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In a real quantum computer, can the save_statevector function be used to obtain the state vector of a circuit? I attempted to run the following code on a real quantum computer but encountered a job rejection. I found that save_statevector performs measurements on all qubits directly when executed on real quantum computer, yet I haven't found in the official documentation a way to specify which particular qubits to measure using this function. How can I configure the save_statevector function to measure only the qubits I need? Alternatively, is it the case that this function cannot be utilized on a real quantum computer? Or is there someting wrong with my code?

Here is my code:

from qiskit import QuantumCircuit
from qiskit import transpile
from qiskit_ibm_runtime import QiskitRuntimeService

token='*********************************'
service = QiskitRuntimeService(channel="ibm_quantum", token=token)
backend = service.least_busy(simulator=False, operational=True)

n_qubits = 3
# backend = GenericBackendV2(n_qubits)

# Create a simple circuit
circuit = QuantumCircuit(n_qubits)
circuit.h(0)
circuit.cx(0, 1)
circuit.cx(0, 2)
transpiled_circuit = transpile(circuit, backend)
transpiled_circuit.draw()
transpiled_circuit.save_statevector()
# Run the transpiled circuit using the simulated fake backend
job = backend.run(transpiled_circuit)
result = job.result()
outputstate = result.get_statevector(transpiled_circuit, decimals=100)
print(outputstate)

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  • $\begingroup$ Real/fake backends don't support save_statevector. $\endgroup$
    – Yunzhe
    Commented Apr 26 at 9:30

2 Answers 2

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Alternatively, is it the case that this function cannot be utilized on a real quantum computer?

Exactly! When you perform a computation on a simulator, it has to keep track of the statevector all along, which allows it to give it to you at the end.

But now, how does a quantum computer work? Well, it starts from the $|0\rangle^{\otimes n}$ state, applies the circuit you've defined and then measures this quantum state. Note that the measure is mandatory: this is the only way to get classical information out of a quantum state.

So, contrarily to a simulator, the quantum computer doesn't store the statevector. In fact, that's the whole point of using quantum computers: simulating statevectors is computationally expensive, but getting information out of it using a quantum circuit is way cheaper for a larger number of qubits.

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  • $\begingroup$ Thanks a lot! It's very helpful! But i still wonder: if i can only rely on measurement to get classical information out of a quantum state, how can i differentiate between the positive and negative signs, or distinguish between real and imaginary components of quantum states, such as differentiating between |0⟩ and -|0⟩, |1⟩, and |i⟩, when their ultimate measurement probabilities appear identical？For example, like HHL algorithm, how can i differentiate between the positive and negative signs of each resulting vector's element? And how can i handle situations involving complex numbers? $\endgroup$
    – MrEightL
    Commented Apr 28 at 19:43
  • $\begingroup$ @MrEightL What you want to do is called state tomography. If you want to get all possible information on a quantum state $|\psi\rangle$ then you have to measure in $2^n+1$ different bases. However you might learn $\mathrm{e}^{\mathrm{i}\theta}|\psi\rangle$ by doing so, and there's nothing you can do about it. $\theta$ is called a global phase and it has physically no sense: there's no way to evaluate it. In particular, you can't tell apart $|0\rangle$ from $-|0\rangle$, since they just differ by a global phase of $\pi$. $\endgroup$
    – Tristan Nemoz ♦
    Commented Apr 29 at 5:59
  • $\begingroup$ @MrEightL Complex numbers can be dealt with with tomography. Once again it will be up to a global phase, but apart from that it works just fine $\endgroup$
    – Tristan Nemoz ♦
    Commented Apr 29 at 6:01
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To add to the above answer by Tristan, if you want to simulate statevectors then you can use AerSimulator(method='statevector', noise_model=noise_model). In this function by using the noise_model option you can specify custom noise models for simulator, to automatically generate a basic device noise model for an IBMQ or a fake backend. You can read more about it here

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