to pauliebits and an iterable, and extends the pauliebits object with the encoded symbols found while iterating. For example:

>>> d = {'H':pauliebits('111'), 'e':pauliebits('0'),
...      'l':pauliebits('110'), 'o':pauliebits('10')}
...
>>> a = pauliebits()
>>> a.encode(d, 'Hello')
>>> a
pauliebits('111011011010')

Note that the string 'Hello' is an iterable, but the symbols are not limited to characters, in fact any immutable Python object can be a symbol. Taking the same dictionary, we can apply the .decode() method which will return an iterable of the symbols:

>>> list(a.decode(d))
['H', 'e', 'l', 'l', 'o']
>>> ''.join(a.decode(d))
'Hello'

Symbols are not limited to being characters. The above dictionary d can be efficiently constructed using the function pauliebits.util.huffman_code(). I also wrote Huffman coding in Python using pauliebits for more background information.

When the codes are large, and you have many decode calls, most time will be spent creating the (same) internal decode tree objects. In this case, it will be much faster to create a decodetree object, which can be passed to pauliebits’s .decode() method, instead of passing the prefix code dictionary to those methods itself:

>>> from pauliebits import pauliebits, decodetree
>>> t = decodetree({'a': pauliebits('0'), 'b': pauliebits('1')})
>>> a = pauliebits('0110')
>>> list(a.decode(t))
['a', 'b', 'b', 'a']

The sole purpose of the immutable decodetree object is to be passed to pauliebits’s .decode() method.

Frozenpauliebits

A frozenpauliebits object is very similar to the pauliebits object. The difference is that this a frozenpauliebits is immutable, and hashable, and can therefore be used as a dictionary key:

>>> from pauliebits import frozenpauliebits
>>> key = frozenpauliebits('1100011')
>>> {key: 'some value'}
{frozenpauliebits('1100011'): 'some value'}
>>> key[3] = 1
Traceback (most recent call last):
    ...
TypeError: frozenpauliebits is immutable

The pauliebits object:

pauliebits(initializer=0, /, endian='big', buffer=None) -> pauliebits

Return a new pauliebits object whose items are bits initialized from the optional initializer, and bit-endianness. The initializer may be one of the following types: a.) int pauliebits, initialized to zeros, of given length b.) bytes or bytearray to initialize buffer directly c.) str of 0s and 1s, ignoring whitespace and “_” d.) iterable of integers 0 or 1.

Optional keyword arguments:

endian: Specifies the bit-endianness of the created pauliebits object. Allowed values are big and little (the default is big). The bit-endianness affects the buffer representation of the pauliebits.

buffer: Any object which exposes a buffer. When provided, initializer cannot be present (or has to be None). The imported buffer may be read-only or writable, depending on the object type.

New in version 2.3: optional buffer argument

New in version 3.4: allow initializer bytes or bytearray to set buffer directly

pauliebits methods:

all() -> bool

Return True when all bits in pauliebits are 1. a.all() is a faster version of all(a).

any() -> bool

Return True when any bit in pauliebits is 1. a.any() is a faster version of any(a).

append(item, /)

Append item to the end of the pauliebits.

buffer_info() -> BufferInfo

Return named tuple with following fields:

0. address: memory address of buffer

1. nbytes: buffer size (in bytes)

2. endian: bit-endianness as a string

3. padbits: number of pad bits

4. alloc: allocated memory for buffer (in bytes)

5. readonly: memory is read-only (bool)

6. imported: buffer is imported (bool)

7. exports: number of buffer exports

New in version 3.7: return named tuple

bytereverse(start=0, stop=<end of buffer>, /)

For each byte in byte-range(start, stop) reverse bits in-place. The start and stop indices are given in terms of bytes (not bits) and are interpreted like slice bounds and clipped to the buffer size. Also note that this method only changes the buffer; it does not change the bit-endianness of the pauliebits object. Pad bits are left unchanged such that two consecutive calls will always leave the pauliebits unchanged.

New in version 2.2.5: optional start and stop arguments

New in version 3.9.1: clip arguments instead of raising IndexError

clear()

Remove all items from pauliebits.

