Quantum simulator
Summary
After building the quantum circuit, we need to specify a back end to run the quantum circuit. In MindSpore Quantum, we can use the quantum Simulator ‘Simulator’ to simulate the quantum circuit. In this tutorial we declare a twobit ‘ProjectQ’ simulator to introduce the key features of the simulator.
Environment preparation
Import the modules that this tutorial depends on.
[1]:
import numpy as np # Import the numpy library and abbreviate to np
from mindquantum.simulator import Simulator # Import the Simulator class from mindquantum. simulator
from mindquantum.core.gates import X, H, RY # Import quantum gate H, X, RY
Description:
Numpy is a powerful Python library used to perform calculations on multidimensional arrays. It supports a large number of dimensional arrays and matrix operations. It also provides a large number of mathematical function libraries for array operations.
MindSpore Quantum is a quantumclassical hybrid computing framework that supports training and reasoning of various quantum neural networks;
The quantum gate to be executed in the quantum circuit set up needs to be imported from mindquantum. core module;
[2]:
sim = Simulator('mqvector', 2) #Declare a twobit mqvector simulator
sim #Display simulator status
[2]:
mqvector simulator with 2 qubits (little endian).
Current quantum state:
1¦00⟩
In MindSpore Quantum, we can import the simulator in the mindQuantum. simulator
module. The Simulator class takes three arguments:
backend
: name of the simulator used. Currently, MindSpore Quantum supportsmqvector
,mqvector_gpu
,mqmatrix
and NoiseBackend as a backend for emulation.n_qubits
: The number of bits used by the simulator, which is 2 here.seed
: the random seed used by the simulator when running the randomness correlation algorithm. By default, the seed is a random number, which is not required.dtype
: the data type that the simulator used. Since the quantum state is a complex number vector, we support mindquantum.complex64 and mindquantum.complex128 as data type. The default data type is mindquantum.complex128
From the output of the simulator, we can see that this is a 2bit simulator of mqvector
and little Endian. Little Endian means that throughout the simulator, we put bits with small bits to the right of the quantum state vector. Next, the output also states what quantum state the simulator is currently in, and after the simulator is initialized, the current quantum state defaults to zero. Note that the quantum simulator always maintains an internal quantum state that changes when we apply a
quantum gate or a quantum circuit to the simulator, but does not change when we simply want to obtain some information about the quantum state. There are two types of operations for the quantum simulator:
Operations that change the quantum state, usually beginning with ‘apply’, mainly include the following
apply_gate
: applies a quantum gate to the simulatorapply_circuit
: applies a quantum circuit to the simulatorapply_hamiltonian
: Apply a Hamiltonian to the simulator. Note that the quantum state of the simulator is no longer a true quantum stateset_qs
: Sets the current quantum state of the simulator directlyreset
: reset the state of the simulator to  0 ⟩ stateOperations that do not change the quantum state, usually beginning with
get
, mainly include the followingget_qs
: gets the current quantum state of the simulatorget_expectation
: calculates the expected value of the simulator’s current quantum state regarding an observed quantityget_expectation_with_grad
: similar to the previous interface, except that this method also calculates the expected value gradient with respect to parameterized quantum linessampling
: in the current quantum state, sampling of the given quantum circuit
Let’s learn the basic operation of the simulator briefly.
Interacts with quantum gates and quantum circuits
[3]:
sim = Simulator('mqvector', 2) #Declare a 2bit mqvector emulator
sim.apply_gate(H.on(0)) #Apply a Hadamard gate to qubit 0
sim #Output quantum simulator information
[3]:
mqvector simulator with 2 qubits (little endian).
Current quantum state:
√2/2¦00⟩
√2/2¦01⟩
Above, we acted a Hadamard gate on the initial state of the quantum simulator and output the quantum state after evolution. Next we generate a parameterized quantum circuit and apply it to the current quantum state.
[5]:
from mindquantum.core.circuit import Circuit # Import Circuit module to build quantum Circuit
circ = Circuit() # Declare an empty quantum circuit
circ += H.on(1) # Add a Hadamard gate to it and apply it to qubit 1
circ += RY('a').on(0) # Add a parameterized RY gate to it and apply it to qubit 0
circ.svg() # Draws a quantum circuit picture in SVG format
[5]:
[6]:
#Apply a quantum circuit. When the circuit is a parameterized quantum circuit, we also need to provide parameter values.
sim.apply_circuit(circ, pr={'a': 1.234})
sim
[6]:
mqvector simulator with 2 qubits (little endian).
Current quantum state:
0.11851349145283657¦00⟩
0.6971044056263442¦01⟩
0.11851349145283657¦10⟩
0.6971044056263442¦11⟩
In the above code, we create a parameterized quantum circuit ‘circ’, which we then apply to the quantum simulator and set parameter ‘A’ to ‘1.234’ by passing in a dictionary. Finally, the quantum state evolved from the quantum simulator is output.
Set and get the simulator state
We use ‘get_qs(ket=False)’ to check the state of the current simulator, The ket argument is a bool that determines whether the state of the current simulator is returned as a ket, numpy.ndarray when ket=False, or ket when ket=True. The default ket = False.
