All Questions
8,076
questions
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Why does the quantum walk operator only have two eigenvectors?
In Child's paper on the relationship between discrete and continuous quantum walks, he makes the following claim.
Although he provides a proof after this:
I don't understand how the walk operator ...
- 87
0
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0
answers
8
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Quantum Signal Operator and the unitary state preparation oracle?
I am looking into IL Chuang and GH Low's Hamiltonian Simulation with Qubitization paper.
I am very confused on the terminology and motivation behind definition 1.
I do not understand what the unitary ...
- 87
2
votes
0
answers
34
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Algorithm for finding Pauli stabilizers of a code
Given the zero logical $ |0_L\rangle $ and one logical $ |1_L\rangle $ for an $ [[n,1,d]] $ code is there a well known/ efficient algorithm for determining which Pauli operators stabilize the code?
- 1,116
0
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37
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About swap gate
As I was reading Qiskit textbook and there is this problem ... How can I swap a $|+\rangle$ to a $|-\rangle$
- 75
0
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1
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38
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Expectation values of non-local operators in Qiskit
Is there a convenient way in Qiskit to calculate the expectation value for a non-local operator, i.e. I would like to calculate:
$$ \langle \Psi|O|\Psi \rangle $$
More precisely, I would like to ...
- 113
0
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0
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42
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Stabilizers Of The H Code
How does one interpret the ... in the third and fourth stabilizers of the H code? Is this $[1, 2, 5, 6, 9, 10, \dots]$ or $[1, 2, 5, 6, 7, 8,\dots]$? Can someone please write this out for $k = 1, 2, 3,...
- 146
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19
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What does it mean for a Qiskit pulse to have a negative amplitude?
I'm going through tutorials on Qiskit Pulse. From this documentation, I can see that it is possible to give a pulse, such as a Gaussian a few different parameters. One of the parameters that I can ...
3
votes
1
answer
57
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How to simulate rectangular surface code with stim?
The Stim package is a tool for simulation and analysis of quantum stabilizer circuits. Stim's built-in surface code circuit generation, stim.Circuit.generated, can run different code tasks (rotated ...
5
votes
2
answers
59
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Reasonable Circuit Depth
So I'm auto-constructing quantum circuits that are being auto-generated from dimacs files along with the addition of the amplification function. It's for a satisfiability problem where the number of ...
1
vote
1
answer
25
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ModuleNotFoundError when running Qiskit RNG
I'm trying to generate random numbers using IBMQ backends with the following code:
...
- 13
1
vote
0
answers
23
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Quantum algortihm for SVD and eigendecompostion
In this paper by Rebentrost, Steffens, and Lloyd, it is stated that:
Such tasks [eigen- and singular value decomposition of a matrix] could be performed efficiently via phase estimation on a ...
- 11
1
vote
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answers
22
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State tomography with Pauli basis measurements for a high number of qubits
My end goal is to recover the quantum state in its computational basis or reduced density matrix of a high number qubit circuit in a real QPU. Taking into account that the number of qubits will be ...
4
votes
2
answers
1k
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Is quantum teleportation fully secure (in principle)?
Suppose two parties Alice and Bob have access to as many EPR pairs as needed, with each one having a qubit of each pair. Now Alice can create a sequence of qubit states $|i_{1}\rangle, |i_{2}\rangle, |...
- 347
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votes
0
answers
15
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Deutsch Algorithm's matrix, what is the matrix? is there one? what is this oracle?
so I'm still new to the field and am in a class on quantum computing. Basically my question is the title. I've been trying to understand where the speed up comes from in qc as in classical it's fairly ...
- 31
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23
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Understanding Shor algorithm fo Elliptic Curves Demonstration
I was reading Shor's discrete logarithm quantum algorithm for elliptic curves. And i have two questions.
In page 7 they say that $x = (x0 - dy) mod q$, where $x0$ is between 0 and q-1, but then they ...
0
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0
answers
21
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Combine qubits together to get additonal accuracy
The Peres-Mermin Magic Squares game at https://en.wikipedia.org/wiki/Quantum_pseudo-telepathy defines a simple circuit that outputs legal winning game outcomes. An "ad-hoc" circuit that does ...
- 25
3
votes
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answers
74
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What other discrete non-trivial non-Clifford groups of gates are there?
I do not know many groups (as in group theory) of quantum gates. Aside from trivial ones, I know there is Pauli group and the Clifford group. Recently I discovered another interesting group generated ...