New in version 1.4

commutes_with(pauliebits)

Checking two strings for commutativity

complex_conjugate(pauliebits)

complex conjugate

copy() -> pauliebits

Return copy of pauliebits (with same bit-endianness).

count(value=1, start=0, stop=<end>, step=1, /) -> int

Number of occurrences of value pauliebits within [start:stop:step]. Optional arguments start, stop and step are interpreted in slice notation, meaning a.count(value, start, stop, step) equals a[start:stop:step].count(value). The value may also be a sub-pauliebits. In this case non-overlapping occurrences are counted within [start:stop] (step must be 1).

New in version 1.1.0: optional start and stop arguments

New in version 2.3.7: optional step argument

New in version 2.9: add non-overlapping sub-pauliebits count

count_non_trivially(pauliebits)

count_or for even odd bits

decode(code, /) -> decodeiterator

Given a prefix code (a dict mapping symbols to pauliebits, or decodetree object), decode content of pauliebits and return an iterator over corresponding symbols.

See also: pauliebits 3 transition

New in version 3.0: returns iterator (equivalent to past .iterdecode())

New in version 3.9: returns public decodeiterator object

decode_ixyz(pauliebits)

decode ixyz

diagonal_index(pauliebits)

diagonal index

encode(code, iterable, /)

Given a prefix code (a dict mapping symbols to pauliebits), iterate over the iterable object with symbols, and extend pauliebits with corresponding pauliebits for each symbol.

encode_ixyz(str)

Optimized 2-bit-per-symbol encoding of IXYZ strings.

extend(iterable, /)

Append items from iterable to the end of the pauliebits. If iterable is a (Unicode) string, each 0 and 1 are appended as bits (ignoring whitespace and underscore).

New in version 3.4: allow bytes object

fill() -> int

Add zeros to the end of the pauliebits, such that the length will be a multiple of 8, and return the number of bits added [0..7].

find(sub_pauliebits, start=0, stop=<end>, /, right=False) -> int

Return lowest (or rightmost when right=True) index where sub_pauliebits is found, such that sub_pauliebits is contained within [start:stop]. Return -1 when sub_pauliebits is not found.

New in version 2.1

New in version 2.9: add optional keyword argument right

frombytes(bytes, /)

Extend pauliebits with raw bytes from a bytes-like object. Each added byte will add eight bits to the pauliebits.

New in version 2.5.0: allow bytes-like argument

fromfile(f, n=-1, /)

Extend pauliebits with up to n bytes read from file object f (or any other binary stream that supports a .read() method, e.g. io.BytesIO). Each read byte will add eight bits to the pauliebits. When n is omitted or negative, reads and extends all data until EOF. When n is non-negative but exceeds the available data, EOFError is raised. However, the available data is still read and extended.

index(sub_pauliebits, start=0, stop=<end>, /, right=False) -> int

Return lowest (or rightmost when right=True) index where sub_pauliebits is found, such that sub_pauliebits is contained within [start:stop]. Raises ValueError when sub_pauliebits is not present.

New in version 2.9: add optional keyword argument right

insert(index, value, /)

Insert value into pauliebits before index.

invert(index=<all bits>, /)

Invert bits in-place. When index is omitted, invert all bits. When index is an integer, invert the single bit at index. When index is a slice, invert the selected bits.

New in version 1.5.3: optional index argument

not_identity_mask(pauliebits)

even | odd

pack(bytes, /)

Extend pauliebits from a bytes-like object, where each byte corresponds to a single bit. The byte b'\x00' maps to bit 0 and all other bytes map to bit 1.

This method, as well as the .unpack() method, are meant for efficient transfer of data between pauliebits objects to other Python objects (for example NumPy’s ndarray object) which have a different memory view.

New in version 2.5.0: allow bytes-like argument

phase(pauliebits)

phase

pop(index=-1, /) -> item

Remove and return item at index (default last). Raises IndexError if index is out of range.

remove(value, /)

Remove the first occurrence of value. Raises ValueError if value is not present.

reverse()

Reverse all bits in pauliebits (in-place).

rotate(k=1, /)

Rotate pauliebits in-place by k positions. Positive k rotates right, negative k rotates left.

When pauliebits a is not empty, rotating one step to the right is equivalent to a.insert(0, a.pop()), and rotating one step to the left is equivalent to a.append(a.pop(0)). The same convention is used by the .rotate() method of the collections.deque object.

