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2019-06-14T13:16:18.000 | {
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"forum": "quantumcom... | stackexchange | How to program a controlled Hadamard-Hadamard gate?
I'm trying to program a controlled gate as the figure below in Qiskit. Should it be sufficient to separate and control individually the Hadamard gates?
enter image description here
It seems like this gate is controlled on the top qubit (which I will call qubit 0)... | 20240930 |
2018-05-17T12:37:39.753 | {
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"forum": "quantumco... | stackexchange | Are there any organised resources available from where I can begin my quantum computing studies?
I am a computer science student and am currently searching for resources from where I can learn about quantum computers, quantum computing models, their working principles, their gates and some simple quantum algorithms.
... | 20240930 |
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"forum": "quantumco... | stackexchange | How can I build a circuit to generate an equal superposition of 3 outcomes for 2 qubits?
Given a $2$ qubit-system and thus $4$ possible measurements results in the basis $\{|00\rangle$, $|01\rangle$, $|10\rangle$, $|11\rangle\}$, how can I prepare the state, where:
1. only $3$ of these $4$ measurement results are ... | 20240930 |
2018-06-10T18:13:30.203 | {
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"forum": "quantumcom... | stackexchange | How to check if 2 qubits are entangled?
I know that 2 qubits are entangled if it is impossible to represent their joint state as a tensor product. But when we are given a joint state, how can we tell if it is possible to represent it as a tensor product? For example, I am asked to tell if the qubits are entangled for... | 20240930 |
2019-02-07T03:06:27.737 | {
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"forum": "quantumc... | stackexchange | Who discovered the phase kickback trick?
Was it David Deutsch? Can you say who was the first paper to mention the phase kickback trick?
The phase kickback trick appears in this paper:
Richard Cleve, Artur Ekert, Chiara Macchiavello, Michele Mosca. Quantum Algorithms Revisited. Proceedings of the Royal Society of L... | 20240930 |
2019-07-15T08:20:10.840 | {
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"forum": "quantumco... | stackexchange | How to create an Ising coupling gate with Qiskit?
I'm trying to apply a time evolution algorithm for a physical system I'm trying to simulate on QISkit, however, in order to do that, I need to use the so-called Ising coupling gate:
$I=\begin{pmatrix} e^{ia} & 0 & 0 &0 \\ 0 & e^{-ia} & 0 & 0 \\ 0 & 0 & e^{-ia} & 0 \\... | 20240930 |
2019-06-29T09:42:48.160 | {
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"forum": "quantumco... | stackexchange | Can a quantum computer run classical algorithms?
I realize that fundamentally speaking quantum and classical computers might as well be apples and oranges, and that for very specific problems such as integer factorization with Shor's algorithm quantum computers blow conventional computers out of the water, but could ... | 20240930 |
2019-01-25T08:14:26.780 | {
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"forum": "quantumco... | stackexchange | Hadamard gate as a product of $R_x$, $R_z$ and a phase
I am having problems with this task.
Since the Hadamard gate rotates a state $180°$ about the $\hat{n} = \frac{\hat{x} + \hat{z}}{\sqrt{2}}$ axis, I imagine the solution can be found the following way:
First rotate $\hat{n}$ so it lies in the $z$-$y$ plane: $$R... | 20240930 |
2021-12-22T14:50:59.800 | {
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"forum": "quantumc... | stackexchange | Does the X (NOT) gate affect superpositions at all?
Does "NOT" gate have any effect on qubit in superposition state? After applying Hadamard gate on qubit seems like the "NOT" gate doesn't have any effect on it. Could somebody describe this behavior?
This depends on what superposition you're in. Recall that the not... | 20240930 |
2023-07-18T06:53:41.143 | {
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"forum": "quantumc... | stackexchange | How to come up with Simon's Algorithm circuit for this 3 qubit system? (given truth table & s)
I have this truth table, knowing that the S = 110. However, how do I come up with a circuit by recognizing the pattern? It has taken me hours but my 2 brain cells don't seem to get it...
I know there must be an intuitive g... | 20240930 |
2020-12-27T23:36:00.073 | {
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"forum": "quantum... | stackexchange | Is there a name for the 3-qubit gate that does NOT NOT NOTHING?
It seems to me that the "disjunction gate" (aside: is that its proper name?) can be thought of as the combination of three gates, G1, G2, and G3, where G2 is the CCNOT gate, and $G1 = G3 = ¬_a \otimes ¬_b \otimes I_c$. For context, see the bottom two row... | 20240930 |
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"forum": "quantumco... | stackexchange | Representing qubit swap using linear algebra
I want to write matrix representation of qubit swap algorithm, but I seem to be stuck. Here is the circuit I am trying to calculate using linear algebra: enter image description here
Initially $q_0 = |0\rangle$ or $\begin{pmatrix}1 & 0\end{pmatrix}^T$ while $q_1 = |1\rang... | 20240930 |
2021-09-07T18:38:26.457 | {
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"forum": "quantumc... | stackexchange | Can all mixed states be written as a convex combination $\rho=\sum_j p_j |\psi_j\rangle\langle \psi_j|$?
States belonging to some space $\mathcal H$ can be described by density operators $\rho\in L(\mathcal H)$ that are positive and have trace one. Pure states are the ones that can be written as $\rho=|\psi\rangle\la... | 20240930 |
2019-07-30T23:36:00.327 | {
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"forum": "quantumc... | stackexchange | Why isn't there a contradiction between the existence of CNOT gate/entanglement and the no-cloning theorem?
Of course I am not implying that I am right and the no cloning theorem is wrong, but I am trying to figure out what is wrong with my reasoning and yet I couldn't find the mistake.
