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1 vote

Computing expectation of a SparsePauliOp using StateVector

You can use Statevector.expectation_value() method as follows: ...
Egretta.Thula's user avatar
4 votes

What's so bad about preparing magic states by measuring Clifford gates?

what is so bad about fault tolerantly preparing magic states by measuring Clifford gates? There's nothing bad about it. See "Very low overhead fault-tolerant magic state preparation using ...
Craig Gidney's user avatar
  • 39.7k
0 votes

What exactly is the computational or standard basis?

You are absolutely right in your statement that there is a freedom in the choice of basis, for instance when looking at an expectation value of an observable $O$ on a state $\lvert \psi \rangle$, you ...
Refik Mansuroglu's user avatar
2 votes

What exactly is the computational or standard basis?

Yes, all of quantum mechanics is essentially linear algebra, so you can indeed take any set of basis vectors or basis states that you want. For the purposes of making proofs in quantum information, ...
Quantum Mechanic's user avatar
4 votes
Accepted

What is the connection between an observable and a gate?

Let us start from some unitary $U$ with corresponding spectral decomposition $U=\sum_{\lambda\in\sigma(U)}\lambda P_\lambda$. Here, $\sigma(U)$ denotes the spectrum (i.e. set of eigenvalues) of $U$ ...
Frederik vom Ende's user avatar
6 votes

Can mixed states be on the boundary of the set of states?

The answer to your question depends on what exactly you mean by "boundary": there is the notion of extreme points and the notion of the topological boundary, i.e. points which in their ...
Frederik vom Ende's user avatar
1 vote

Expressibility and Entanglement Capability of the Parameterized Quantum Circuits

Use StateVector class to get the state vector. Then convert the Statevector into array to do matrix operations. ...
Geetha's user avatar
  • 11
0 votes
Accepted

Quantum algorithms to implement polynomial oracles

A definitive answer in the positive is provided by this paper by Guo et. al.: https://arxiv.org/pdf/2107.10764
Rahul Sarkar's user avatar
0 votes

What does it mean for a gate to "commute with a measurement"?

I agree with @Simona99's answer. If you want to formulate it in terms of a quantum channel, consider the quantum channel $\mathcal{E}[\rho] = \sum_i \Pi_i \rho \Pi_i$ that corresponds to a measurement ...
Refik Mansuroglu's user avatar
1 vote

What does it mean for a gate to "commute with a measurement"?

I think that mathematically you have an observable and this observable is described by an operator. The gate commute with measurement if the commutator between the gate and the operator associated to ...
Simona99's user avatar
  • 200
0 votes

Is working with the |+> , |-> basis any harder than the |0>, |1> basis?

$[[5, 1, 3]]$ is tri-symmetric for $X,Y,Z$ basis so I believe it won't showcase any bias for different basis choices. For CSS codes (without transversal $H$), the answer seems quite apparent when your ...
Yunzhe's user avatar
  • 871
1 vote

Is working with the |+> , |-> basis any harder than the |0>, |1> basis?

It entirely depends on the code you are using. For CSS codes, Z-basis and X-basis states are typically equally easy. They both have transversal initialization, the CNOT treats them symmetrically, etc.
Craig Gidney's user avatar
  • 39.7k
8 votes

Relation between expectation value and counts in reference to qiskit

The expectation value is defined for a quantum state $|\psi\rangle$ and a Hamiltonian $H$ as $\langle\psi|H|\psi\rangle$. Since $H$ is Hermitian, this quantity is a real number, even though both $H$ ...
Tristan Nemoz's user avatar
  • 7,022
0 votes
Accepted

States that verify behaviour of Pauli operators in Clifford circuits

I would like to programmatically verify this claim that the circuit commutes with all the elements of P . You want stim.Circuit.has_flow. ...
Craig Gidney's user avatar
  • 39.7k
0 votes

How does qiskit implement a given superposition in the actual quantum computer?

As the first question is answered in comments, I'll only answer the second question here. To initialize your custom state, you can use either initialize() or ...
Shravan Patel's user avatar
0 votes

How to get the Bloch sphere angles given an arbitrary qubit?

I found that the accepted answer does not allow $ |\alpha| $ or $ |\beta| $ to be zero. To allow this, I first find the phase/argument of $ \alpha $ and then rotate $ \beta $ with a factor $ \exp(-i\...
boudewijn21's user avatar
1 vote
Accepted

How to convert from choi to chi matrix in qiskit

The constructor of Chi class accepts an instance of Choi. So, if _choi is your Choi matrix, ...
Egretta.Thula's user avatar

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