# Mid-circuit measurement: slow and memory explosion **URL:** \ **Category:** PennyLane Help\ **Created:** [November 1, 2024, 3:03pm UTC](https://discuss.pennylane.ai/t/mid-circuit-measurement-slow-and-memory-explosion/7452 "2024-11-01T15:03:07Z")\ **Posts on this page:** 4\ **Page:** 1
**Author:** ![adrien\_dev](https://avatars.discourse-cdn.com/v4/letter/a/9dc877/32.png) [@adrien\_dev](https://discuss.pennylane.ai/u/adrien_dev)\ **Post date:** [November 1, 2024, 3:03pm UTC](https://discuss.pennylane.ai/t/mid-circuit-measurement-slow-and-memory-explosion/7452/1 "2024-11-01T15:03:07Z")
Hi, I’m looking to implement a complex absorbing potential, as described in this article: [Efficient solution of the non-unitary time-dependent Schrodinger equation on a quantum computer with complex absorbing potential – Quantum](https://quantum-journal.org/papers/q-2024-04-08-1311/). To achieve this, I need to apply non-unitary operations, which requires using a mid-circuit measurement on an ancilla qubit. However, I’m encountering two main issues: - The mid-circuit measurements significantly slow down the simulation. When I comment out the mid-circuit measurement line, the calculation runs 100 times faster. - I quickly receive a memory overflow error when I increase the number of propagation step. Again, when I comment out the mid-circuit measurement line, the error message does not appear anymore. I’m wondering if there might be something about mid-circuit measurement that I am overlooking. Thanks in advance! Adrien Here it is my code: ```auto # Import package import pennylane as qml import numpy as np import scipy # Building position grid n_pos=7 n_qubit=n_pos+1 x_max=100 x=np.linspace(-x_max/2,x_max/2,2**n_pos) # Creation of the k-grid k=2*np.pi*scipy.fftpack.fftfreq(2**n_pos,delta_x) k=scipy.fftpack.fftshift(k) # Preparation of the initial Gaussian Wave Packet def state_vector_gaussian(x,x_0,delta,p_0): # x_0 : initial position of the wavepacket # delta: width of the wavepacket #p_0 : initial momentum of the wavepacket phi_0=(1/(2*np.pi*delta**2))**(1/4)*np.exp(-(x-x_0)**2/(4*delta**2))*np.exp(p_0*(x-x_0)*1j) return phi_0 Ini_gauss=state_vector_gaussian(x,0,2,0) # Normalizing Initial Wavepacket Ini_gauss=Ini_gauss/np.linalg.norm(Ini_gauss) #Kinetic Energy Operator in the momentum representation m=1 T=(k)**2/(2*m)*np.eye(2**n_pos) # Complex absorbing potential def CAP(x,xc,eta,b): W = eta*abs(x+xc)**b*np.heaviside(-(x+xc),0)+eta*abs(x-xc)**b*np.heaviside((x-xc),0) return W xc=45 eta=1 b=2 W=CAP(x,xc,eta,b) W=W*np.eye(2**n_pos) # Wavepacket propagation dev = qml.device("default.qubit", wires=n_qubit) @qml.qnode(dev) def Propagation_CAP(ini_state,T,W,N_step,delta_t): #Building matrice of propagator Prop_T=scipy.linalg.expm(-T*delta_t*1j) #Building dilation matrix Diag=scipy.linalg.expm(W*(-delta_t)) Off_diag=scipy.linalg.sqrtm(np.eye(2**n_pos)-scipy.linalg.expm(W*(-2*delta_t))) U_dial=np.kron(np.array([[1,0],[0,-1]]),Diag)+np.kron(np.array([[0,1],[1,0]]),Off_diag) # Preparation of initial gaussian qml.MottonenStatePreparation(ini_state,wires=range(1,n_qubit)) #Propagation loop for i in range(N_step): qml.PauliX(1) qml.QFT(wires=range(1,n_qubit)) qml.PauliX(1) qml.QubitUnitary(Prop_T,wires=range(1,n_qubit)) qml.PauliX(1) qml.adjoint(qml.QFT)(wires=range(1,n_qubit)) qml.PauliX(1) qml.QubitUnitary(U_dial,wires=range(n_qubit)) qml.measure(0, postselect=0) return qml.probs(wires=range(1,n_qubit)) delta_t=0.1 State=Propagation_CAP(Ini_gauss,T,W,15,delta_t) ``` The full error message is ```auto --------------------------------------------------------------------------- MemoryError Traceback (most recent call last) Cell In[90], line 1 ----> 1 State=Propagation_CAP(Ini_gauss,T,W,50,delta_t) File ~\anaconda3\envs\Pen\Lib\site-packages\pennylane\workflow\qnode.py:1020, in QNode. __call__ (self, *args, **kwargs) 1018 if qml.capture.enabled(): 1019 return qml.capture.qnode_call(self, *args, **kwargs) -> 1020 return self._impl_call(*args, **kwargs) File ~\anaconda3\envs\Pen\Lib\site-packages\pennylane\workflow\qnode.py:1008, in QNode._impl_call(self, *args, **kwargs) 1005 self._update_gradient_fn(shots=override_shots, tape=self._tape) 1007 try: -> 1008 res = self._execution_component(args, kwargs, override_shots=override_shots) 1009 finally: 1010 if old_interface == "auto": File ~\anaconda3\envs\Pen\Lib\site-packages\pennylane\workflow\qnode.py:957, in QNode._execution_component(self, args, kwargs, override_shots) 951 warnings.filterwarnings( 952 action="ignore", 953 message=r".*argument is deprecated and will be removed in version 0.39.*", 954 category=qml.PennyLaneDeprecationWarning, 955 ) 956 # pylint: disable=unexpected-keyword-arg --> 957 res = qml.execute( 958 (self._tape,), 959 device=self.device, 960 gradient_fn=self.gradient_fn, 961 interface=self.interface, 962 transform_program=full_transform_program, 963 inner_transform=inner_transform_program, 964 config=config, 965 gradient_kwargs=self.gradient_kwargs, 966 override_shots=override_shots, 967 **execute_kwargs, 968 ) 969 res = res[0] 971 # convert result to the interface in case the qfunc has no parameters File ~\anaconda3\envs\Pen\Lib\site-packages\pennylane\workflow\execution.py:660, in execute(tapes, device, gradient_fn, interface, transform_program, inner_transform, config, grad_on_execution, gradient_kwargs, cache, cachesize, max_diff, override_shots, expand_fn, max_expansion, device_batch_transform, device_vjp, mcm_config) 658 # Exiting early if we do not need to deal with an interface boundary 659 if no_interface_boundary_required: --> 660 results = inner_execute(tapes) 661 return post_processing(results) 663 if ( 664 device_vjp 665 and getattr(device, "short_name", "") in ("lightning.gpu", "lightning.kokkos") 666 and interface in jpc_interfaces 667 ): # pragma: no cover File ~\anaconda3\envs\Pen\Lib\site-packages\pennylane\workflow\execution.py:212, in _make_inner_execute..inner_execute(tapes, **_) 209 transformed_tapes, transform_post_processing = transform_program(tapes) 211 if transformed_tapes: --> 212 results = device.execute(transformed_tapes, execution_config=execution_config) 213 else: 214 results = () File ~\anaconda3\envs\Pen\Lib\site-packages\pennylane\devices\modifiers\simulator_tracking.py:30, in _track_execute..execute(self, circuits, execution_config) 28 @wraps(untracked_execute) 29 def execute(self, circuits, execution_config=DefaultExecutionConfig): ---> 30 results = untracked_execute(self, circuits, execution_config) 31 if isinstance(circuits, QuantumScript): 32 batch = (circuits,) File ~\anaconda3\envs\Pen\Lib\site-packages\pennylane\devices\modifiers\single_tape_support.py:32, in _make_execute..execute(self, circuits, execution_config) 30 is_single_circuit = True 31 circuits = (circuits,) ---> 32 results = batch_execute(self, circuits, execution_config) 33 return results[0] if is_single_circuit else results File ~\anaconda3\envs\Pen\Lib\site-packages\pennylane\logging\decorators.py:61, in log_string_debug_func..wrapper_entry(*args, **kwargs) 54 s_caller = "::L".join( 55 [str(i) for i in inspect.getouterframes(inspect.currentframe(), 2)[1][1:3]] 56 ) 57 lgr.debug( 58 f"Calling {f_string} from {s_caller}", 59 **_debug_log_kwargs, 60 ) ---> 61 return func(*args, **kwargs) File ~\anaconda3\envs\Pen\Lib\site-packages\pennylane\devices\default_qubit.py:630, in DefaultQubit.execute(self, circuits, execution_config) 627 prng_keys = [self.get_prng_keys()[0] for _ in range(len(circuits))] 629 if max_workers is None: --> 630 