Based on Wikipedia
In physic... | 20240930 |
2020-08-13T05:33:40.047 | {
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"forum": "quantum... | stackexchange | Can anyone provide me with an example of the for Grover's algorithm on one qubit?
I'm having trouble understanding Grover's Algorithm, so I'd like to start with the case with 1 qubit. But I don't see anyone build it for 1 qubit, only 2 is the minimum. Is it because that's impossible or too trivial? Can anyone provide... | 20240930 |
2020-10-05T23:18:07.213 | {
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} | 2020-10-05T15:54:56.633 | quantumcomputing_stackexchange_com-14025-14031 | {
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"forum": "quantumc... | stackexchange | Quantum tensor product closer to Kronecker product?
Coming more from a computer science background, I never really studied tensor products, covariant/contravariant tensors etc. So until now, I was seeing the "tensor product" operation mostly as (what appears to be) a Kronecker product between the matrix representatio... | 20240930 |
2021-04-07T13:07:44.260 | {
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"forum": "quantumc... | stackexchange | Do global phases matter when a gate is converted into a controlled gate?
Let's say that we have a unitary matrix M such that: $$ M = e^{i\pi/8}\begin{pmatrix} 1 & 0 \\ 0 & e^{i\pi/12} \\ \end{pmatrix} $$ If we were to apply this unitary matrix to the state $|1\rangle$, we would get: $$ M|1\rangle\ =\ e^{i\pi/8+i\pi/1... | 20240930 |
2022-01-24T19:21:18.953 | {
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"forum": "quantum... | stackexchange | What does $ A - \langle A \rangle $ mean?
I've seen the uncertainty of $A$ written as $$ (\Delta A)^2 = \big\langle (A - \langle A \rangle)^2 \big\rangle\,. $$ But what does this even mean since $ A $ is an operator and $ \langle A \rangle $ is a scalar? How can we compute the difference of the two?
For any vector $v... | 20240930 |
2021-05-18T14:25:16.427 | {
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"forum": "quantum... | stackexchange | Sympy suddently does not work together with TFQ
I work with tensorflow-quantum and use sympy for parameter updating.
Suddenly, without (manually) updating or changing anything this error comes up:
File "/home/eli/anaconda3/lib/python3.8/site-packages/tensorflow_quantum/core/serialize/serializer.py", line 93, in _... | 20240930 |
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"forum": "quantum... | stackexchange | A 32x32 matrix with the best rank * span_weight
Answers must contain a 32x32 matrix (or smaller). An answer is better if its matrix has a higher product of rank and span weight.
In "Subsystem codes with spatially local generators". Sergey Bravyi proves that you can turn a bit matrix into a local planar subsystem cod... | 20240930 |
2020-08-24T16:41:52.140 | {
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"forum": "quantu... | stackexchange | Consequences of $MIP^\ast=RE$ Regarding Quantum Algorithms
The (pending-peer review) proof of $MIP^\ast=RE$ in this pre-print has been hailed as a significant breakthrough. The significance of this result is addressed by Henry Yuen (one of the authors) in this blog post. Scott Aaronson also lists some of the major im... | 20240930 |
2022-05-20T17:03:18.837 | {
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"forum": "quantum... | stackexchange | T-depth in Qiskit
How to find T-depth in Qiskit? Is there any inbuilt function or some method to find T-depth? I know that the .depth() function exists which returns circuit depth (i.e., length of critical path), but is there any method for T-depth?
The depth method can be customized with a gate subset you want to ... | 20240930 |
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"answer_view_count": 0... | stackexchange | What is the difference between quantum annealing and adiabatic quantum computation models?
From what I understood, there seems to be a difference between quantum annealing and adiabatic quantum computation models but the only thing I found on this subject implies some strange results (see below).
My question is the ... | 20240930 |
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"answer_view_count": 0... | stackexchange | Does a study guide exist that starts from a "purely CS background" and advances towards "making a new quantum programming language"?
I am from a computer science background and I find it difficult to decide on the resources I should focus on while learning quantum computing, since there is so much to read/watch. My u... | 20240930 |
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"answer_view_count": 0... | stackexchange | Why isn't the circuit performing a measurement in the Bell basis?
Nielsen and Chuang (on page 188 exercise 4.33) says that the circuit including CNOT and Hadamard is performing a measurement in the Bell basis. But I can't see how.
enter image description here
The matrix representing the circuit functionality is:
... | 20240930 |
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"answer_view_count": ... | stackexchange | Symmetry of tensor product w.r.t. Vazirani 2-qubit video
Quantum Computing (QC) pioneer Vazirani has graciously long provided some nice videos on an intro to QC. E.g. in "2 qubit gates + tensor product" (2014) he introduces the tensor product w.r.t. QC gates. I was generally able to follow this video but think there w... | 20240930 |
2021-05-07T13:21:22.030 | {
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"answer_last_activity_date": "2021-05-07T13:21:22.030",
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"answer_view_count":... | stackexchange | Quantum circuit for a three-qubit bit-flip code
I know a three-qubit bit-flip code has a common encoding circuit as follows, encoding circuit of the three-qubit bit-flip code
Further, as in page 35 in Gottesman's paper, the encoding circuit can also be constructed through stabilizer generators. He illustrated the en... | 20240930 |
2019-12-09T05:38:27.250 | {
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} | 2019-02-18T19:50:04.987 | quantumcomputing_stackexchange_com-5521-5522 | {
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"answer_last_editor_user_id": 119,
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"answer_view_count": ... | stackexchange | How to add control to gates in Cirq?
