File size: 33,619 Bytes
b7d9967
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
# This code is part of Qiskit.
#
# (C) Copyright IBM 2018, 2022.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.

"""The Variational Quantum Deflation Algorithm for computing higher energy states.



See https://arxiv.org/abs/1805.08138.

"""
from __future__ import annotations

import logging
import warnings
from collections.abc import Callable
from time import time
import numpy as np

from qiskit.circuit import QuantumCircuit, Parameter
from qiskit.circuit.library import RealAmplitudes
from qiskit.opflow.primitive_ops.pauli_op import PauliOp
from qiskit.providers import Backend
from qiskit.opflow import (
    OperatorBase,
    ExpectationBase,
    ExpectationFactory,
    StateFn,
    CircuitStateFn,
    ListOp,
    CircuitSampler,
    PauliSumOp,
)
from qiskit.opflow.gradients import GradientBase
from qiskit.utils.validation import validate_min
from qiskit.utils.backend_utils import is_aer_provider
from qiskit.utils.deprecation import deprecate_func
from qiskit.utils import QuantumInstance
from ..list_or_dict import ListOrDict
from ..optimizers import Optimizer, SLSQP, Minimizer
from ..variational_algorithm import VariationalAlgorithm, VariationalResult
from .eigen_solver import Eigensolver, EigensolverResult
from ..minimum_eigen_solvers.vqe import _validate_bounds, _validate_initial_point
from ..exceptions import AlgorithmError
from ..aux_ops_evaluator import eval_observables

logger = logging.getLogger(__name__)


class VQD(VariationalAlgorithm, Eigensolver):
    r"""Deprecated: Variational Quantum Deflation algorithm.



    The VQD class has been superseded by the

    :class:`qiskit.algorithms.eigensolvers.VQD` class.

    This class will be deprecated in a future release and subsequently

    removed after that.



    `VQD <https://arxiv.org/abs/1805.08138>`__ is a quantum algorithm that uses a

    variational technique to find

    the k eigenvalues of the Hamiltonian :math:`H` of a given system.



    The algorithm computes excited state energies of generalised hamiltonians

    by optimising over a modified cost function where each succesive eigen value

    is calculated iteratively by introducing an overlap term with all

    the previously computed eigenstaes that must be minimised, thus ensuring

    higher energy eigen states are found.



    An instance of VQD requires defining three algorithmic sub-components:

    an integer k denoting the number of eigenstates to calculate, a trial

    state (a.k.a. ansatz)which is a :class:`QuantumCircuit`,

    and one of the classical :mod:`~qiskit.algorithms.optimizers`.

    The ansatz is varied, via its set of parameters, by the optimizer,

    such that it works towards a state, as determined by the parameters

    applied to the ansatz, that will result in the minimum expectation values

    being measured of the input operator (Hamiltonian). The algorithm does

    this by iteratively refining each excited state to be orthogonal to all

    the previous excited states.



    An optional array of parameter values, via the *initial_point*, may be provided as the

    starting point for the search of the minimum eigenvalue. This feature is particularly useful

    such as when there are reasons to believe that the solution point is close to a particular

    point.



    The length of the *initial_point* list value must match the number of the parameters

    expected by the ansatz being used. If the *initial_point* is left at the default

    of ``None``, then VQD will look to the ansatz for a preferred value, based on its

    given initial state. If the ansatz returns ``None``,

    then a random point will be generated within the parameter bounds set, as per above.

    If the ansatz provides ``None`` as the lower bound, then VQD

    will default it to :math:`-2\pi`; similarly, if the ansatz returns ``None``

    as the upper bound, the default value will be :math:`2\pi`.



    """

    @deprecate_func(

        additional_msg=(

            "Instead, use the class ``qiskit.algorithms.eigensolvers.VQD``."

            "See https://qisk.it/algo_migration for a migration guide."

