o jge@sdZddlZddlmZddlmZddlmZddlm Z ddl m Z ddl m Z dd lmZdd lmZdd lmZdd lmZmZdd lmZddlmZddlmZmZmZddlm Z ddl!m"Z"ddl#m$Z$m%Z%ddl&m'Z'gdZ(GdddeZ)Gddde)eZ*Gddde)eZ+Gddde)Z,Gddde,e*Z-Gdd d e,e+Z.d!d"Z/d#d$Z0d3d&d'Z1d4d)d*Z2d4d+d,Z3d3d-d.Z4d/d0Z5d3d1d2Z6dS)5zQubits for quantum computing. Todo: * Finish implementing measurement logic. This should include POVM. * Update docstrings. * Update tests. N)Add)Mul)Integer)Pow)S) conjugate)log_sympify) SYMPY_INTS)Matrixzeros) prettyForm) ComplexSpace)KetBraState) QuantumError represent) numpy_ndarrayscipy_sparse_matrix)bitcount) QubitQubitBraIntQubit IntQubitBraqubit_to_matrixmatrix_to_qubitmatrix_to_density measure_allmeasure_partialmeasure_partial_oneshotmeasure_all_oneshotc@sdeZdZdZeddZeddZeddZedd Z ed d Z d d Z ddZ ddZ dS) QubitStatez"Base class for Qubit and QubitBra.cCst|dkrt|dtr|djSt|dkr+t|dtr+tdd|dD}n tdd|D}tdd|D}|D]}|tjtjfvrOt d|q?|S)Nrcss$|] }|dkr tjntjVqdS)0NrZeroOne.0qbr-S/var/www/html/zoom/venv/lib/python3.10/site-packages/sympy/physics/quantum/qubit.py Es"z(QubitState._eval_args..css0|]}|dkr tjn|dkrtjn|VqdS)r&1Nr'r*r-r-r.r/Gs.cs|]}t|VqdSNr )r+argr-r-r.r/Hz$Qubit values must be 0 or 1, got: %r) len isinstancer$ qubit_valuesstrtuplerr(r) ValueError)clsargselementr-r-r. _eval_args<s zQubitState._eval_argscCstdt|S)N)rr5)r;r<r-r-r._eval_hilbert_spaceQszQubitState._eval_hilbert_spacecCs t|jS)z"The number of Qubits in the state.)r5r7selfr-r-r. dimensionYs zQubitState.dimensioncC|jSr2rCrAr-r-r.nqubits^szQubitState.nqubitscCrD)z,Returns the values of the qubits as a tuple.)labelrAr-r-r.r7bszQubitState.qubit_valuescCrDr2rErAr-r-r.__len__kszQubitState.__len__cCs|jt|j|dS)Nr%)r7intrC)rBbitr-r-r. __getitem__nszQubitState.__getitem__cGsRt|j}|D]}t|j|d}||dkrd||<qd||<q|jt|S)zFlip the bit(s) given.r%r)listr7rIrC __class__r9)rBbitsnewargsirJr-r-r.flipus    zQubitState.flipN)__name__ __module__ __qualname____doc__ classmethodr>r@propertyrCrFr7rHrKrQr-r-r-r.r$5s      r$c@sDeZdZdZeddZddZddZdd Zd d Z d d Z dS)raA multi-qubit ket in the computational (z) basis. We use the normal convention that the least significant qubit is on the right, so ``|00001>`` has a 1 in the least significant qubit. Parameters ========== values : list, str The qubit values as a list of ints ([0,0,0,1,1,]) or a string ('011'). Examples ======== Create a qubit in a couple of different ways and look at their attributes: >>> from sympy.physics.quantum.qubit import Qubit >>> Qubit(0,0,0) |000> >>> q = Qubit('0101') >>> q |0101> >>> q.nqubits 4 >>> len(q) 4 >>> q.dimension 4 >>> q.qubit_values (0, 1, 0, 1) We can flip the value of an individual qubit: >>> q.flip(1) |0111> We can take the dagger of a Qubit to get a bra: >>> from sympy.physics.quantum.dagger import Dagger >>> Dagger(q) <0101| >>> type(Dagger(q)) Inner products work as expected: >>> ip = Dagger(q)*q >>> ip <0101|0101> >>> ip.doit() 1 cCtSr2)rrAr-r-r. dual_classzQubit.dual_classcKs|j|jkr tjStjSr2)rGrr)r(rBbrahintsr-r-r._eval_innerproduct_QubitBras z!Qubit._eval_innerproduct_QubitBracKs|jdi|S)Nr2)_represent_ZGate)rBoptionsr-r-r._represent_default_basisszQubit._represent_default_basisc Ks|dd}d}d}t|jD] }|||7}|d}qdgd|j}d|t|<|dkr2t|S|dkrCddl}|j|dd S|d krVdd l m } | j |dd SdS) zBRepresent this qubits in the computational basis (ZGate). formatsympyr%rr?numpyNcomplex)dtype scipy.sparse)sparse) getreversedr7rCrIr rdarray transposescipyrh csr_matrix) rBbasisr`_formatndefinite_stateitresultnprhr-r-r.r_s"     