My question is very simple. I know there is a method to add a control to previously defined gates. I saw in the API of cirq that there is a command Controlled gate (here). I'm not understanding though how would this work. Suppose for example I want to add a control to an XPowGate ... | 20240930 |
2023-07-13T20:59:41.290 | {
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} | 2023-07-10T21:02:58.763 | quantumcomputing_stackexchange_com-33357-33358 | {
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"answer_view_count":... | stackexchange | Universal Gate Set, Magic States, and costliness of the T gate
The usual universal gate set is $\mathcal{C} + T$ where $\mathcal{C}$ is the Clifford group and $T = \begin{pmatrix} 1 & 0 \\ 0 & e^{i\pi/4} \end{pmatrix} $ is the $\pi/8$ rotation gate. In practice we find a code that has $\mathcal{C}$ transversal and th... | 20240930 |
2023-09-19T21:32:08.477 | {
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} | 2021-05-05T20:31:02.513 | quantumcomputing_stackexchange_com-17358-17359 | {
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"answer_last_editor_user_id": 119,
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"answer_view_count":... | stackexchange | How do you build a circuit to make an equal superposition of $n$ outcomes?
Suppose we start with $|00...0\rangle$. We want to build an equal superposition over $|0\rangle + ... + |n-1\rangle$.
When $n=2^m$ for some $m$, I know I can do this using $H^{\otimes m}$.
What is the general circuit for this (i.e. in case $... | 20240930 |
2018-03-31T14:10:37.630 | {
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} | 2018-03-31T13:47:03.780 | quantumcomputing_stackexchange_com-1527-1528 | {
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"answer_view_count":... | stackexchange | What do double wires mean in quantum circuits, and how do they relate to if statements?
The circuit
enter image description here
can be translated to the following code:
operation Teleport(msg, there) {
let register = AllocateRegister();
let here = register;
H(here);
CNOT(here, there);
CNOT(msg... | 20240930 |
2018-10-31T12:54:31.140 | {
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} | 2018-09-18T08:30:32.567 | quantumcomputing_stackexchange_com-4249-4250 | {
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"answer_last_editor_user_id": 124,
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"answer_view_count": ... | stackexchange | Decomposition of an arbitrary 1-qubit gate into a specific gateset
Any 1-qubit special gate can be decomposed into a sequence of rotation gates ($R_z$, $R_y$ and $R_z$). This allows us to have the general 1-qubit special gate in matrix form:
$$ U\left(\theta,\phi,\lambda\right)=\left(\begin{array}{cc} e^{-i(\phi+\la... | 20240930 |
2018-04-01T10:11:08.240 | {
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} | 2018-03-14T19:59:21.727 | quantumcomputing_stackexchange_com-112-116 | {
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"answer_last_editor_user_id": 144,
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"answer_score": 17,
"answer_view_count": ... | stackexchange | What is the difference between a qubit and classical bit?
As I understand it, the main difference between quantum and non-quantum computers is that quantum computers use qubits while non-quantum computers use (classical) bits.
What is the difference between qubits and classical bits?
A bit is a binary unit of info... | 20240930 |
2020-06-01T17:56:20.087 | {
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} | 2020-05-31T06:58:23.373 | quantumcomputing_stackexchange_com-12254-12255 | {
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"answer_last_editor_user_id": 332,
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"answer_score": 5,
"answer_view_count":... | stackexchange | Moore's law for quantum computers
Moore's law states that performance of classical computers doubles every two years (later revised to 18 months) and a price for computing resources halves during same time period.
Currently, it seems that similar statement can be made for quantum annealers in term of number of qubit... | 20240930 |
2019-08-16T08:11:59.490 | {
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} | 2018-04-23T10:17:42.513 | quantumcomputing_stackexchange_com-1885-1888 | {
"answer_comment_count": 1,
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"answer_last_editor_user_id": 409,
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"answer_score": 49,
"answer_view_count":... | stackexchange | What is meant by "Noisy Intermediate-Scale Quantum" (NISQ) technology?
Preskill introduced recently this term, see for example Quantum Computing in the NISQ era and beyond (arXiv). I think the term (and the concept behind it) is of sufficient importance that it deserves to be explained here in a pedagogical manner. P... | 20240930 |
2019-05-16T19:50:35.597 | {
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} | 2019-05-16T16:03:28.727 | quantumcomputing_stackexchange_com-6163-6166 | {
"answer_comment_count": 3,
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"answer_last_editor_user_id": 491,
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"answer_view_count": ... | stackexchange | Trace distance of two classical-quantum states
I have these two classical-quantum states:
$$\rho = \sum_{a} \lvert a\rangle \langle a\lvert \otimes q^a \\ \mu = \sum_{a} \lvert a\rangle \langle a\lvert \otimes r^a $$
Where $a$ are the classical basis vectors, $q^a, r^a$ are arbitrary matrices dependent on $a$.
Now,... | 20240930 |
2020-08-10T20:33:50.230 | {
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} | 2020-08-09T15:22:43.527 | quantumcomputing_stackexchange_com-13238-13249 | {
"answer_comment_count": 7,
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"answer_last_activity_date": "2020-08-10T20:33:50.230",
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"answer_last_editor_user_id": 491,
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"answer_score": 5,
"answer_view_count":... | stackexchange | How is it not a contradiction that it is possible to build fault tolerant circuits with strictly contractive (e.g.: depolarizing noise) channels?
This paper discusses strictly contractive channels, i.e. channels that strictly decrease the trace distance between any two input quantum states.
It is shown that if a qua... | 20240930 |
2018-10-03T07:03:46.383 | {
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} | 2018-10-03T01:07:27.773 | quantumcomputing_stackexchange_com-4333-4334 | {
"answer_comment_count": 0,
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"answer_last_editor_user_id": 1837,
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"answer_view_count"... | stackexchange | Protocol for entaglement swapping
Suppose there are 3 parties, of which 2 pairs share an EPR pair and can communicate classically. What is a protocol that results in the third pair sharing an EPR pair?