        ),

        since="0.24.0",

    )
    def __init__(

        self,

        ansatz: QuantumCircuit | None = None,

        k: int = 2,

        betas: list[float] | None = None,

        optimizer: Optimizer | Minimizer | None = None,

        initial_point: np.ndarray | None = None,

        gradient: GradientBase | Callable | None = None,

        expectation: ExpectationBase | None = None,

        include_custom: bool = False,

        max_evals_grouped: int = 1,

        callback: Callable[[int, np.ndarray, float, float, int], None] | None = None,

        quantum_instance: QuantumInstance | Backend | None = None,

    ) -> None:
        """



        Args:

            ansatz: A parameterized circuit used as ansatz for the wave function.

            k: the number of eigenvalues to return. Returns the lowest k eigenvalues.

            betas: beta parameters in the VQD paper.

                Should have length k - 1, with k the number of excited states.

                These hyperparameters balance the contribution of each overlap term to the cost

                function and have a default value computed as the mean square sum of the

                coefficients of the observable.

            optimizer: A classical optimizer. Can either be a Qiskit optimizer or a callable

                that takes an array as input and returns a Qiskit or SciPy optimization result.

            initial_point: An optional initial point (i.e. initial parameter values)

                for the optimizer. If ``None`` then VQD will look to the ansatz for a preferred

                point and if not will simply compute a random one.

            gradient: An optional gradient function or operator for optimizer.

                Only used to compute the ground state at the moment.

            expectation: The Expectation converter for taking the average value of the

                Observable over the ansatz state function. When ``None`` (the default) an

                :class:`~qiskit.opflow.expectations.ExpectationFactory` is used to select

                an appropriate expectation based on the operator and backend. When using Aer

                qasm_simulator backend, with paulis, it is however much faster to leverage custom

                Aer function for the computation but, although VQD performs much faster

                with it, the outcome is ideal, with no shot noise, like using a state vector

                simulator. If you are just looking for the quickest performance when choosing Aer

                qasm_simulator and the lack of shot noise is not an issue then set `include_custom`

                parameter here to ``True`` (defaults to ``False``).

            include_custom: When `expectation` parameter here is None setting this to ``True`` will

                allow the factory to include the custom Aer pauli expectation.

            max_evals_grouped: Max number of evaluations performed simultaneously. Signals the

                given optimizer that more than one set of parameters can be supplied so that

                multiple points to compute the gradient can be passed and if computed in parallel

                potentially the expectation values can be computed in parallel. Typically this is

                possible when a finite difference gradient is used by the optimizer such that

                improve overall execution time. Deprecated if a gradient operator or function is

                given.

            callback: a callback that can access the intermediate data during the optimization.

                Four parameter values are passed to the callback as follows during each evaluation

                by the optimizer for its current set of parameters as it works towards the minimum.

                These are: the evaluation count, the optimizer parameters for the ansatz, the

                evaluated mean, the evaluated standard deviation, and the current step.

            quantum_instance: Quantum Instance or Backend



        """
        validate_min("max_evals_grouped", max_evals_grouped, 1)

        with warnings.catch_warnings():
            warnings.simplefilter("ignore")
            super().__init__()

        self._max_evals_grouped = max_evals_grouped
        self._circuit_sampler: CircuitSampler | None = None
        self._expectation = None
        self.expectation = expectation
        self._include_custom = include_custom

        # set ansatz -- still supporting pre 0.18.0 sorting

        self._ansatz: QuantumCircuit | None = None
        self.ansatz = ansatz

        self.k = k
        self.betas = betas

        self._optimizer: Optimizer | None = None
        self.optimizer = optimizer

        self._initial_point: np.ndarray | None = None
        self.initial_point = initial_point
        self._gradient: GradientBase | Callable | None = None
        self.gradient = gradient
        self._quantum_instance: QuantumInstance | None = None

        if quantum_instance is not None:
            self.quantum_instance = quantum_instance

        self._eval_time = None
        self._eval_count = 0
        self._callback: Callable[[int, np.ndarray, float, float, int], None] | None = None
        self.callback = callback

        logger.info(self.print_settings())

    @property
    def ansatz(self) -> QuantumCircuit:
        """Returns the ansatz."""
        return self._ansatz

    @ansatz.setter
    def ansatz(self, ansatz: QuantumCircuit | None):
        """Sets the ansatz.