zQubit._represent_ZGatecKs|dg}t|}t|dkrttd|j}|||}tt|dddD] }||t||}q*t||jkrB|dSt|S)Nindicesrr%) rirLr5rangerFsort_reduced_densityrIr)rBr\kwargsrv sorted_idxnew_matrPr-r-r. _eval_traces  zQubit._eval_tracec Ksdd}t|fi|}|j}|d}t|}t|D]*} t|D]#} tdD]} || | |} || | |} || | f|| | f7<q)q#q|S)zCompute the reduced density matrix by tracing out one qubit. The qubit argument should be of type Python int, since it is used in bit operations cSs,d|d}||?d|>||@||>S)Nr?r%r-)jkqubitbit_maskr-r-r.find_index_that_is_projecteds  z.find_index_that_is_projectedr?)rcolsr r rx)rBmatrixrr`r old_matrixold_sizenew_size new_matrixrPrrcolrowr-r-r.rzs      zQubit._reduced_densityN) rRrSrTrUrVrYr^rar_r~rzr-r-r-r.rs6  rc@eZdZdZeddZdS)raA multi-qubit bra in the computational (z) basis. We use the normal convention that the least significant qubit is on the right, so ``|00001>`` has a 1 in the least significant qubit. Parameters ========== values : list, str The qubit values as a list of ints ([0,0,0,1,1,]) or a string ('011'). See also ======== Qubit: Examples using qubits cCrXr2)rrAr-r-r.rYrZzQubitBra.dual_classNrRrSrTrUrVrYr-r-r-r.rsrc@sJeZdZdZed ddZeddZddZd d Zd d Z eZ eZ dS) IntQubitStatez>A base class for qubits that work with binary representations.Ncs$tdkrtdtrtStddDs)tdtddDf|durQt|ttfs.z!values must be integers, got (%s)csr1r2)typerr-r-r.r/)r4z$nqubits must be an integer, got (%s)zAtoo many positional arguments (%s). should be (number, nqubits=n)csg|] }d|?d@qS)rr%r-r+rPr<r-r. 7sz,IntQubitState._eval_args..r?)r5r6r$r>allr:r9rIrr_eval_args_with_nqubitsrjrxrabs)r;r<rFrvaluesr7r-rr.r>"s&    zIntQubitState._eval_argscsHtt}||krtd|ffddtt|D}t|S)Nz cannot represent %s with %s bitscsg|]}|?d@qS)r%r-rnumberr-r.rFsz9IntQubitState._eval_args_with_nqubits..)rrr:rjrxr$r>)r;rrFneedr7r-rr.r@s   z%IntQubitState._eval_args_with_nqubitscCs0d}d}t|jD] }|||7}|d>}q |S)z(Return the numerical value of the qubit.rr%)rjr7)rBrrqrPr-r-r.as_intIs   zIntQubitState.as_intcGs t|Sr2)r8r)rBprinterr<r-r-r. _print_labelR zIntQubitState._print_labelcGs|j|g|R}t|Sr2)rr)rBrr<rGr-r-r._print_label_prettyUsz!IntQubitState._print_label_prettyr2) rRrSrTrUrVr>rrrr_print_label_repr_print_label_latexr-r-r-r.rs   rc@s$eZdZdZeddZddZdS)raxA qubit ket that store integers as binary numbers in qubit values. The differences between this class and ``Qubit`` are: * The form of the constructor. * The qubit values are printed as their corresponding integer, rather than the raw qubit values. The internal storage format of the qubit values in the same as ``Qubit``. Parameters ========== values : int, tuple If a single argument, the integer we want to represent in the qubit values. This integer will be represented using the fewest possible number of qubits. If a pair of integers and the second value is more than one, the first integer gives the integer to represent in binary form and the second integer gives the number of qubits to use. List of zeros and ones is also accepted to generate qubit by bit pattern. nqubits : int The integer that represents the number of qubits. This number should be passed with keyword ``nqubits=N``. You can use this in order to avoid ambiguity of Qubit-style tuple of bits. Please see the example below for more details. Examples ======== Create a qubit for the integer 5: >>> from sympy.physics.quantum.qubit import IntQubit >>> from sympy.physics.quantum.qubit import Qubit >>> q = IntQubit(5) >>> q |5> We can also create an ``IntQubit`` by passing a ``Qubit`` instance. >>> q = IntQubit(Qubit('101')) >>> q |5> >>> q.as_int() 5 >>> q.nqubits 3 >>> q.qubit_values (1, 0, 1) We can go back to the regular qubit form. >>> Qubit(q) |101> Please note that ``IntQubit`` also accepts a ``Qubit``-style list of bits. So, the code below yields qubits 3, not a single bit ``1``. >>> IntQubit(1, 1) |3> To avoid ambiguity, use ``nqubits`` parameter. Use of this keyword is recommended especially when you provide the values by variables. >>> IntQubit(1, nqubits=1) |1> >>> a = 1 >>> IntQubit(a, nqubits=1) |1> cCrXr2)rrAr-r-r.rYrZzIntQubit.dual_classcKs t||Sr2)rr^r[r-r-r._eval_innerproduct_IntQubitBrarz'IntQubit._eval_innerproduct_IntQubitBraN)rRrSrTrUrVrYrr-r-r-r.r]s F  rc@r)rzBA qubit bra that store integers as binary numbers in qubit values.cCrXr2)rrAr-r-r.rYrZzIntQubitBra.dual_classNrr-r-r-r.rsrc s(d}t|tr d}t|trd}|jddkr&|jd}t|d}d}t}n|jddkr<|jd}t|d}d}t}ntd |t|tsMtd |d}t |D]2|r^|df}n|df}|d vrlt |}|rfd d t |D}| ||||}qSt|t t tfr|}|S)aUConvert from the matrix repr. to a sum of Qubit objects. Parameters ---------- matrix : Matrix, numpy.matrix, scipy.sparse The matrix to build the Qubit representation of. This works with SymPy matrices, numpy matrices and scipy.sparse sparse matrices. Examples ======== Represent a state and then go back to its qubit form: >>> from sympy.physics.quantum.qubit import matrix_to_qubit, Qubit >>> from sympy.physics.quantum.represent import represent >>> q = Qubit('01') >>> matrix_to_qubit(represent(q)) |01> rcrdrgrr%r?FTz*Matrix must be a row/column vector, got %rz>Matrix must be a row/column vector of size 2**nqubits, got: %r)rdrgcs g|] }td|>@dkqS)r%r)rI)r+xrPr-r.rs z#matrix_to_qubit..)r6rrshaperrrrrrxrereverserrrexpand) rrbmlistlenrFketr;rtr= qubit_arrayr-rr.rsJ         rcCs<ddlm}|}dd|D}t|dkrtjS||S)z Works by finding the eigenvectors and eigenvalues of the matrix. We know we can decompose rho by doing: sum(EigenVal*|Eigenvect>.)sympy.physics.quantum.densityr eigenvectsr5rr()matreigenr<r-r-r.rs  rrccCs t||dS)zConverts an Add/Mul of Qubit objects into it's matrix representation This function is the inverse of ``matrix_to_qubit`` and is a shorthand for ``represent(qubit)``. )rbr)rrbr-r-r.rs rTcCst||}|dkrDg}|r|}t|j}tt|td}t|D]}||rA|t t ||d||t ||fq&|St d)aPerform an ensemble measurement of all qubits. Parameters ========== qubit : Qubit, Add The qubit to measure. This can be any Qubit or a linear combination of them. format : str The format of the intermediate matrices to use. Possible values are ('sympy','numpy','scipy.sparse'). Currently only 'sympy' is implemented. Returns ======= result : list A list that consists of primitive states and their probabilities. Examples ======== >>> from sympy.physics.quantum.qubit import Qubit, measure_all >>> from sympy.physics.quantum.gate import H >>> from sympy.physics.quantum.qapply import qapply >>> c = H(0)*H(1)*Qubit('00') >>> c H(0)*H(1)*|00> >>> q = qapply(c) >>> measure_all(q) [(|00>, 1/4), (|01>, 1/4), (|10>, 1/4), (|11>, 1/4)] rcr?)rF8This function cannot handle non-SymPy matrix formats yet) r normalizedmaxrrImathrrxappendrrrNotImplementedError)rrb normalizemresultssizerFrPr-r-r.r s" "  "r c Cst||}t|ttfrt|f}|dkrL|r|}t||}g}|D]%}d}||j|d7}|dkrI|r>t|} nt|} | | |fq$|St d)aPerform a partial ensemble measure on the specified qubits. Parameters ========== qubits : Qubit The qubit to measure. This can be any Qubit or a linear combination of them. bits : tuple The qubits to measure. format : str The format of the intermediate matrices to use. Possible values are ('sympy','numpy','scipy.sparse'). Currently only 'sympy' is