That is the problem I'm given, I'm lost on how to do it, let alone what it means to "share an EPR pair" in the end.... | 20240930 |
2018-12-03T16:20:11.307 | {
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} | 2018-12-03T06:58:50.657 | quantumcomputing_stackexchange_com-4846-4847 | {
"answer_comment_count": 0,
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"answer_last_activity_date": "2018-12-03T16:20:11.307",
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"answer_last_editor_user_id": 1837,
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"answer_score": 8,
"answer_view_count"... | stackexchange | Are projective measurement bases always orthonormal?
Are projective measurement bases always orthonormal?
Yes.
Remember that you require several properties of a projective measurement including $P_i^2=P_i$ for each projector, and $$ \sum_iP_i=\mathbb{I}. $$ The first of these show you that the $P_i$ have eigenvalu... | 20240930 |
2019-06-08T03:00:10.630 | {
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} | 2019-06-07T21:39:40.613 | quantumcomputing_stackexchange_com-6375-6377 | {
"answer_comment_count": 2,
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"answer_last_activity_date": "2019-06-08T03:00:10.630",
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"answer_last_editor_user_id": 2879,
"answer_owner_user_id": 2879,
"answer_score": 5,
"answer_view_count"... | stackexchange | Error syndromes and recovery procedure in bit flip code
This question relates to exercise 10.4 in Nielsen and Chuang.
For syndrome diagnosis, the textbook provides an example where one has four projectors, by which, you can identify where a one qubit error has occurred. In this scheme, the syndrome measurement does... | 20240930 |
2019-06-28T21:03:59.953 | {
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"answer_view_count"... | stackexchange | Implementing the one-bit Deutsch Oracle algorithm using phase
The standard method of implementing the one-bit Deutsch Oracle algorithm is to use two qbits, one as input & one as output (which allows you to write the non-reversible constant functions in a reversible way). However, I've heard there is a different way o... | 20240930 |
2019-09-30T16:09:21.657 | {
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} | 2019-09-29T22:11:43.573 | quantumcomputing_stackexchange_com-8355-8356 | {
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"answer_last_editor_user_id": 8623,
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"answer_score": 6,
"answer_view_count"... | stackexchange | Notation question: How would one read $|0\rangle (|0\rangle+|0\rangle)$?
For example in Deutsch's Algorithm, we apply $H$ to $|0\rangle$ and $|1\rangle$ respectively. I have seen the notation this result in the state: $$\frac{1}{2}(|0\rangle+|1\rangle)(|0\rangle-|1\rangle)$$ However, it is unclear to me how exactly I... | 20240930 |
2020-04-21T15:51:38.077 | {
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} | 2020-01-21T20:45:19.510 | quantumcomputing_stackexchange_com-9614-9615 | {
"answer_comment_count": 4,
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"answer_view_count"... | stackexchange | How to interpret a 4 qubit quantum circuit as a matrix?
This is part of Simon Algorithm (Initial state + some Oracle function) There is a post that explains how to interpret circuits (How to interpret a quantum circuit as a matrix?), but I'm not sure how to apply to the following circuit.
Circuit built with IMB plat... | 20240930 |
2023-08-26T16:50:33.507 | {
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} | 2019-07-30T14:35:56.333 | quantumcomputing_stackexchange_com-6898-6899 | {
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"answer_last_editor_user_id": 9474,
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"answer_view_count"... | stackexchange | How do the Knill-Laflamme conditions $E_k^\dagger E_l\in{\cal M}$ and $\{M,E_k^\dagger E_l\}=0$ help us correct errors?
Suppose we have a stabilizer group $\mathcal{M}$, the Knill-Laflamme condition for error correction states
An error with Kraus operators $\{E_k\}$ is correctable if either $$E^\dagger_kE_l\in\mathc... | 20240930 |
2022-10-17T13:34:43.363 | {
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} | 2021-03-17T06:58:42.817 | quantumcomputing_stackexchange_com-16533-16538 | {
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"answer_view_count... | stackexchange | Can I find the axis of rotation for any single-qubit gate?
Suppose I have an arbitrary qiskit $U_3$ gate: $U_3(\theta,\phi,\lambda)$. Is there a way I can find which axis the gate is rotating around? In other words, given any real numbers $\theta,\phi,\lambda$, can I find the vector $\hat n = (n_x,n_y,n_z)$ that the ... | 20240930 |
2021-02-09T16:31:41.467 | {
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"answer_view_count... | stackexchange | Implementing Grover's oracle with multiple solutions in Qiskit
I want to turn a state
$$ |\Psi_1⟩ = \frac{1}{\sqrt{8}}(|000⟩+|001⟩+|010⟩+|011⟩+|100⟩+|101⟩+|110⟩+|111⟩) $$
into
$$ |\Psi_2⟩ = \frac{1}{\sqrt{8}}(|000⟩+|001⟩+|010⟩+|011⟩+|100⟩-|101⟩-|110⟩+|111⟩) $$
using a phase oracle before applying Grover's amplif... | 20240930 |
2021-04-20T06:24:24.133 | {
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} | 2020-10-15T11:04:19.710 | quantumcomputing_stackexchange_com-14170-14171 | {
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"answer_view_coun... | stackexchange | Intuition behind the construction of an ansatz circuit
I'm learning about the VQE algorithm. When I looked at the declaration in Qiskit I saw you need to pass an ansatz which prepares the state. I looked at some commonly used ansatz functions, e.g. EfficientSU2 of Qiskit, and I saw many of them use $R_y$ and $X$ gate... | 20240930 |
2021-03-08T17:55:46.593 | {
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"answer_view_cou... | stackexchange | Is there an identity for the partial transpose of a product of operators?