        Args:

            ansatz: The parameterized circuit used as an ansatz.

                If None is passed, RealAmplitudes is used by default.



        """
        if ansatz is None:
            ansatz = RealAmplitudes()

        self._ansatz = ansatz

    @property
    def gradient(self) -> GradientBase | Callable | None:
        """Returns the gradient."""
        return self._gradient

    @gradient.setter
    def gradient(self, gradient: GradientBase | Callable | None):
        """Sets the gradient."""
        self._gradient = gradient

    @property
    def quantum_instance(self) -> QuantumInstance | None:
        """Returns quantum instance."""
        return self._quantum_instance

    @quantum_instance.setter
    def quantum_instance(self, quantum_instance: QuantumInstance | Backend) -> None:
        """Sets a quantum_instance."""
        if not isinstance(quantum_instance, QuantumInstance):
            quantum_instance = QuantumInstance(quantum_instance)

        self._quantum_instance = quantum_instance
        self._circuit_sampler = CircuitSampler(
            quantum_instance, param_qobj=is_aer_provider(quantum_instance.backend)
        )

    @property
    def initial_point(self) -> np.ndarray | None:
        """Returns initial point."""
        return self._initial_point

    @initial_point.setter
    def initial_point(self, initial_point: np.ndarray):
        """Sets initial point"""
        self._initial_point = initial_point

    @property
    def max_evals_grouped(self) -> int:
        """Returns max_evals_grouped"""
        return self._max_evals_grouped

    @max_evals_grouped.setter
    def max_evals_grouped(self, max_evals_grouped: int):
        """Sets max_evals_grouped"""
        self._max_evals_grouped = max_evals_grouped
        self.optimizer.set_max_evals_grouped(max_evals_grouped)

    @property
    def include_custom(self) -> bool:
        """Returns include_custom"""
        return self._include_custom

    @include_custom.setter
    def include_custom(self, include_custom: bool):
        """Sets include_custom. If set to another value than the one that was previsously set,

        the expectation attribute is reset to None.

        """
        if include_custom != self._include_custom:
            self._include_custom = include_custom
            self.expectation = None

    @property
    def callback(self) -> Callable[[int, np.ndarray, float, float, int], None] | None:
        """Returns callback"""
        return self._callback

    @callback.setter
    def callback(self, callback: Callable[[int, np.ndarray, float, float, int], None] | None):
        """Sets callback"""
        self._callback = callback

    @property
    def expectation(self) -> ExpectationBase | None:
        """The expectation value algorithm used to construct the expectation measurement from

        the observable."""
        return self._expectation

    @expectation.setter
    def expectation(self, exp: ExpectationBase | None) -> None:
        self._expectation = exp

    def _check_operator_ansatz(self, operator: OperatorBase):
        """Check that the number of qubits of operator and ansatz match."""
        if operator is not None and self.ansatz is not None:
            if operator.num_qubits != self.ansatz.num_qubits:
                # try to set the number of qubits on the ansatz, if possible
                try:
                    self.ansatz.num_qubits = operator.num_qubits
                except AttributeError as ex:
                    raise AlgorithmError(
                        "The number of qubits of the ansatz does not match the "
                        "operator, and the ansatz does not allow setting the "
                        "number of qubits using `num_qubits`."
                    ) from ex

    @property
    def optimizer(self) -> Optimizer:
        """Returns optimizer"""
        return self._optimizer

    @optimizer.setter
    def optimizer(self, optimizer: Optimizer | None):
        """Sets the optimizer attribute.



        Args:

            optimizer: The optimizer to be used. If None is passed, SLSQP is used by default.