return tuple( 631 _simulate_wrapper( 632 c, 633 { 634 "rng": self._rng, 635 "debugger": self._debugger, 636 "interface": interface, 637 "state_cache": self._state_cache, 638 "prng_key": _key, 639 "mcm_method": execution_config.mcm_config.mcm_method, 640 "postselect_mode": execution_config.mcm_config.postselect_mode, 641 }, 642 ) 643 for c, _key in zip(circuits, prng_keys) 644 ) 646 vanilla_circuits = convert_to_numpy_parameters(circuits)[0] 647 seeds = self._rng.integers(2**31 - 1, size=len(vanilla_circuits)) File ~\anaconda3\envs\Pen\Lib\site-packages\pennylane\devices\default_qubit.py:631, in (.0) 627 prng_keys = [self.get_prng_keys()[0] for _ in range(len(circuits))] 629 if max_workers is None: 630 return tuple( --> 631 _simulate_wrapper( 632 c, 633 { 634 "rng": self._rng, 635 "debugger": self._debugger, 636 "interface": interface, 637 "state_cache": self._state_cache, 638 "prng_key": _key, 639 "mcm_method": execution_config.mcm_config.mcm_method, 640 "postselect_mode": execution_config.mcm_config.postselect_mode, 641 }, 642 ) 643 for c, _key in zip(circuits, prng_keys) 644 ) 646 vanilla_circuits = convert_to_numpy_parameters(circuits)[0] 647 seeds = self._rng.integers(2**31 - 1, size=len(vanilla_circuits)) File ~\anaconda3\envs\Pen\Lib\site-packages\pennylane\devices\default_qubit.py:896, in _simulate_wrapper(circuit, kwargs) 895 def _simulate_wrapper(circuit, kwargs): --> 896 return simulate(circuit, **kwargs) File ~\anaconda3\envs\Pen\Lib\site-packages\pennylane\logging\decorators.py:61, in log_string_debug_func..wrapper_entry(*args, **kwargs) 54 s_caller = "::L".join( 55 [str(i) for i in inspect.getouterframes(inspect.currentframe(), 2)[1][1:3]] 56 ) 57 lgr.debug( 58 f"Calling {f_string} from {s_caller}", 59 **_debug_log_kwargs, 60 ) ---> 61 return func(*args, **kwargs) File ~\anaconda3\envs\Pen\Lib\site-packages\pennylane\devices\qubit\simulate.py:379, in simulate(circuit, debugger, state_cache, **execution_kwargs) 376 return tuple(results) 378 ops_key, meas_key = jax_random_split(prng_key) --> 379 state, is_state_batched = get_final_state( 380 circuit, debugger=debugger, prng_key=ops_key, **execution_kwargs 381 ) 382 if state_cache is not None: 383 state_cache[circuit.hash] = state File ~\anaconda3\envs\Pen\Lib\site-packages\pennylane\logging\decorators.py:61, in log_string_debug_func..wrapper_entry(*args, **kwargs) 54 s_caller = "::L".join( 55 [str(i) for i in inspect.getouterframes(inspect.currentframe(), 2)[1][1:3]] 56 ) 57 lgr.debug( 58 f"Calling {f_string} from {s_caller}", 59 **_debug_log_kwargs, 60 ) ---> 61 return func(*args, **kwargs) File ~\anaconda3\envs\Pen\Lib\site-packages\pennylane\devices\qubit\simulate.py:199, in get_final_state(circuit, debugger, **execution_kwargs) 196 if len(circuit) > 0 and isinstance(circuit[0], qml.operation.StatePrepBase): 197 prep = circuit[0] --> 199 state = create_initial_state(sorted(circuit.op_wires), prep, like=INTERFACE_TO_LIKE[interface]) 201 # initial state is batched only if the state preparation (if it exists) is batched 202 is_state_batched = bool(prep and prep.batch_size is not None) File ~\anaconda3\envs\Pen\Lib\site-packages\pennylane\devices\qubit\initialize_state.py:43, in create_initial_state(wires, prep_operation, like) 41 if not prep_operation: 42 num_wires = len(wires) ---> 43 state = np.zeros((2,) * num_wires, dtype=complex) 44 state[(0,) * num_wires] = 1 45 return qml.math.asarray(state, like=like) MemoryError: Unable to allocate 4.00 EiB for an array with shape (2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2) and data type complex128 ``` Here it is the version that I use: ```auto Name: PennyLane Version: 0.38.0 Summary: PennyLane is a cross-platform Python library for quantum computing, quantum machine