The partial transpose of an operator $M$ with respect to subsystem $A$ is given by $$ M^{T_A} := \left(\sum_{abcd} M^{ab}_{cd} \underbrace{|a\rangle \langle b| }_{A}\otimes \underbrace{|c \rangle \langle d|}_B\right)= \left(\sum_{abcd} M^{ab}_... | 20240930 |
2024-02-08T03:36:34.573 | {
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"answer_view_cou... | stackexchange | What unitary commutes with all local Pauli operators?
I was thinking about this problem of identifying a set of unitary operations (other than the identity operation) that commute with local pauli $\sigma_X$ and $\sigma_Z$ matrices, i.e. find $U$ such that $[U, \sigma_{X, i}] = [U, \sigma_{Z, i}] = 0 ~ \forall i \in ... | 20240930 |
2022-02-17T21:55:04.437 | {
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"answer_view_cou... | stackexchange | Commutation rules between Pauli $X$ and controlled-Hadamard
Are there any known commutation rules between the $X$ gate and the $CH$ gate?
There are two cases: $X$ on the controlled qubit and $X$ on the target.
$X$ on the controlled qubit
For the first case, note that for any controlled unitary $CU$, we have
$$ (... | 20240930 |
2022-02-19T07:43:34.110 | {
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"answer_view_cou... | stackexchange | Schmidt decomposition for tripartite system $ABC$ with vanishing mutual information between $A$ and $C$
Suppose I have a tripartite system $ABC$ in a pure state $|\psi_{ABC}\rangle$ with mutual information $I(A:C)=0$. This implies that the reduced density matrix $\rho_{AC}$ factorizes as $\rho_{AC} = \rho_A \otimes ... | 20240930 |
2021-12-14T02:24:23.363 | {
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"answer_view_cou... | stackexchange | Should one learn the math of quantum computing from a "pure" perspective, or are quantum computing texts "good enough"?
Math for quantum computing includes advanced linear algebra, functional analysis, group and representation theory, probability theory, and more.
There are plenty of pure math books out there for th... | 20240930 |
2022-06-09T14:29:20.213 | {
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"answer_view_cou... | stackexchange | What is the speedup for Deutsch-Jozsa algorithm?
It is often said that Simon’s algorithm provided the first example of an exponential speedup over the best known classical algorithm. However, the Deutsch-Jozsa algorithm was published before Simon’s and looks to me that it also provides an exponential speedup since it... | 20240930 |
2021-04-28T20:23:04.380 | {
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"answer_view_cou... | stackexchange | Bloch sphere visualization using Cirq, ProjectQ, PyQuil
Is there a way to visualize the Bloch sphere using Cirq, ProjectQ, and/or PyQuil, as it is possible using plot_bloch_vector in Qiskit?
The answer seems to be "no" for all three. From what I can find, Cirq and PyQuil default to QuTiP for Bloch sphere visualizat... | 20240930 |
2024-07-18T16:43:29.030 | {
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"answer_view_cou... | stackexchange | Is there any mathematical technique to find the exact solution of a QUBO problem?
Suppose I am given a QUBO problem consisting in the minimization of a quadratic function $\vec{x}^T Q \vec{x}$ over a binary-valued vector $\vec{x} \in \{0, 1\}^n$, with $Q$ a symmetric indefinite real matrix. Is it possible to compute ... | 20240930 |
2024-07-03T15:14:21.313 | {
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"answer_view_cou... | stackexchange | Qutrit Steane Code
There is a well known 5 qubit code $ [[5,1,3]] $ with stabilizer generators
$$ XZZXI \\ IXZZX \\ XIXZZ \\ ZXIXZ $$ There is a corresponding $ [[5,1,3]]_3 $ code for qutrits given by
\begin{align*} & XZZ^\dagger X^\dagger I \\ & IXZZ^\dagger X^\dagger \\ & X^\dagger IXZZ^\dagger \\ & Z^\dagger X^\... | 20240930 |
2023-12-21T09:45:34.837 | {
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"answer_view_cou... | stackexchange | What mathematical object is the set of quantum states of a qudit? How should one write this?
It is tempting to write $|\psi\rangle \in \mathbb{C}^d$ for a qudit state, but this isn't very precise because of global phases.
What's a better notation for the set of states of a qudit?
The qudit Hilbert space is $\mathbb... | 20240930 |
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"answer_view_cou... | stackexchange | If Alice measures a qubit and doesn't tell Bob the result, what's Alice's state from Bob's perspective?
Suppose Alice has a qubit $|\phi\rangle=\alpha|0\rangle+\beta|1\rangle$ and measures it. Bob knows the initial state but not the result of her measurement.
So after the measurement, Alice knows what state her qubi... | 20240930 |
2024-09-27T23:16:13.497 | {
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"answer_view_cou... | stackexchange | Is $SO(2)$ with any entangling gate universal?
Let $E \in SU(2^k)$ be any entangling gate (for some $k \geq 2)$. Then my question is simply whether or not it is known that $SO(2) \cup \{ E \}$ is universal for $\mathsf{BQP}$?
Clearly it seems that this ought to be true, in light of the standard facts that any entangl... | 20240930 |
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"forum": "quantumcompu... | stackexchange | State produced by spontaneous parametric down-conversion (SPDC)
I'm researching SPDC's efficacy for use in an optical quantum computing model and I've been trying to figure out exactly what state the photons are in when they come out (as represented by a vector, for example), if I'm using type 1 SPDC and I'm looking... | 20240930 |
2018-03-28T11:19:22.200 | {
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"forum": "quantumcomp... | stackexchange | How can quantum decoherence be managed?
I've stumbled myself upon this article on Wikipedia, which says:
Decoherence can be viewed as the loss of information from a system into the environment (often modeled as a heat bath), since every system is loosely coupled with the energetic state of its surroundings.