        """
        if optimizer is None:
            optimizer = SLSQP()

        if isinstance(optimizer, Optimizer):
            optimizer.set_max_evals_grouped(self.max_evals_grouped)

        self._optimizer = optimizer

    @property
    def setting(self):
        """Prepare the setting of VQD as a string."""
        ret = f"Algorithm: {self.__class__.__name__}\n"
        params = ""
        for key, value in self.__dict__.items():
            if key[0] == "_":
                if "initial_point" in key and value is None:
                    params += "-- {}: {}\n".format(key[1:], "Random seed")
                else:
                    params += f"-- {key[1:]}: {value}\n"
        ret += f"{params}"
        return ret

    def print_settings(self):
        """Preparing the setting of VQD into a string.



        Returns:

            str: the formatted setting of VQD.

        """
        ret = "\n"
        ret += "==================== Setting of {} ============================\n".format(
            self.__class__.__name__
        )
        ret += f"{self.setting}"
        ret += "===============================================================\n"
        if self.ansatz is not None:
            ret += "{}".format(self.ansatz.draw(output="text"))
        else:
            ret += "ansatz has not been set"
        ret += "===============================================================\n"
        ret += f"{self._optimizer.setting}"
        ret += "===============================================================\n"
        return ret

    def construct_expectation(

        self,

        parameter: list[float] | list[Parameter] | np.ndarray,

        operator: OperatorBase,

        return_expectation: bool = False,

    ) -> OperatorBase | tuple[OperatorBase, ExpectationBase]:
        r"""

        Generate the ansatz circuit and expectation value measurement, and return their

        runnable composition.



        Args:

            parameter: Parameters for the ansatz circuit.

            operator: Qubit operator of the Observable

            return_expectation: If True, return the ``ExpectationBase`` expectation converter used

                in the construction of the expectation value. Useful e.g. to compute the standard

                deviation of the expectation value.



        Returns:

            The Operator equalling the measurement of the ansatz :class:`StateFn` by the

            Observable's expectation :class:`StateFn`, and, optionally, the expectation converter.



        Raises:

            AlgorithmError: If no operator has been provided.

            AlgorithmError: If no expectation is passed and None could be inferred via the

                ExpectationFactory.

        """
        if operator is None:
            raise AlgorithmError("The operator was never provided.")

        self._check_operator_ansatz(operator)

        # if expectation was never created, try to create one
        if self.expectation is None:
            expectation = ExpectationFactory.build(
                operator=operator,
                backend=self.quantum_instance,
                include_custom=self._include_custom,
            )
        else:
            expectation = self.expectation

        wave_function = self.ansatz.assign_parameters(parameter)

        observable_meas = expectation.convert(StateFn(operator, is_measurement=True))
        ansatz_circuit_op = CircuitStateFn(wave_function)
        expect_op = observable_meas.compose(ansatz_circuit_op).reduce()

        if return_expectation:
            return expect_op, expectation

        return expect_op

    def construct_circuit(

        self,

        parameter: list[float] | list[Parameter] | np.ndarray,

        operator: OperatorBase,

    ) -> list[QuantumCircuit]:
        """Return the circuits used to compute the expectation value.



        Args:

            parameter: Parameters for the ansatz circuit.

            operator: Qubit operator of the Observable



        Returns:

            A list of the circuits used to compute the expectation value.

        """
        expect_op = self.construct_expectation(parameter, operator).to_circuit_op()

        circuits = []

        # recursively extract circuits
        def extract_circuits(op):
            if isinstance(op, CircuitStateFn):
                circuits.append(op.primitive)
            elif isinstance(op, ListOp):
                for op_i in op.oplist:
                    extract_circuits(op_i)

        extract_circuits(expect_op)

        return circuits

    @classmethod
    def supports_aux_operators(cls) -> bool:
        return True

    def _eval_aux_ops(

        self,

        parameters: np.ndarray,

        aux_operators: ListOrDict[OperatorBase],

        expectation: ExpectationBase,

        threshold: float = 1e-12,

    ) -> ListOrDict[tuple[complex, complex]]:
        # Create new CircuitSampler to avoid breaking existing one's caches.
        sampler = CircuitSampler(self.quantum_instance)

        if isinstance(aux_operators, dict):
            list_op = ListOp(list(aux_operators.values()))
        else:
            list_op = ListOp(aux_operators)

        aux_op_meas = expectation.convert(StateFn(list_op, is_measurement=True))
        aux_op_expect = aux_op_meas.compose(CircuitStateFn(self.ansatz.bind_parameters(parameters)))
        aux_op_expect_sampled = sampler.convert(aux_op_expect)

