# Questions tagged [stabilizer-state]

Stabilizer states are quantum states that can be efficiently represented by some set of Pauli operators of which the state is a +1 eigenstate. Stabilizer states are used commonly in many areas of quantum computation, such as error correction, teleportation and state verification.

63 questions
Filter by
Sorted by
Tagged with
1 vote
33 views

### Gottesman-Knill theorem -- last measurement step

In the Gottesman-Knill theorem, the stabilizer set is updated after each Clifford gate. These steps are quite simple. At the end, the measurement is simulated. In some on-line explanations, I have ...
1 vote
65 views

47 views

### Why does the qubit give random results in the circuit with rearranged CNOTs for Steane's seven qubit code in Stim?

The following is a part of the syndrome measurement circuit for Steane's seven qubit code in Stim(For ease of viewing, the TICK is omitted.). Since we are considering the detection of X errors, we use ...
1 vote
46 views

### Stabilizer Matrices for Mutually Unbiased Bases - what goes wrong here?

In section VIII D of this paper, the authors describe a circuit synthesis procedure to find the unitary transformation (as a quantum circuit) which diagonalizes a set of mutually commuting pauli ...
33 views

### Destructive measurement surface code: parity interpretation

In the surface code the logical $Z_L$ operator is measured destructively at the end with the following procedure: Measure all data qubits in the $Z$ basis with outcome $D_i \in \{\pm 1\}$ Compute ...
105 views

### Simulating stabilizer groups

Can any existing software be used (either directly or with a bit of persuading) to work with general stabilizer groups? From what I can see, tableau-based options like Stim and Qiskit can be used to ...
175 views

### Does Gottesman-Knill theorem apply with any computational basis input?

On Wikipedia, the Gottesman-Knill theorem is said to state the following: A quantum circuit using only the following elements can be simulated efficiently on a classical computer. Preparation of ...
17 views

### Applying a single-qubit Pauli measurement to 3 or more pure non-orthogonal $n$-qubit stabilizer states

If we have 3 or more pure non-orthogonal $n$-qubit stabilizer states, where $n \ge 2$, is it true that there always exists a single-qubit Pauli measurement that will map these states to a set of post-...
40 views

### Example of code where codewords cannot be stabilizer states

Are there any known examples of $((n,K,d))$ codes with $d \geq 2$ for which it is not possible to find a basis of codewords that are stabilizer states? A code word stabilized (CWS) code is defined ...
164 views

183 views

### Are there any packages that can calculate stabilizer tableau of a QECC

I'm experimenting with some small quantum error correcting codes (QECC). For example $[[5,1,3]]$, $[[8,3,3]]$ or toric codes $[[2d^2,2,d]]$ ($d=2,3,\cdots$). The last one being defined by redundant ...
3k views

### What is a stabilizer state?

I am reading through the paper "Direct Fidelity Estimation from Few Pauli Measurements" (arXiv:1104.4695) and it mentions 'stabilizer state'. "The number of repetitions depends on the ...
1 vote
78 views

111 views

### Stabilizer code: error detection why does it matter?

State vectors take more space when we have to specify certain states. In stabilizer formalism, we can specify these states in a much more compact way. But in error correction then we say that the ...
314 views

### Gottesman Knill theorem: why $O(n^2)$ classical operation to keep track of a Clifford gate

Starting from a state stabilized by Pauli matrices, and using only Clifford operations Gottesman Knill theorem ensures us that such algorithm can be classically simulated. Indeed, if I call my initial ...
399 views

### How to generate all stabilizer states numerically?

I would like to obtain a list of all stabilizer states in the given dimension (not necessarily qubit systems). What is an efficient way of generating this list numerically?
191 views

### Inner Product of Stabilizer States

The end of Section III in the paper Improved Simulation of Stabilizer Circuits by Aaronson and Gottesman shows how to compute the inner product of stabilizer states $|\psi\rangle$ and $|\varphi\rangle$...
233 views

### What is a Qiskit stabilizer

I wonder what is a Qiskit stabilizer and why we need it. Also I want to know the difference between stabilizer and extended stabilizer.