<...>
... | 20240930 |
2018-04-17T08:53:49.653 | {
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"forum": "quantumcom... | stackexchange | Simulating Clifford + few-T circuits
I want to simulate large stabilizer circuits (H/S/CNOT/MEASURE/feedforward) with a small number of T gates mixed in. How can I do this in a way that scales exponentially only in the number of T gates? Are there existing implementations?
Taking your comment to Kiro to its logical... | 20240930 |
2019-08-28T14:13:30.463 | {
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"forum": "quantumcom... | stackexchange | Exercise 10.34 of Nielsen and Chuang : $-I$ not element of stabilizer group iff $g_j^2=I$ and $g_j \neq I$ where $g_j$ generators
I am stuck with this exercice of Nielsen and Chuang:
Let $S = \langle g1,... ,gl \rangle $.Show that $−I$ is not an element of S if and only if $g^2_j = I$ for all $j$,and $g_j \neq − I$ ... | 20240930 |
2018-06-21T13:16:32.857 | {
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"forum": "quantumcom... | stackexchange | Nielsen & Chuang Exercise 2.2 - “Matrix representations: example”
Reproduced from Exercise 2.2 of Nielsen & Chuang's Quantum Computation and Quantum Information (10th Anniversary Edition):
Suppose $V$ is a vector space with basis vectors $|0\rangle$ and $|1\rangle$, and $A$ is a linear operator from $V$ to $V$ such ... | 20240930 |
2018-03-25T13:24:04.950 | {
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"forum": "quantumco... | stackexchange | Who built the first quantum computer using at least two qubits?
In my previous question I asked who invented a quantum computer using qubits.
As a follow-up to this question I want to ask who built the first quantum computer using at least two qubits.
During my research I have discovered that in 1998, Jonathan A. J... | 20240930 |
2019-05-01T19:33:54.160 | {
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"forum": "quantumco... | stackexchange | Can an isometry leave entropy invariant?
Consider two finite dimensional Hilbert spaces $A$ and $B$. If I have an isometry $V:A\rightarrow A\otimes B$, under what condition can I find a unitary $U:A\otimes B\to A\otimes B$ such that $$U\rho_{A}\otimes |\psi\rangle\langle \psi|_BU^\dagger=V\rho_{A}V^\dagger$$
for som... | 20240930 |
2019-06-14T11:08:40.500 | {
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"forum": "quantumc... | stackexchange | Is swap gate equivalent to just exchanging the wire of the two qubits?
Is swap gate equivalent to just exchanging the wire of the two qubits?like this
if yes why not just switching the wire whenever we want to apply a swap gate?
Yes, it is equivalent. That's a perfectly valid way to represent it in a quantum circu... | 20240930 |
2020-04-07T07:26:32.043 | {
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"forum": "quantumc... | stackexchange | $H = e^{i\pi/4} \sqrt{iNOT}$?
In the paper Valley qubit in Gated MoS$_2$ monolayer quantum dot, a description of how a $NOT$ gate would be performed on a qubit in the described device is given.
The authors say that in the described implementation the operation performed is an $iNOT$ gate, and that the Hadamard opera... | 20240930 |
2020-08-07T10:06:36.003 | {
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"forum": "quantumc... | stackexchange | Is the partial trace $\mathrm{Tr}_B(\rho)$ equal to $\sum_k \mathrm{Tr}[(\sigma_k\otimes I)^\dagger \rho]\sigma_k$?
Assume a composite quantum systes with state $|\psi_{AB}\rangle$ or better $\rho=|\psi_{AB}\rangle\langle\psi_{AB}|$. I want to know the state of system $A$ only, i.e. $\rho_A$.
Is there any difference ... | 20240930 |
2022-03-02T07:56:51.630 | {
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"forum": "quantumc... | stackexchange | Eastin Knill Theorem and groups of transversal gates
The Eastin-Knill Theorem shows that the transversal gates always form a group and that moreover this group is a finite subgroup of the group of all unitaries.
For many codes, for example all self dual CSS codes, the group of transversal gates is exactly the Cliffor... | 20240930 |
2021-03-17T16:54:33.903 | {
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"forum": "quantumc... | stackexchange | Can I simultaneously plot 2 vectors on a single Bloch sphere and rotate the angle of visualization?
I'm trying to plot 2 vectors on the same Bloch sphere. From the qiskit documentation here, we can find plot_bloch_vector(bloch, title='', ax=None, figsize=None, coord_type='cartesian'). So I'm not quite sure if we coul... | 20240930 |
2018-07-02T19:17:56.293 | {
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"forum": "quantumco... | stackexchange | How do you send an array of qubits to an operation in Q#?
I have the following operation in my .qs files:
operation myOp(qubits: Qubit[]) : () {
// uses elements from the qubit array
}
How do I send an array of qubits to this in the driver file? The following did not work:
Qubit[] qubits = new Qubit... | 20240930 |
2021-11-27T08:21:58.310 | {
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"forum": "quantumc... | stackexchange | Show that if the Lindblad satisfy $\sum_\mu L_\mu L_\mu^\dagger=\sum_\mu L_\mu^\dagger L_\mu$ then the von Neumann entropy increases monotonically
How can we show that when the Lindblad operators satisfy the condition:
$$\sum_{\mu}L_{\mu} L_{\mu}^{\dagger} = \sum_{\mu} L_{\mu}^{\dagger}L_{\mu},\tag{1}$$
the master ... | 20240930 |
2018-05-30T10:52:10.287 | {
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"forum": "quantumco... | stackexchange | How to obtain arbitrary distribution in quantum database
I was working on the Grover's algorithm and the most common example is for a unitary distribution in a quantum database, for example:
$|\psi\rangle = \frac{1}{2}|00\rangle + \frac{1}{2}|01\rangle + \frac{1}{2}|10\rangle + \frac{1}{2}|11\rangle.$
Is there a wa... | 20240930 |
2020-02-03T19:17:09.007 | {
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"forum": "quantumc... | stackexchange | Does quantum computing already possess the level of abstraction to be explicable even without knowledge of physics?