        # compute means
        values = np.real(aux_op_expect_sampled.eval())

        # compute standard deviations
        variances = np.real(expectation.compute_variance(aux_op_expect_sampled))
        if not isinstance(variances, np.ndarray) and variances == 0.0:
            # when `variances` is a single value equal to 0., our expectation value is exact and we
            # manually ensure the variances to be a list of the correct length
            variances = np.zeros(len(aux_operators), dtype=float)
        std_devs = np.sqrt(variances / self.quantum_instance.run_config.shots)

        # Discard values below threshold
        aux_op_means = values * (np.abs(values) > threshold)
        # zip means and standard deviations into tuples
        aux_op_results = zip(aux_op_means, std_devs)

        # Return None eigenvalues for None operators if aux_operators is a list.
        # None operators are already dropped in compute_minimum_eigenvalue if aux_operators is a
        # dict.
        if isinstance(aux_operators, list):
            aux_operator_eigenvalues: ListOrDict[tuple[complex, complex]] = [None] * len(
                aux_operators
            )
            key_value_iterator = enumerate(aux_op_results)
        else:
            aux_operator_eigenvalues = {}
            key_value_iterator = zip(aux_operators.keys(), aux_op_results)

        for key, value in key_value_iterator:
            if aux_operators[key] is not None:
                aux_operator_eigenvalues[key] = value

        return aux_operator_eigenvalues

    def compute_eigenvalues(

        self, operator: OperatorBase, aux_operators: ListOrDict[OperatorBase] | None = None

    ) -> EigensolverResult:
        super().compute_eigenvalues(operator, aux_operators)

        if self.quantum_instance is None:
            raise AlgorithmError(
                "A QuantumInstance or Backend must be supplied to run the quantum algorithm."
            )
        self.quantum_instance.circuit_summary = True

        # this sets the size of the ansatz, so it must be called before the initial point
        # validation
        self._check_operator_ansatz(operator)

        # set an expectation for this algorithm run (will be reset to None at the end)
        initial_point = _validate_initial_point(self.initial_point, self.ansatz)

        bounds = _validate_bounds(self.ansatz)
        # We need to handle the array entries being zero or Optional i.e. having value None
        if aux_operators:
            zero_op = PauliSumOp.from_list([("I" * self.ansatz.num_qubits, 0)])

            # Convert the None and zero values when aux_operators is a list.
            # Drop None and convert zero values when aux_operators is a dict.
            if isinstance(aux_operators, list):
                key_op_iterator = enumerate(aux_operators)
                converted: ListOrDict[OperatorBase] = [zero_op] * len(aux_operators)
            else:
                key_op_iterator = aux_operators.items()
                converted = {}
            for key, op in key_op_iterator:
                if op is not None:
                    converted[key] = zero_op if op == 0 else op

            aux_operators = converted

        else:
            aux_operators = None

        if self.betas is None:
            upper_bound = (
                abs(operator.coeff)
                if isinstance(operator, PauliOp)
                else abs(operator.coeff) * sum(abs(operation.coeff) for operation in operator)
            )
            self.betas = [upper_bound * 10] * (self.k)
            logger.info("beta autoevaluated to %s", self.betas[0])

        result = VQDResult()
        result.optimal_point = []
        result.optimal_parameters = []
        result.optimal_value = []
        result.cost_function_evals = []
        result.optimizer_time = []
        result.eigenvalues = []
        result.eigenstates = []

        if aux_operators is not None:
            aux_values = []

        for step in range(1, self.k + 1):

            self._eval_count = 0
            energy_evaluation, expectation = self.get_energy_evaluation(
                step, operator, return_expectation=True, prev_states=result.optimal_parameters
            )