- 1,584
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8
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QuTiP, Continuous variable systems: Calculating the expectation value of an operator from the covariance matrix
Let's say I have the covariance matrix for a 4-mode system, $\sigma$, which is an $8 \times 8 $ matrix (the first moments are zero). I want to calculate the expectation value for an operator, for ...
2
votes
1
answer
29
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Is there an expression for the partial trace of a vectorized density matrix?
Is there an expression for the partial trace of vectorized density matrix? I did some literature review but didn't find not much relevant information.
- 147
1
vote
1
answer
32
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Is there an alternative algorithm to extract a probability of states of qubit after measuring?
Let a simple quantum circuit consist of one qubit and one classical bit. Initially, a qubit has the $|0\rangle$-state and then goes through some sequence of quantum gates, see the circuit below.
The ...
- 111
0
votes
1
answer
10
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Invert colors in qutip plot_wigner function
In QuTiP, it is possible to plot Wigner functions with positive (shown in blue) and negative (shown in red) values.
For example, the following code displays the Wigner function of a Schrodinger cat ...
0
votes
1
answer
19
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How to get the matched nodes using Matching.decode() in PyMatching?
In the module matching.py of PyMatching, it is possible to construct Matching objects to decode matching graphs using the minimum-weight perfect matching decoder.
The ...
1
vote
0
answers
18
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References discussing the carbon footprint expected for fault-tolerant quantum computers?
There are many problems regarding the scalability of quantum computers, how we need good quantum error correcting codes that scale well and protect well the logical encodings against many possible ...
- 1,997
2
votes
0
answers
13
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Lowest energy problem with additional constraints
Consider the following minimization problem:
\begin{align}
&\min_{\rho} \mathrm{Tr}[\rho H] \\
\text{such that:}& \\
&Tr[\rho A_i] \leq 0 \ \ \forall A_i, \ i \in \{1,2,3,...\}
\end{align}
...
- 21
0
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1
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25
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What is the structure of Qiskit's amplitude-encoded quantum circuit?
A problem that has been ignored before is that Ansatz does not know that classical data becomes quantum data. Although Qiskit provides the Initialize() function that can be initialized directly.
I'm ...
- 388
3
votes
1
answer
61
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How do we compute quantum walks for a graph?
I am reading Childs' paper on discrete and continuous quantum walks. I do not really understand why quantum walks are useful--- as implementing the quantum walk operator requires knowing the principal ...
- 87
3
votes
0
answers
82
views
Thermodynamic Speed Limit to Quantum Computing
There's a lot of mystifying jargon in the field of quantum computation, so I would like to pose a question from elementary physics to maybe help clarify things. Is it not true that the speed of a real-...
- 31
5
votes
2
answers
52
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What's the most efficient decomposition in terms of T-count of the 4-qubit Toffoli with 1 ancilla?
When decomposing the 4-qubit Toffoli in the Clifford+T universal gate set with 1 ancilla qubit, what is the most efficient implementation one can get in terms of T-count? I can only find papers that ...
- 53
2
votes
1
answer
92
views
How can I see the circuit that was actually executed on the device in pennylane?
I do a VQE using the pennylane UCCSD ansatz for execution on the 'default.qubit' device and am interested in the actual circuit that is executed on the device (ideally without making changes in any ...
- 77
5
votes
1
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50
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Action of a channel on an "unphysical" state
Suppose we are given a rule $\Phi$ which is completely positive and trace preserving operation takes an input qubit state $\rho$ to an output qubit state $\rho^\prime$ (as an example of such rule see ...
- 548
1
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2
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45
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How to calculate CNOT gate for three-qubit (1-control, 2-target) states as a matrix?
How can I calculate CNOT gate with 1 control and 2 target qubits as matrix?
2
votes
2
answers
272
views
Why is an X gate a quantum coin flip?
I am reading this page of Qiskit's textbook. I noticed that it extends coin games to quantum computers by defining an $X$ gate to be a classical coin flip. However, I do not understand this. For ...
- 87
0
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0
answers
41
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How can the result of 1 million transformations on a qubit be verified to be correct?
I tried to do almost a million transformations on a qubit.
I made a three qubit circuit with equal superposition of |0> and |1> (using Hadamard gate) and on the first qubit (qubit 0), added one ...
- 1
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votes
0
answers
16
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How to stretch duration of standard gates of an IBM Backend?
I want to stretch the duration of standard gates of an IBM backend to amplify noise (as proposed in one of the earliest implementations of zero noise extrapolation (ZNE) (https://arxiv.org/abs/1805....