Currently, quantum computer science (in contrast to classical computer science) can mostly only be understood if one has a good inside knowledge of physics, or more precisely quantum physics. Only then ... | 20240930 |
2018-09-22T23:57:34.600 | {
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"forum": "quantumco... | stackexchange | How to construct the "Inversion About the Mean" operator?
It seems like it should be simple, based on how Nielsen and Chuang talk about it, but I cannot seem to correctly implement the Inversion About the Mean operator ($2|\psi\rangle \langle\psi| - \mathcal{I}$) that is used in the Grover search algorithm, especiall... | 20240930 |
2020-03-16T12:58:41.333 | {
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"forum": "quantumc... | stackexchange | How should I understand the link between $x$ and $| x \rangle $?
In the paper "Quantum Expectation-Maximization for Gaussian Mixture Models" I encountered the following proposition :
Consider two vectors x,y and $\theta$ the angle between x and y, $\theta < \frac{\pi}{2}$. Then $||x - y|| \leq \epsilon$ implies $|| ... | 20240930 |
2018-12-19T20:45:38.230 | {
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"forum": "quantumco... | stackexchange | Is there any (really) quantum procedure that's an algorithm and not a Las Vegas algorithm?
Let me take Grover's algorithm as an example. In most cases, Grover's algorithm is able to yield with a high probability the desired term of the superposition. When the superposition has more than 4 terms, there's a small chanc... | 20240930 |
2021-02-03T18:27:32.037 | {
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"forum": "quantumc... | stackexchange | Shouldn't the input state of Deutsh-Jozsa's algorithm look like $|0\rangle^{\otimes n}\otimes |1\rangle$ rather than $|0\rangle^{\otimes n}|1\rangle$?
According to this wikipedia page the initial state in Deutsch–Jozsa algorithm is written as follows: $$|0\rangle^{\otimes n} |1\rangle$$
shouldn't it look like this?:... | 20240930 |
2021-01-31T21:37:44.690 | {
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"forum": "quantumc... | stackexchange | If the eigenvalues of $Z$ are $\pm1$, why are the computational basis states labeled with "$0$" and "$1$"?
The computational basis is also known as the $Z$-basis as the kets $|0\rangle,|1\rangle$ are chosen as the eigenstates of the Pauli gate \begin{equation} Z=\begin{pmatrix}1 & 0 \\ 0 & -1\end{pmatrix}. \end{equat... | 20240930 |
2022-12-11T09:25:09.943 | {
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"forum": "quantum... | stackexchange | What is a POVM?
I am having a hard time understanding what exactly a Measurement is by its definition? What I read is that a POVM $M$ is defined by its set of elements $M_i$. So is $M$ itself an operator? In circuit diagrams its a little "Measure" box, but I've never seen it written down in operator+braket formalism,... | 20240930 |
2020-08-16T11:59:14.027 | {
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"forum": "quantum... | stackexchange | Can classical linear algebra solvers implement quantum algorithms with similar speed-ups?
A quantum algorithm begins with a register of qubits in an initial state, a unitary operator (the algorithm) manipulates the state of those qubits, and then the state of the qubits is read out (or at least some information about... | 20240930 |
2021-04-25T22:42:44.860 | {
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"forum": "quantum... | stackexchange | What algorithm does Qiskit use to decompose arbitrary n-qubit unitaries on Rotations + CNOT?
I found that Qiskit uses Unroll3qOrMore in the transpiler class function to decompose an arbitrary $n > 2$ unitary and represent it as a directed acyclic graph (DAG). But I can't find an algorithm (or paper for it). Could you... | 20240930 |
2022-03-10T03:30:10.407 | {
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"answer_view_count":... | stackexchange | Is quantum computing just pie in the sky?
I have a computer science degree. I work in IT, and have done so for many years. In that period "classical" computers have advanced by leaps and bounds. I now have a terabyte disk drive in my bedroom drawer amongst my socks, my phone has phenomenal processing power, and compu... | 20240930 |
2018-03-14T13:37:40.833 | {
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"answer_last_editor_user_id": 15,
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"answer_view_count": 0,... | stackexchange | How does bra-ket notation work?
Quantum algorithms frequently use bra-ket notation in their description. What do all of these brackets and vertical lines mean? For example: $|ψ⟩=α|0⟩+β|1⟩$
While this is arguably a question about mathematics, this type of notation appears to be used frequently when dealing with quant... | 20240930 |
2019-02-16T23:20:59.130 | {
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} | 2019-02-14T20:34:27.120 | quantumcomputing_stackexchange_com-5490-5492 | {
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"answer_view_count": 0,... | stackexchange | A two qubit state in a special form
How can a pure two-qubit state $|\psi\rangle = a |00\rangle + b|01\rangle + c|10\rangle + d|11\rangle$, be written in the following form
\begin{equation} |\psi_{\alpha}\rangle = \sqrt{\alpha}|01\rangle + \sqrt{1-\alpha} |10\rangle. \end{equation} How can one prove this. And what ... | 20240930 |
2022-10-22T09:12:23.517 | {
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"answer_view_count": 0,... | stackexchange | How can we be sure that for every $A$, $A^\dagger A$ has a positive square root?
In the Polar Decomposition section in Nielsen and Chuang (page 78 in the 2002 edition), there is a claim that any matrix $A$ will have a decomposition $UJ$ where $J$ is positive and is equal to $\sqrt{A^\dagger A}$.