            # Convert the gradient operator into a callable function that is compatible with the
            # optimization routine. Only used for the ground state currently as Gradient() doesnt
            # support SumOps yet
            if isinstance(self._gradient, GradientBase):
                gradient = self._gradient.gradient_wrapper(
                    StateFn(operator, is_measurement=True) @ StateFn(self.ansatz),
                    bind_params=list(self.ansatz.parameters),
                    backend=self._quantum_instance,
                )
            else:
                gradient = self._gradient

            start_time = time()

            if callable(self.optimizer):
                opt_result = self.optimizer(  # pylint: disable=not-callable
                    fun=energy_evaluation, x0=initial_point, jac=gradient, bounds=bounds
                )
            else:
                opt_result = self.optimizer.minimize(
                    fun=energy_evaluation, x0=initial_point, jac=gradient, bounds=bounds
                )

            eval_time = time() - start_time

            result.optimal_point.append(opt_result.x)
            result.optimal_parameters.append(dict(zip(self.ansatz.parameters, opt_result.x)))
            result.optimal_value.append(opt_result.fun)
            result.cost_function_evals.append(opt_result.nfev)
            result.optimizer_time.append(eval_time)

            eigenvalue = (
                StateFn(operator, is_measurement=True)
                .compose(CircuitStateFn(self.ansatz.bind_parameters(result.optimal_parameters[-1])))
                .reduce()
                .eval()
            )

            result.eigenvalues.append(eigenvalue)
            result.eigenstates.append(self._get_eigenstate(result.optimal_parameters[-1]))

            if aux_operators is not None:
                bound_ansatz = self.ansatz.bind_parameters(result.optimal_point[-1])
                aux_value = eval_observables(
                    self.quantum_instance, bound_ansatz, aux_operators, expectation=expectation
                )
                aux_values.append(aux_value)

            if step == 1:

                logger.info(
                    "Ground state optimization complete in %s seconds.\n"
                    "Found opt_params %s in %s evals",
                    eval_time,
                    result.optimal_point,
                    self._eval_count,
                )
            else:
                logger.info(
                    (
                        "%s excited state optimization complete in %s s.\n"
                        "Found opt_params %s in %s evals"
                    ),
                    str(step - 1),
                    eval_time,
                    result.optimal_point,
                    self._eval_count,
                )

        # To match the signature of NumpyEigenSolver Result
        result.eigenstates = ListOp([StateFn(vec) for vec in result.eigenstates])
        result.eigenvalues = np.array(result.eigenvalues)
        result.optimal_point = np.array(result.optimal_point)
        result.optimal_value = np.array(result.optimal_value)
        result.cost_function_evals = np.array(result.cost_function_evals)
        result.optimizer_time = np.array(result.optimizer_time)

        if aux_operators is not None:
            result.aux_operator_eigenvalues = aux_values

        return result

    def get_energy_evaluation(

        self,

        step: int,

        operator: OperatorBase,

        return_expectation: bool = False,

        prev_states: list[np.ndarray] | None = None,

    ) -> Callable[[np.ndarray], float | list[float]] | tuple[
        Callable[[np.ndarray], float | list[float]], ExpectationBase
    ]:
        """Returns a function handle to evaluates the energy at given parameters for the ansatz.



        This return value is the objective function to be passed to the optimizer for evaluation.



        Args:

            step: level of energy being calculated. 0 for ground, 1 for first excited state...

            operator: The operator whose energy to evaluate.

            return_expectation: If True, return the ``ExpectationBase`` expectation converter used

                in the construction of the expectation value. Useful e.g. to evaluate other

                operators with the same expectation value converter.

            prev_states: List of parameters from previous rounds of optimization.





        Returns:

            A callable that computes and returns the energy of the hamiltonian

            of each parameter, and, optionally, the expectation



        Raises:

            RuntimeError: If the circuit is not parameterized (i.e. has 0 free parameters).