implemented. Returns ======= result : list A list that consists of primitive states and their probabilities. Examples ======== >>> from sympy.physics.quantum.qubit import Qubit, measure_partial >>> from sympy.physics.quantum.gate import H >>> from sympy.physics.quantum.qapply import qapply >>> c = H(0)*H(1)*Qubit('00') >>> c H(0)*H(1)*|00> >>> q = qapply(c) >>> measure_partial(q, (0,)) [(sqrt(2)*|00>/2 + sqrt(2)*|10>/2, 1/2), (sqrt(2)*|01>/2 + sqrt(2)*|11>/2, 1/2)] rcrr) rr6r rrIr_get_possible_outcomesHrrr) rrNrbrrpossible_outcomesoutputoutcomeprob_of_outcome next_matrixr-r-r.r!Ts0 $  r!c Csxddl}t||}|dkr8|}t||}|}d}|D]}||j|d7}||kr5t|SqdStd)aPerform a partial oneshot measurement on the specified qubits. A oneshot measurement is equivalent to performing a measurement on a quantum system. This type of measurement does not return the probabilities like an ensemble measurement does, but rather returns *one* of the possible resulting states. The exact state that is returned is determined by picking a state randomly according to the ensemble probabilities. Parameters ---------- qubits : Qubit The qubit to measure. This can be any Qubit or a linear combination of them. bits : tuple The qubits to measure. format : str The format of the intermediate matrices to use. Possible values are ('sympy','numpy','scipy.sparse'). Currently only 'sympy' is implemented. Returns ------- result : Qubit The qubit that the system collapsed to upon measurement. rNrcr)randomrrrrrr) rrNrbrrr random_number total_probrr-r-r.r"s   r"c Cst|j}tt|d}g}tdt|>D] }|td|dqg}|D] }|d|>q)td|D]!}d}tt|D]} ||| @rQ|| d7}qC|||||<q9|S)aGet the possible states that can be produced in a measurement. Parameters ---------- m : Matrix The matrix representing the state of the system. bits : tuple, list Which bits will be measured. Returns ------- result : list The list of possible states which can occur given this measurement. These are un-normalized so we can derive the probability of finding this state by taking the inner product with itself 皙?r%r?r) rrrIrlog2rxr5rr ) rrNrrFoutput_matricesrP bit_masksrJtruenessrr-r-r.rs   rcCsddl}t|}|dkr@|}|}d}d}|D]}|||7}||kr*n|d7}qtt|ttt |j dSt d)adPerform a oneshot ensemble measurement on all qubits. A oneshot measurement is equivalent to performing a measurement on a quantum system. This type of measurement does not return the probabilities like an ensemble measurement does, but rather returns *one* of the possible resulting states. The exact state that is returned is determined by picking a state randomly according to the ensemble probabilities. Parameters ---------- qubits : Qubit The qubit to measure. This can be any Qubit or a linear combination of them. format : str The format of the intermediate matrices to use. Possible values are ('sympy','numpy','scipy.sparse'). Currently only 'sympy' is implemented. Returns ------- result : Qubit The qubit that the system collapsed to upon measurement. rNrcr%rr) rrrrrrrIrrrrr)rrbrrrtotalrtrPr-r-r.r#s  "r#)rc)rcT)7rUrsympy.core.addrsympy.core.mulrsympy.core.numbersrsympy.core.powerrsympy.core.singletonr$sympy.functions.elementary.complexesr&sympy.functions.elementary.exponentialrsympy.core.basicr sympy.external.gmpyr sympy.matricesr r sympy.printing.pretty.stringpictrsympy.physics.quantum.hilbertrsympy.physics.quantum.staterrrsympy.physics.quantum.qexprrsympy.physics.quantum.representr!sympy.physics.quantum.matrixutilsrrmpmath.libmp.libintmathr__all__r$rrrrrrrrr r!r"rr#r-r-r-r.sF              L>N F   8 K03