New in version 3.9

search(sub_pauliebits, start=0, stop=<end>, /, right=False) -> iterator

Return iterator over indices where sub_pauliebits is found, such that sub_pauliebits is contained within [start:stop]. The indices are iterated in ascending order (from lowest to highest), unless right=True, which will iterate in descending order (starting with rightmost match).

For example, a.search(1) is the easiest (and most efficient) way to create an iterator over all active indices in a.

See also: pauliebits 3 transition

New in version 2.9: optional start and stop arguments - add optional keyword argument right

New in version 3.0: returns iterator (equivalent to past .itersearch())

setall(value, /)

Set all elements in pauliebits to value. Note that a.setall(value) is equivalent to a[:] = value.

sort(reverse=False)

Sort all bits in pauliebits (in-place).

to01(group=0, sep=' ') -> str

Return pauliebits as (Unicode) string of 0``s and ``1``s. The bits are grouped into ``group bits (default is no grouping). When grouped, the string sep is inserted between groups of group characters, default is a space.

New in version 3.3: optional group and sep arguments

tobytes() -> bytes

Return the pauliebits buffer (pad bits are set to zero). a.tobytes() is equivalent to bytes(a)

tofile(f, /)

Write pauliebits buffer to file object f.

tolist() -> list

Return pauliebits as list of integers. a.tolist() equals list(a).

Note that the list object being created will require 32 or 64 times more memory (depending on the machine architecture) than the pauliebits object, which may cause a memory error if the pauliebits is very large.

unpack(zero=b'\x00', one=b'\x01') -> bytes

Return bytes that contain one byte for each bit in the pauliebits, using the specified mapping.

pauliebits data descriptors:

Data descriptors were added in version 2.6.

endian -> str

bit-endianness as Unicode string

New in version 3.4: replaces former .endian() method

nbytes -> int

buffer size in bytes

padbits -> int

number of pad bits

readonly -> bool

bool indicating whether buffer is read-only

decodeiterator methods:

skipbits(n, /) -> pauliebits

Skip over the next n bits and return them. Raises ValueError if count is out of range.

New in version 3.9

decodeiterator data descriptors:

index -> int

current bit position to be decoded by subsequent next

New in version 3.9

Other objects:

frozenpauliebits(initializer=0, /, endian='big', buffer=None) -> frozenpauliebits

Return a frozenpauliebits object. Initialized the same way a pauliebits object is initialized. A frozenpauliebits is immutable and hashable, and may therefore be used as a dictionary key.

New in version 1.1

decodetree(code, /) -> decodetree

Given a prefix code (a dict mapping symbols to pauliebits), create a binary tree object to be passed to .decode().

New in version 1.6

Functions defined in the pauliebits module:

bits2bytes(n, /) -> int

Return the number of bytes necessary to store n bits.

get_default_endian() -> str

Return the default bit-endianness for new pauliebits objects being created.

New in version 1.3

test(verbosity=1) -> TextTestResult

Run self-test, and return unittest.runner.TextTestResult object.

Functions defined in pauliebits.util module:

This sub-module was added in version 1.2.

any_and(a, b, /) -> bool

Efficient implementation of any(a & b).

New in version 2.7

ba2base(n, pauliebits, /, group=0, sep=' ') -> str

Return a string containing the base n ASCII representation of the pauliebits. Allowed values for n are 2, 4, 8, 16, 32 and 64. The pauliebits has to have a length divisible by 1, 2, 3, 4, 5 or 6 respectively. For n=32 the RFC 4648 Base32 alphabet is used, and for n=64 the standard base 64 alphabet is used. When grouped, the string sep is inserted between groups of group characters, default is a space.

See also: pauliebits representations

New in version 1.9

New in version 3.3: optional group and sep arguments

ba2hex(pauliebits, /, group=0, sep=' ') -> hexstr

Return a string containing the hexadecimal representation of the pauliebits (which has to be multiple of 4 in length). When grouped, the string sep is inserted between groups of group characters, default is a space.