- 389
2
votes
1
answer
46
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Solving a Bloch sphere where alpha is imaginary
$$
\begin{array}{l}
|\psi\rangle=\frac{\sqrt{3 i}}{2}|0\rangle-\frac{1}{2}|1\rangle \\
|\psi\rangle=0.924|0\rangle-0.382 i |1\rangle
\end{array}
$$
Basically I’m trying to convert these to a standard ...
- 31
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votes
2
answers
24
views
Can I create a quantum circuit from a list of operations in pennylane?
Say, I have a list of operations which are pennylane gates, can I create a circuit from it?
I tried:
...
- 77
2
votes
0
answers
46
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Entangling attack on BB84 protocol
I am trying to solve the exercise 5.3 from the book "A Gentle Introduction to Quantum Computing". The exercise reads as follows:
Suppose Eve attacks the BB84 quantum key distribution of ...
1
vote
0
answers
57
views
How to compute Haar average over the unitary group of a ratio of homogeneous polynomials?
I am interested in the following Haar average over the unitary group:
$\mathbb{E}_U\Big[\frac{tr(U^{\otimes p}|j\rangle\langle j|(U^\dagger)^{\otimes p}\rho \otimes \sigma ...)}{tr(U^{\otimes q}|j\...
0
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0
answers
31
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Quantum measurement on Bloch Sphere
I'm reading the paper "Data re-uploading for a universal quantum classifier".
This paper proposes the classification process as follows
$x_i $ with different rotation angle $\theta_i$
...
- 51
0
votes
2
answers
39
views
What can I use instead of mct (multi-controlled Toffoli)? (Grover's algorithm)
I implemented the general diffuser (for arbitrary qubits) in Grover's algorithm in terms of an Multi-controlled Toffoli (MCT) gate (it flips target when all controlled gates are 1). However, this gate ...
- 1
1
vote
2
answers
50
views
Check if a Pauli string belongs to a stabilizer tableau
Given a Pauli string and a stabilizer tableau, how do I know that the Pauli string belongs to the tableau, i.e. can be written as a product of strings already in the tableau. Thanks.
- 13
2
votes
2
answers
156
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Matrix representation of SWAP on two qubit registers?
There is a matrix that can represent a swap gate-- a gate that essentially swaps two qubits. This matrix, $S$, is:
$$
\begin{bmatrix}
1 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & ...
- 87
3
votes
1
answer
108
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Show that $E_k=(I\otimes\langle e_k|)U(I\otimes|e_0\rangle)$ implies $U=\begin{bmatrix}[E_1]&\cdots\\ [E_2]&\cdots\\\vdots&\ddots\end{bmatrix}$
In Page 365, Operator-sum representation, Chapter 8, Quantum Computation and Quantum Information by Nielsen and Chuang, it is given that
We have a principal system $Q$ and an environment $E$ and $U$ ...
- 383
2
votes
1
answer
66
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Hilbert space vs RKHS
I believe in quantum machine learning, it is interesting to talk about RKHS(reproducing kernel Hilbert space) and Hilbert space where a quantum state lives in. How do we think of these two spaces? Are ...
- 417
2
votes
2
answers
69
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Quasiprobability decomposition of the CZ-gate
I was trying to obtain the quasiprobability decomposition of the CNOT gate by using the information in this paper.
The authors give us the example for the CZ gate (Figure 2, i.e. the one below).
The ...
- 305
1
vote
1
answer
38
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Using entropy quantum computing for solving optimization problems
I would like to follow up on this question (What is Entropy Quantum Computing?).
Company Quantum Computing Inc. announced that they made their quantum computer aimed at solving binary optimization ...
- 12.1k
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votes
1
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25
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I was solving matrix of beam splitter in python but got stuck in understanding the library
What does this command physically mean?
block_diag([[1]], BSunitaries[2], [[1]])
Can any one tell me in matrix form
Source :...
1
vote
0
answers
24
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Difference between IBM and Google Quantum Circuit?
I am wondering what the internal differences between IBM and Google quantum circuits are.
They look so different. Google team seems to design their circuit in a fully-connected manner, while the chips ...
- 11
2
votes
1
answer
66
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Are relative phase Toffoli gates universal for reversible circuits?
Let us define a new three qubit gate as:
$$\begin{bmatrix}
1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & 1 ...
- 1,584
1
vote
1
answer
52
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XOR game quantum strategy expected payoff?
I am reading Thomas Vidick, Quantum multiplayer games, testing and rigidity. On top of p.4,
$$\text{E}[a\cdot b] = \sum_{i,j\in \{0,1\}}(-1)^{i+j}\text{Pr}\big((a,b)=(i,j)\big)$$
I do not understand ...
- 157