            AlgorithmError: If operator was not provided.



        """

        num_parameters = self.ansatz.num_parameters
        if num_parameters == 0:
            raise RuntimeError("The ansatz must be parameterized, but has 0 free parameters.")

        if operator is None:
            raise AlgorithmError("The operator was never provided.")

        if step > 1 and (len(prev_states) + 1) != step:
            raise RuntimeError(
                f"Passed previous states of the wrong size."
                f"Passed array has length {str(len(prev_states))}"
            )

        self._check_operator_ansatz(operator)
        overlap_op = []

        ansatz_params = self.ansatz.parameters
        expect_op, expectation = self.construct_expectation(
            ansatz_params, operator, return_expectation=True
        )

        for state in range(step - 1):

            prev_circ = self.ansatz.bind_parameters(prev_states[state])
            overlap_op.append(~CircuitStateFn(prev_circ) @ CircuitStateFn(self.ansatz))

        def energy_evaluation(parameters):
            parameter_sets = np.reshape(parameters, (-1, num_parameters))
            # Dict associating each parameter with the lists of parameterization values for it
            param_bindings = dict(zip(ansatz_params, parameter_sets.transpose().tolist()))

            sampled_expect_op = self._circuit_sampler.convert(expect_op, params=param_bindings)
            means = np.real(sampled_expect_op.eval())

            for state in range(step - 1):
                sampled_final_op = self._circuit_sampler.convert(
                    overlap_op[state], params=param_bindings
                )
                cost = sampled_final_op.eval()
                means += np.real(self.betas[state] * np.conj(cost) * cost)

            if self._callback is not None:
                variance = np.real(expectation.compute_variance(sampled_expect_op))
                estimator_error = np.sqrt(variance / self.quantum_instance.run_config.shots)
                for i, param_set in enumerate(parameter_sets):
                    self._eval_count += 1
                    self._callback(self._eval_count, param_set, means[i], estimator_error[i], step)
            else:
                self._eval_count += len(means)

            return means if len(means) > 1 else means[0]

        if return_expectation:
            return energy_evaluation, expectation

        return energy_evaluation

    def _get_eigenstate(self, optimal_parameters) -> list[float] | dict[str, int]:
        """Get the simulation outcome of the ansatz, provided with parameters."""
        optimal_circuit = self.ansatz.bind_parameters(optimal_parameters)
        state_fn = self._circuit_sampler.convert(StateFn(optimal_circuit)).eval()
        if self.quantum_instance.is_statevector:
            state = state_fn.primitive.data  # VectorStateFn -> Statevector -> np.array
        else:
            state = state_fn.to_dict_fn().primitive  # SparseVectorStateFn -> DictStateFn -> dict

        return state


class VQDResult(VariationalResult, EigensolverResult):
    """Deprecated: VQD Result.



    The VQDResult class has been superseded by the

    :class:`qiskit.algorithms.eigensolvers.VQDResult` class.

    This class will be deprecated in a future release and subsequently

    removed after that.



    """

    @deprecate_func(

        additional_msg=(

            "Instead, use the class ``qiskit.algorithms.eigensolvers.VQDResult``."

            "See https://qisk.it/algo_migration for a migration guide."

        ),

        since="0.24.0",

    )
    def __init__(self) -> None:
        super().__init__()
        self._cost_function_evals: int | None = None

    @property
    def cost_function_evals(self) -> int | None:
        """Returns number of cost optimizer evaluations"""
        return self._cost_function_evals

    @cost_function_evals.setter
    def cost_function_evals(self, value: int) -> None:
        """Sets number of cost function evaluations"""
        self._cost_function_evals = value

    @property
    def eigenstates(self) -> np.ndarray | None:
        """return eigen state"""
        return self._eigenstates

    @eigenstates.setter
    def eigenstates(self, value: np.ndarray) -> None:
        """set eigen state"""
        self._eigenstates = value