[7]:
print(sim.get_qs()) #View the simulator status and return the result in numpy.ndarray form
[0.11851349+0.j 0.69710441+0.j 0.11851349+0.j 0.69710441+0.j]
[8]:
print(sim.get_qs(True)) #View the simulator status and return the result in ket form
0.11851349145283657¦00⟩
0.6971044056263442¦01⟩
0.11851349145283657¦10⟩
0.6971044056263442¦11⟩
During actual code writing, we often need to specify an initial state for the simulator to start evolving, which can be done using ‘set_qs()’.
For example, we want the emulator state to be
Step 1: We calculate the vector form of the target state:
Step 2: We assign this vector to the simulator using ‘set_qs()’ as its state:
[9]:
sim.set_qs(np.array([3**0.5, 0, 0, 6**0.5])) #Set simulator state without normalization
print(sim.get_qs(True)) #View simulator Status
0.5773502691896258¦00⟩
0.816496580927726¦11⟩
Viewing the simulator status through get_qs()
can find that the current simulator status is we want to set the \(\frac{\sqrt{3}}{3}00⟩+\frac{\sqrt{6}}{3}11⟩\).
In the actual programming process, we often need to simulate the circuit for several times, which will lead to a very large memory consumption by opening the simulator more than once. We can reuse the simulator by resetting the existing simulator, thus reducing the memory consumption.
We use ‘reset()’ to reset the simulator:
[10]:
sim.reset() #Reset simulator
print(sim.get_qs()) #View simulator Status
[1.+0.j 0.+0.j 0.+0.j 0.+0.j]
It can be found that the current simulator is reset to the initial \(100⟩\) state, which is equivalent to a brand new simulator.
Therefore, we can set up a corresponding quantum simulator and run a custom quantum circuit according to the quantum initial state we need. Get your hands on your first quantum circuit!
Quantum circuit sampling
Circuit sampling refers to performing multiple simulation measurements on quantum circuits, and statistically measuring the frequency of occurrence of various results. Sampling does not change the state in the quantum circuit.
sampling(circuit, pr=None, shots=1, seed=None)
is the sampling method provided in MindSpore Quantum
, which accepts four parameters:
circuit (Circuit)
：Quantum circuit for which sampling is desired, note that at least one measurement operation (i.e. sampling point) must be included in the circuit.pr (Union[None, dict, ParameterResolver])
：parameter resolver，Whencircuit
is a parameterized circuit, the value of the parameter needs to be given.shots (int)
：The number of times to sample, default 1.seed
：The random seed for sampling, which is a random number by default and can be omitted.
[11]:
# Nonparameterized circuit sampling:
from mindquantum.core.gates import Measure # Introduce measurement gate
circ = Circuit() # Initialize the quantum circuit
circ += H.on(0) # The H gate acts on qubit 0
circ += X.on(1, 0) # The X gate acts on qubit 1 and is controlled by qubit 0
circ += Measure('q0').on(0) # Apply a measurement on qubit 0 and name this measurement 'q0'
circ += Measure('q1').on(1) # Apply a measurement to qubit 1 and name this measurement 'q1'
circ.svg() # Draw a quantum circuit picture in SVG format
[11]:
[13]:
sim.reset()
result = sim.sampling(circ, shots=1000) # Sample the circuit defined above 1000 times
result
[13]:
shots: 1000 Keys: q1 q0│0.00 0.13 0.259 0.389 0.518 0.647 ───────────┼───────────┴───────────┴───────────┴───────────┴───────────┴ 00│▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒ │ 11│▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓ │ {'00': 482, '11': 518}
MindSpore Quantum also provides the function of drawing SVG diagrams from sampling results:
[14]:
result.svg() # Print out measurement results in SVG format
[14]:
We can see that in sampling 1000 times, ‘00’ appears 499 times and ‘11’ appears 501 times. The circuit we built actually produces a Bell state \(\frac{\sqrt{2}}{2}00⟩+\frac{\sqrt{2}}{2}11⟩\). Intuitively, we can see that the probability of measuring the state to get ‘00’ is \(\frac{1}{2}\), the probability of getting ‘11’ is \(\frac{1}{2}\), the sampling result consistent with probability, slight errors are caused by simulator noise.
[15]:
# Parameterized circuit sampling:
para_circ = Circuit() # Initialize the quantum circuit
para_circ += H.on(0) # The H gate acts on qubit 0
para_circ += X.on(1, 0) # The X gate acts on qubit 1 and is controlled by qubit 0
para_circ += RY('theta').on(1) # The RY(theta) gate acts on the qubit 1
para_circ += Measure('0').on(0) # Apply a measurement on qubit 0 and name this measurement 'q0'
para_circ += Measure('q1').on(1) # Apply a measurement to qubit 1 and name this measurement 'q1'
para_circ.svg() # Draw a quantum circuit picture in SVG format
[15]:
[16]:
sim.reset()
# Assign the circuit parameter 'theta' defined above to 0 and sample 1000 times
result = sim.sampling(para_circ, {'theta': 0}, shots=1000)
result.svg()
[16]:
We can see that ‘00’ appears 495 times and ‘11’ appears 505 times in the sampling result. In fact, the RY gate parameter is assigned to 0, which is the I gate and equivalent to not doing any operation on the circuit. Therefore, the sampling circuit is essentially the same as the above Nonparameterized circuit. It can be observed that the results of two times sampling are almost the same, as expected.
Supported simulator
The simulator that supported by MindSpore Quantum is shown as below:
Name 
Feature 
GPU supported 
single precision 
double precision 


