# All 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 ...
8 views

### 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 ...
34 views

### 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?
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As I was reading Qiskit textbook and there is this problem ... How can I swap a $|+\rangle$ to a $|-\rangle$
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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 ...
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42 views

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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 ...
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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 ...
21 views

### 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 ...
74 views

### 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 ...
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1 vote
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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 ...
29 views

### 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.
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1 vote
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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 ...
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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 ...
19 views

### 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
18 views

### 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 ...
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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} ...
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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 ...
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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 ...
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-...
52 views

### 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 ...
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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 ...
50 views

### 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 ...
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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?
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 ...
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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 ...
16 views

### 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....
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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 ...
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### 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: ...
46 views

### 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
57 views

I am interested in the following Haar average over the unitary group: $\mathbb{E}_U\Big[\frac{tr(U^{\otimes p}|j\rangle\langle j|(U^\dagger)^{\otimes p}\rho \otimes \sigma ...)}{tr(U^{\otimes q}|j\... 0 votes 0 answers 31 views ### Quantum measurement on Bloch Sphere I'm reading the paper "Data re-uploading for a universal quantum classifier". This paper proposes the classification process as follows$x_i $with different rotation angle$\theta_i$... • 51 0 votes 2 answers 39 views ### What can I use instead of mct (multi-controlled Toffoli)? (Grover's algorithm) I implemented the general diffuser (for arbitrary qubits) in Grover's algorithm in terms of an Multi-controlled Toffoli (MCT) gate (it flips target when all controlled gates are 1). However, this gate ... • 1 1 vote 2 answers 50 views ### Check if a Pauli string belongs to a stabilizer tableau Given a Pauli string and a stabilizer tableau, how do I know that the Pauli string belongs to the tableau, i.e. can be written as a product of strings already in the tableau. Thanks. • 13 2 votes 2 answers 156 views ### Matrix representation of SWAP on two qubit registers? There is a matrix that can represent a swap gate-- a gate that essentially swaps two qubits. This matrix,$S\$, is: $$\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & ... 3 votes 1 answer 108 views ### Show that E_k=(I\otimes\langle e_k|)U(I\otimes|e_0\rangle) implies U=\begin{bmatrix}[E_1]&\cdots\\ [E_2]&\cdots\\\vdots&\ddots\end{bmatrix} In Page 365, Operator-sum representation, Chapter 8, Quantum Computation and Quantum Information by Nielsen and Chuang, it is given that We have a principal system Q and an environment E and U ... • 383 2 votes 1 answer 66 views ### Hilbert space vs RKHS I believe in quantum machine learning, it is interesting to talk about RKHS(reproducing kernel Hilbert space) and Hilbert space where a quantum state lives in. How do we think of these two spaces? Are ... • 417 2 votes 2 answers 69 views ### Quasiprobability decomposition of the CZ-gate I was trying to obtain the quasiprobability decomposition of the CNOT gate by using the information in this paper. The authors give us the example for the CZ gate (Figure 2, i.e. the one below). The ... • 305 1 vote 1 answer 38 views ### Using entropy quantum computing for solving optimization problems I would like to follow up on this question (What is Entropy Quantum Computing?). Company Quantum Computing Inc. announced that they made their quantum computer aimed at solving binary optimization ... • 12.1k 0 votes 1 answer 25 views ### I was solving matrix of beam splitter in python but got stuck in understanding the library What does this command physically mean? block_diag([[1]], BSunitaries[2], [[1]]) Can any one tell me in matrix form Source :... 1 vote 0 answers 24 views ### Difference between IBM and Google Quantum Circuit? I am wondering what the internal differences between IBM and Google quantum circuits are. They look so different. Google team seems to design their circuit in a fully-connected manner, while the chips ... 2 votes 1 answer 66 views ### Are relative phase Toffoli gates universal for reversible circuits? Let us define a new three qubit gate as:$$\begin{bmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 ...
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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 ...