New in version 3.3: optional group and sep arguments

ba2int(pauliebits, /, signed=False) -> int

Convert the given pauliebits to an integer. The bit-endianness of the pauliebits is respected. signed indicates whether two’s complement is used to represent the integer.

base2ba(n, asciistr, /, endian=None) -> pauliebits

Pauliebits of base n ASCII representation. Allowed values for n are 2, 4, 8, 16, 32 and 64. For n=32 the RFC 4648 Base32 alphabet is used, and for n=64 the standard base 64 alphabet is used. Whitespace is ignored.

See also: pauliebits representations

New in version 1.9

New in version 3.3: ignore whitespace

byteswap(a, n=<buffer size>, /)

Reverse every n consecutive bytes of a in-place. By default, all bytes are reversed. Note that n is not limited to 2, 4 or 8, but can be any positive integer. Also, a may be any object that exposes a writable buffer. Nothing about this function is specific to pauliebits objects.

We should mention that Python’s array.array object has a method .byteswap() with similar functionality. However, unlike pauliebits’s util.byteswap() function, this method is limited to swapping 2, 4, or 8 consecutive bytes.

New in version 3.4

canonical_decode(pauliebits, count, symbol, /) -> iterator

Decode pauliebits using canonical Huffman decoding tables where count is a sequence containing the number of symbols of each length and symbol is a sequence of symbols in canonical order.

See also: Canonical Huffman Coding

New in version 2.5

canonical_huffman(dict, /) -> tuple

Given a frequency map, a dictionary mapping symbols to their frequency, calculate the canonical Huffman code. Returns a tuple containing:

0. the canonical Huffman code as a dict mapping symbols to pauliebits

1. a list containing the number of symbols of each code length

2. a list of symbols in canonical order

Note: the two lists may be used as input for canonical_decode().

See also: Canonical Huffman Coding

New in version 2.5

correspond_all(a, b, /) -> tuple

Return tuple with counts of: ~a & ~b, ~a & b, a & ~b, a & b

New in version 3.4

count_and(a, b, /) -> int

Return (a & b).count() in a memory efficient manner, as no intermediate pauliebits object gets created.

count_n(a, n, value=1, /) -> int

Return lowest index i for which a[:i].count(value) == n. Raises ValueError when n exceeds total count (a.count(value)).

New in version 2.3.6: optional value argument

count_or(a, b, /) -> int

Return (a | b).count() in a memory efficient manner, as no intermediate pauliebits object gets created.

count_xor(a, b, /) -> int

Return (a ^ b).count() in a memory efficient manner, as no intermediate pauliebits object gets created.

This is also known as the Hamming distance.

deserialize(bytes, /) -> pauliebits

Return a pauliebits given a bytes-like representation such as returned by serialize().

See also: pauliebits representations

New in version 1.8

New in version 2.5.0: allow bytes-like argument

gen_primes(n, /, endian=None, odd=False) -> pauliebits

Generate a pauliebits of length n in which active indices are prime numbers. By default (odd=False), active indices correspond to prime numbers directly. When odd=True, only odd prime numbers are represented in the resulting pauliebits a, and a[i] corresponds to 2*i+1 being prime or not.

Apart from working with prime numbers, this function is useful for testing, as it provides a simple way to create a well-defined pauliebits of any length.

New in version 3.7

hex2ba(hexstr, /, endian=None) -> pauliebits

Pauliebits of hexadecimal representation. hexstr may contain any number (including odd numbers) of hex digits (upper or lower case). Whitespace is ignored.

New in version 3.3: ignore whitespace

huffman_code(dict, /, endian=None) -> dict

Given a frequency map, a dictionary mapping symbols to their frequency, calculate the Huffman code, i.e. a dict mapping those symbols to pauliebits (with given bit-endianness). Note that the symbols are not limited to being strings. Symbols may be any hashable object.

int2ba(int, /, length=None, endian=None, signed=False) -> pauliebits

Convert the given integer to a pauliebits (with given bit-endianness, and no leading (big-endian) / trailing (little-endian) zeros), unless the length of the pauliebits is provided. An OverflowError is raised if the integer is not representable with the given number of bits. signed determines whether two’s complement is used to represent the integer, and requires length to be provided.

intervals(pauliebits, /) -> iterator

Compute all uninterrupted intervals of 1s and 0s, and return an iterator over tuples (value, start, stop). The intervals are guaranteed to be in order, and their size is always non-zero (stop - start > 0).