Full amplitude simulator 
❌ 
✅ 
✅ 

GPU version full amplitude simulator 
✅ 
✅ 
✅ 

Density matrix simulator 
❌ 
✅ 
✅ 
Simulate noise system：Noise Simulator 
✅ 
✅ 
✅ 
How to choose simulator
We know that the dimension of quantum states increases exponentially as the number of bits increases, so the physical memory required to simulate largebit quantum systems will increase dramatically. Below, we give the memory space required to store a fullamplitude quantum state at different bits:
Qubit number 
mindquantum.complex128 
mindquantum.complex64 

6 
1kB 
0.5kB 
16 
1MB 
0.5MB 
26 
1GB 
0.5GB 
30 
16GB 
8GB 
36 
1TB 
0.5TB 
40 
16TB 
8TB 
46 
1PB 
0.5PB 
It can be seen that when simulating largebit systems, we can consider using singleprecision types to reduce the memory usage. In MindSpore Quantum, we can easily modify the data type of the simulator by dtype
:
[17]:
import mindquantum as mq
from mindquantum.simulator import Simulator
sim = Simulator('mqvector', 2, dtype=mq.complex64)
print(sim)
mqvector simulator with 2 qubits (little endian), dtype: mindquantum.complex64.
Current quantum state:
1¦00⟩
Below we give some rules of thumb to help you choose different simulators reasonably:
Qubit number less than 8 bits:
mqvector
. In small bits, the CPU will run faster than the GPU.Qubit number larger than 8 bits:
mqvector_gpu
. At large bits, the GPU will take advantage of its parallel computing.Simulating mixed state:
mqmatrix
.mqmatrix
is a density matrix simulator and therefore supports the simulation of mixed state.Simulating noise system：NoiseBackend. You can easily add quantum channel into circuit by this simulator, so that you can simulate a noisy quantum system.
Quantum chemistry simulation:
mindquantum.complex128
. This task always need to simulate the ground state to chemical accuracy, so we suggest double precision.Quantum machine learning:
mindquantum.complex64
. Machine learning task is always not sensitive to data precision, so we suggest single precision.
If you want to learn more about how to measure quantum circuits and understand the theoretical explanation of the distribution of sampling results, please click: Quantum Measurement Tutorial.
[18]:
from mindquantum.utils.show_info import InfoTable
InfoTable('mindquantum', 'scipy', 'numpy')
[18]:
Software  Version 

mindquantum  0.9.0 
scipy  1.10.1 
numpy  1.21.6 
System  Info 
Python  3.9.13 
OS  Linux x86_64 
Memory  16.62 GB 
CPU Max Thread  16 
Date  Wed Aug 23 16:19:50 2023 