Projected Variational Quantum Dynamics (Qiskit/qiskit#8304)

* pvqd dradt

* update as theta + difference

* black

* refactor test

* update to new time evo framework

* add gradients

* use gradient only if supported

* polishing!

- reno
- remove old pvqd file
- allow attributes to be None
- more tests

* fix algorithms import

* changes from code review

* add more tests for  different ops

* refactor PVQD to multiple files

* remove todo

* comments from review

* rm OrderedDict from unitary

no idea why this unused import existed, that should be caught before this PR?

* changes from code review

* remove function to attach intial states

* include comments from review

- support MatrixOp
- default for timestep
- update reno with refs
- test step and get_loss

* make only quantum instance and optimizer optional, and use num_timesteps

* fix docs

* add comment why Optimizer is optional

* use class attributes to document mutable attrs

* rm duplicate quantum_instance doc

* fix attributes docs

Co-authored-by: mergify[bot] <37929162+mergify[bot]@users.noreply.github.com>

qiskit_algorithms/__init__.py

@@ -108,6 +108,8 @@
     RealEvolver
     ImaginaryEvolver
     TrotterQRTE
+    PVQD
+    PVQDResult
     EvolutionResult
     EvolutionProblem
 
@@ -246,6 +248,7 @@
 from .exceptions import AlgorithmError
 from .aux_ops_evaluator import eval_observables
 from .evolvers.trotterization import TrotterQRTE
+from .evolvers.pvqd import PVQD, PVQDResult
 
 __all__ = [
     "AlgorithmResult",
@@ -292,6 +295,8 @@
     "PhaseEstimationScale",
     "PhaseEstimation",
     "PhaseEstimationResult",
+    "PVQD",
+    "PVQDResult",
     "IterativePhaseEstimation",
     "AlgorithmError",
     "eval_observables",

qiskit_algorithms/evolvers/evolution_problem.py

@@ -31,7 +31,7 @@ def __init__(
         self,
         hamiltonian: OperatorBase,
         time: float,
-        initial_state: Union[StateFn, QuantumCircuit],
+        initial_state: Optional[Union[StateFn, QuantumCircuit]] = None,
         aux_operators: Optional[ListOrDict[OperatorBase]] = None,
         truncation_threshold: float = 1e-12,
         t_param: Optional[Parameter] = None,
@@ -41,7 +41,9 @@ def __init__(
         Args:
             hamiltonian: The Hamiltonian under which to evolve the system.
             time: Total time of evolution.
-            initial_state: Quantum state to be evolved.
+            initial_state: The quantum state to be evolved for methods like Trotterization.
+                For variational time evolutions, where the evolution happens in an ansatz,
+                this argument is not required.
             aux_operators: Optional list of auxiliary operators to be evaluated with the
                 evolved ``initial_state`` and their expectation values returned.
             truncation_threshold: Defines a threshold under which values can be assumed to be 0.

qiskit_algorithms/evolvers/pvqd/__init__.py

@@ -0,0 +1,18 @@
+# This code is part of Qiskit.
+#
+# (C) Copyright IBM 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 projected Variational Quantum Dynamic (p-VQD) module."""
+
+from .pvqd_result import PVQDResult
+from .pvqd import PVQD
+
+__all__ = ["PVQD", "PVQDResult"]