learning, and quantum chemistry. Train a quantum computer the same way as a neural network. Home-page: https://github.com/PennyLaneAI/pennylane Author: Author-email: License: Apache License 2.0 Location: C:\Users\adrid\anaconda3\envs\Pen\Lib\site-packages Requires: appdirs, autograd, autoray, cachetools, networkx, numpy, packaging, pennylane-lightning, requests, rustworkx, scipy, toml, typing-extensions Required-by: PennyLane_Lightning Platform info: Windows-10-10.0.22631-SP0 Python version: 3.11.10 Numpy version: 2.1.2 Scipy version: 1.14.1 Installed devices: - default.clifford (PennyLane-0.38.0) - default.gaussian (PennyLane-0.38.0) - default.mixed (PennyLane-0.38.0) - default.qubit (PennyLane-0.38.0) - default.qubit.autograd (PennyLane-0.38.0) - default.qubit.jax (PennyLane-0.38.0) - default.qubit.legacy (PennyLane-0.38.0) - default.qubit.tf (PennyLane-0.38.0) - default.qubit.torch (PennyLane-0.38.0) - default.qutrit (PennyLane-0.38.0) - default.qutrit.mixed (PennyLane-0.38.0) - default.tensor (PennyLane-0.38.0) - null.qubit (PennyLane-0.38.0) - lightning.qubit (PennyLane_Lightning-0.38.0) ``` ---
**Author:** ![CatalinaAlbornoz](https://yyz2.discourse-cdn.com/flex012/user_avatar/discuss.pennylane.ai/catalinaalbornoz/32/1196_2.png) [@CatalinaAlbornoz](https://discuss.pennylane.ai/u/CatalinaAlbornoz)\ **Post date:** [November 4, 2024, 5:40pm UTC](https://discuss.pennylane.ai/t/mid-circuit-measurement-slow-and-memory-explosion/7452/2 "2024-11-04T17:40:24Z")
Hi @adrien_dev , welcome to the Forum! It’s normal for it to be slower using mid-circuit measurements. PennyLane currently offers three methods to simulate mid-circuit measurements on classical computers: the deferred measurements principle, dynamic one-shot sampling, and a tree-traversal approach. These methods differ in their memory requirements and computational cost, as well as their compatibility with other features such as shots and differentiation methods. Check the table [here](https://docs.pennylane.ai/en/stable/introduction/dynamic_quantum_circuits.html#simulation-techniques) to see the details. In your case, since you’re not using shots, the deferred measurements method is being used by default. This method adds an auxiliary qubit to the circuit for each mid-circuit measurement, leading to overheads of both memory and simulation time that scale exponentially with the number of measurements. What I see in your code is that you’re adding one mid-circuit measurement per step. In the code you shared that would mean 15 mid-circuit measurements. This means that you’re inadvertently adding 15 extra qubits into your code. I would recommend in this case that you change the mcm\_method. If you’re ok with adding shots for example you can add the one-shot method as shown below. ```auto dev = qml.device("default.qubit",shots=10) @qml.qnode(dev, mcm_method="one-shot") ``` Let me know if this works for you. ---
**Author:** ![adrien\_dev](https://avatars.discourse-cdn.com/v4/letter/a/9dc877/32.png) [@adrien\_dev](https://discuss.pennylane.ai/u/adrien_dev)\ **Post date:** [November 4, 2024, 8:31pm UTC](https://discuss.pennylane.ai/t/mid-circuit-measurement-slow-and-memory-explosion/7452/3 "2024-11-04T20:31:40Z")
Thank you Catalina! That solves the memory issue. It’s still a bit slow, but as you mentioned, that’s normal, and I can work on optimizing it. ---
**Author:** ![CatalinaAlbornoz](https://yyz2.discourse-cdn.com/flex012/user_avatar/discuss.pennylane.ai/catalinaalbornoz/32/1196_2.png) [@CatalinaAlbornoz](https://discuss.pennylane.ai/u/CatalinaAlbornoz)\ **Post date:** [November 5, 2024, 10:17pm UTC](https://discuss.pennylane.ai/t/mid-circuit-measurement-slow-and-memory-explosion/7452/4 "2024-11-05T22:17:39Z")
That’s great to hear @adrien_dev !