Firstly, how can we ... | 20240930 |
2024-07-17T14:25:36.603 | {
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"answer_view_count": 0... | stackexchange | Are operators unitary on a real quantum computer?
The question is more from the physical side of quantum computers. Can we say that operators are unitary or due to the NISQ nature, the operator (impact on particles) in reality deviates from this property? Links to primary sources are welcome.
A unitary operator rep... | 20240930 |
2021-06-17T15:47:55.243 | {
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"answer_view_count": 0... | stackexchange | Can Kraus operators change a mixed state into a pure state?
It seems that Kraus operators cannot change a pure state into a mixed one (wrong). For any pure state can be written as $|\psi\rangle\langle\psi|$, so after the Kraus operators. It becomes $$\sum_l\Pi_l|\psi\rangle\langle\psi|\Pi_l^\dagger = |\phi\rangle\lan... | 20240930 |
2018-06-24T19:58:38.243 | {
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"answer_view_count": ... | stackexchange | Measuring ancillas in Shor's algorithm
When considering Shor's algorithm, we use ancilla qubits to effectively obtain the state $$\sum_x \left|x,f(x)\right>$$ for the function $f(x) = a^x \mod N$.
As I have learned it, we then measure the ancilla qubits, to obtain, say $f(x) = b$ and get the state $$\sum_{x\mid f(x)... | 20240930 |
2023-08-04T19:02:05.677 | {
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} | 2023-08-04T17:33:43.080 | quantumcomputing_stackexchange_com-33683-33685 | {
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"answer_last_editor_user_id": 119,
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"answer_view_count":... | stackexchange | Injecting arbitrary rotations into the surface code
I'm trying to find an exact resource count for specific QFTs.
A QFT generally needs small power-of-two rotations. These can be constructed out of Clifford+T, but I'm wondering if one can inject them directly into a surface code and do some gate teleportation.
One ... | 20240930 |
2018-10-18T10:22:05.653 | {
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"answer_view_count":... | stackexchange | How is computation done in a 2D surface code array?
In a 2D surface code lattice, there are some data qubits and some measurement qubits. Suppose we want to do a 2-qubit computation, for example, let say, an X-gate on qubit-1 followed by a CNOT gate with qubit-1 as the control bit and qubit-2 as the target bit.
Q: H... | 20240930 |
2018-03-25T20:16:47.497 | {
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"answer_view_count":... | stackexchange | What is the mathematical justification for the "universality" of the universal set of quantum gates (CNOT, H, Z, X and π/8)?
In this answer I mentioned that the CNOT, H, X, Z and $\pi/8$ gates form a universal set of gates, which given in sufficient number of gates can get arbitrarily close to replicating any unitary... | 20240930 |
2018-10-19T13:16:01.027 | {
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"answer_view_count"... | stackexchange | Practical implementation of Hamiltonian Evolution
Following from this question, I tried to look at the cited article in order to simulate and solve that same problem... without success. Mainly, I still fail to understand how the authors managed to simulate the Hamiltonian evolution through the circuit shown at the bo... | 20240930 |
2018-04-22T06:17:33.763 | {
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} | 2018-04-21T11:24:29.037 | quantumcomputing_stackexchange_com-1855-1856 | {
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"answer_view_count"... | stackexchange | What counts as an "ancilla" qubit?
I am getting confused about the meaning of the term "ancilla" qubit. It's use seems to vary a lot in different situations. I have read (in numerous places) that an ancilla is a constant input - but in nearly all of the algorithms I know (Simion's, Grover's, Deutsch etc) all the qubi... | 20240930 |
2021-05-06T15:08:18.887 | {
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"answer_view_count... | stackexchange | Is there any way to obtain the number of qubits of a given backend in Qiskit?
I'm testing out a program in different IBMQ mock backends, and I want the program to use the maximum number of qubits in each case. Is there any function/method to extract the number of qubits of a given backend, so that I don't have to man... | 20240930 |
2022-08-11T22:16:33.770 | {
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"answer_view_count... | stackexchange | Swap test vs measurement in a specific basis
I have two states $|\psi\rangle$ and $|\phi\rangle$. The swap test allows to estimate $|\langle \psi | \phi \rangle|^2$ by using the controlled SWAP gate and a couple of Hadamard gates. To obtain the estimate we repetitively measure the first qubit in the computational bas... | 20240930 |
2024-03-03T14:41:09.943 | {
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} | 2020-07-04T22:21:32.010 | quantumcomputing_stackexchange_com-12785-12817 | {
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"answer_last_editor_user_id": 2927,
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"answer_view_count... | stackexchange | Can you transform a quantum program into an arrangement of slits?
Is it possible (in theory) to convert any problem that can be solved on a quantum computer into an arrangement of slits carved into a piece of metal foil, and then to run the program by shining light on the foil and observing the pattern of light that... | 20240930 |
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"answer_view_count"... | stackexchange | What is the matrix for the operator that implements a function to tell the parity of its argument?
$\newcommand{\qr}[1]{|#1\rangle}$ I gave myself the task of building an operator that implements the following function: $f(0) = 0$, $f(1) = 1$, $f(2) = 1$, $f(3) = 0$. I restricted myself to $x$ up to 2 bits. That is, ... | 20240930 |
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"answer_view_count... | stackexchange | Compute the large $n$ distribution of $|\langle z_i|\psi\rangle|^2$ over Haar random quantum states
Let $|\psi\rangle$ be a $n$ qubit Haar-random quantum state. I am trying to show that in the limit of large $n$, for each $z_{i} \in \{0, 1\}^{n}$, $$ |\langle 0|\psi\rangle|^{2}, |\langle 1|\psi\rangle|^{2}, \ldots, |... | 20240930 |
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