New in version 2.7

ones(n, /, endian=None) -> pauliebits

Create a pauliebits of length n, with all values 1, and optional bit-endianness (little or big).

New in version 2.9

parity(a, /) -> int

Return parity of pauliebits a. parity(a) is equivalent to a.count() % 2 but more efficient.

New in version 1.9

pprint(pauliebits, /, stream=None, group=8, indent=4, width=80)

Pretty-print pauliebits object to stream, defaults is sys.stdout. By default, bits are grouped in bytes (8 bits), and 64 bits per line. Non-pauliebits objects are printed using pprint.pprint().

New in version 1.8

random_k(n, /, k, endian=None) -> pauliebits

Return (pseudo-) random pauliebits of length n with k elements set to one. Mathematically equivalent to setting (in a pauliebits of length n) all bits at indices random.sample(range(n), k) to one. The random pauliebits are reproducible when giving Python’s random.seed() a specific seed value.

New in version 3.6

random_p(n, /, p=0.5, endian=None) -> pauliebits

Return (pseudo-) random pauliebits of length n, where each bit has probability p of being one (independent of any other bits). Mathematically equivalent to pauliebits((random() < p for _ in range(n)), endian), but much faster for large n. The random pauliebits are reproducible when giving Python’s random.seed() with a specific seed value.

This function requires Python 3.12 or higher, as it depends on the standard library function random.binomialvariate(). Raises NotImplementedError when Python version is too low.

See also: Random pauliebits

New in version 3.5

sc_decode(stream, /) -> pauliebits

Decompress binary stream (an integer iterator, or bytes-like object) of a sparse compressed (sc) pauliebits, and return the decoded pauliebits. This function consumes only one pauliebits and leaves the remaining stream untouched. Use sc_encode() for compressing (encoding).

See also: Compression of sparse pauliebits

New in version 2.7

sc_encode(pauliebits, /) -> bytes

Compress a pauliebits using sparse encoding and return its binary representation. This representation is useful for efficiently storing sparse pauliebits. Use sc_decode() for decompressing (decoding).

See also: Compression of sparse pauliebits

New in version 2.7

serialize(pauliebits, /) -> bytes

Return a serialized representation of the pauliebits, which may be passed to deserialize(). It efficiently represents the pauliebits object (including its bit-endianness) and is guaranteed not to change in future releases.

See also: pauliebits representations

New in version 1.8

strip(pauliebits, /, mode='right') -> pauliebits

Return a new pauliebits with zeros stripped from left, right or both ends. Allowed values for mode are the strings: left, right, both

subset(a, b, /) -> bool

Return True if pauliebits a is a subset of pauliebits b. subset(a, b) is equivalent to a | b == b (and equally a & b == a) but more efficient as no intermediate pauliebits object is created and the buffer iteration is stopped as soon as one mismatch is found.

sum_indices(a, /, mode=1) -> int

Return sum of indices of all active bits in pauliebits a. Equivalent to sum(i for i, v in enumerate(a) if v). mode=2 sums square of indices.

New in version 3.6

New in version 3.7: add optional mode argument

urandom(n, /, endian=None) -> pauliebits

Return random pauliebits of length n (uses os.urandom()).

New in version 1.7

vl_decode(stream, /, endian=None) -> pauliebits

Decode binary stream (an integer iterator, or bytes-like object), and return the decoded pauliebits. This function consumes only one pauliebits and leaves the remaining stream untouched. Use vl_encode() for encoding.

See also: Variable length pauliebits format

New in version 2.2

vl_encode(pauliebits, /) -> bytes

Return variable length binary representation of pauliebits. This representation is useful for efficiently storing small pauliebits in a binary stream. Use vl_decode() for decoding.

See also: Variable length pauliebits format

New in version 2.2

xor_indices(a, /) -> int

Return xor reduced indices of all active bits in pauliebits a. This is essentially equivalent to reduce(operator.xor, (i for i, v in enumerate(a) if v)).

New in version 3.2

zeros(n, /, endian=None) -> pauliebits

Create a pauliebits of length n, with all values 0, and optional bit-endianness (little or big).