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4 views

How close or far apart are the distributions generated by two Haar random states?

Consider two $n$ qubit Haar-random quantum states $|\psi\rangle$ and $|\phi\rangle$. Let $D_{|\psi\rangle}$ and $D_{|\phi\rangle}$ be the two probability distributions (over $n$-bit strings) obtained ...
1
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2answers
8 views

Maximum number of qubits suppoted by the Qasm simulator

By using the Qiskit qasm-simulator, I want to simulate a quantum circuit of 40 qubits. However, the number of qubits 40 is greater than maximum number (24) for qasm-simulator. Is there any possibility ...
0
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0answers
7 views

Numerical optimization of QRAC

I need to optimize a general version of 3$\rightarrow$1 QRAC where Bob is asked to retrieve one of the XOR combinations of the bits( If ABC is the given string to Alice, then Bob would be asked to ...
1
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1answer
22 views

Changing the sign of relative phase

Say I have a qubit in the state (ignoring normalization) $$|\phi\rangle = \alpha|0\rangle + e^{i\alpha}\beta|1\rangle.$$ How can I invert the sign of its phase, thus making it $$\alpha|0\rangle + e^{-...
0
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1answer
30 views

A CNOT between two Hadamard gates: why does the CNOT changed the output of the second Hadamard gate?

Applying the Hadamard gate twice in a row, it restores the original input: https://algassert.com/quirk#circuit={%22cols%22:[[%22H%22],[%22H%22]]} However, if a CNOT control is added between the two ...
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0answers
22 views

What does it mean “the N uses of classical-quantum channel”?

I was reading a paper "Quantum Polar codes by M.M wilde", where he discusses the N uses of the channel in the classical-quantum channel setting. What does he mean by "multiple channel ...
2
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1answer
48 views

IBMQ: Can I implement a quantum measurement in the middle of a quantum circuit?

I am executing a quantum circuit on an IBM quantum device. The circuit is simple: A single qubit (start from $|0\rangle$), Rx($\pi/2$) Measure (in z) 3 .Rx($-\pi/2$) Measure (in z) The final ...
1
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1answer
23 views

How to measure a quantum circuit's execution time on a real IBM device?

I am executing a quantum circuit on an IBM quantum device and I need to start a timer as soon as the job in the queue starts running. I have already used: ...
0
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0answers
15 views

RAC for XOR functions

I need the optimal encoding protocol for 3 $\rightarrow$ 1 Classical RAC such that the receiver is able to retrieve any one of the initial bits, as well as the XOR combinations of those bits. ( If a, ...
2
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2answers
64 views

In shadow tomography, how is the state reconstructed from its shadows?

I'm reading Huang et al. (2020) (nature physics), where the authors present a version of Aaronson's shadow tomography scheme as follows (see page 11 in the arXiv version): We want to estimate a state $...
3
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1answer
70 views

Is there an efficient way to realize a Toffoli with control qubits fixed at $|+\rangle$?

I wrote a circuit that makes use of Toffoli gates, but it is too inefficient for my purpose. In my circuit the states of control qubits are fixed to $|+\rangle$ state. So I wanted to know if there is ...
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2answers
104 views

Question about a circuit from “Quantum Computing for Computer Scientists”

I am trying to implement a basic quantum computing emulator. In the chapter on Grover's algorithm, we're shown the following circuit: They demonstrate Grover's algorithm with a function $f$ that ...
3
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0answers
82 views

Which codes can implement transversal non-Clifford gates

A paper Three-dimensional surface codes: Transversal gates and fault-tolerant architectures discusses 3D surface codes and shows that CZ and CCZ gates are transversal in [these] codes. They give a ...
2
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1answer
56 views

Can I teleport a string of 0s and 1s?

I have recently started with quantum computing and created a quantum teleportation circuit to transmit a qubit state from q_0 to ...
4
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0answers
63 views

In Nielsen and Chuang, how can $\frac{1}{2(e-1)}$ result from $\frac12\int_{e-1}^{2^{t-1}-1}dl\frac{1}{l^2}$?

From Nielsen and Chuang's book: $\textit{Quantum computation and quantum information}$, how can (5.34) equal (5.33)? I.e. $$\dfrac{1}{2} \int_{e-1}^{2^{t-1}-1} dl \dfrac{1}{l^2} = \dfrac{1}{2(e-1)}.$$...
2
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1answer
62 views

Discrepancy in inner product between tensor products

I have noticed one identity in case of tensor product from this post. But I can't understand why it is true. $\langle v_i| \otimes \langle w_j| \cdot |w_k\rangle \otimes |v_m\rangle = \langle v_i|v_m\...
1
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1answer
47 views

Inequality in overlap of quantum states

For quantum states $\vert\psi_1\rangle, \vert\psi_2\rangle, \vert\phi\rangle$, is it true that $$\tag{1}\langle \phi\vert\psi_1\rangle\langle\psi_1\vert\phi\rangle\langle \phi\vert\psi_2\rangle\langle\...
4
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0answers
41 views

How do we realise photonic gates?

I am interested in photonic computing, and I am curious how the gates work. I once saw a picture of a photonic CNOT gate that used just mirrors and polarizers. I have not been able to find any ...
3
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2answers
106 views

Does 1 qubit correspond to 2 bits?

In a lot of presentation I always see people say that $n$ qbit are approximately $2^n$ classical bit. Those talks where oriented for a broad audience, so they left out a lot of things. Deep down I ...
2
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1answer
42 views

In Uhlmann's theorem, should the polar decomposition be written as $A=|A|V$ or $A=V|A|$?

In the proof of Uhlmann's theorem, the book writes the polar decomposition: $A = |A|V$, with $|A| = \sqrt{A^\dagger A}$. Shouldn't it be $V|A|$ instead? The former case is $A^\dagger A = V^\dagger|A||...
3
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0answers
34 views

IBMQ backends: How can I know the repetition rate and depth limits of real devices?

When trying to execute complex quantum circuits on IBMQ real devices, one can encounter a typical error (ERROR_RUNNING_JOB) with the message ...
2
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0answers
33 views

In QAOA why do we need $m \log(m)$ repititions to get at least $F_{p}(\beta , \gamma) - 1$ with probability of $1 - 1/m$?

In the original QAOA paper from Farhi https://arxiv.org/pdf/1411.4028.pdf, it is stated in chapter 2 last paragraph (page 6) that: when measuring $F_{p}(\beta , \gamma)$ we get an outcome of at least ...
2
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0answers
54 views

How to write the classical algorithm for lights out problem?

I am very new to quantum computing and I have started learning the concepts watching the IBM summerschool videos and trying to solve the IBM quantum challenge problems. One of their problems is ...
3
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1answer
60 views

How are the eigenvalues of $\rho=\frac12(|a\rangle\!\langle a| +|b\rangle\!\langle b|)$ derived?

Let's say I have a density matrix of the following form: $$ \rho := \frac{1}{2} (|a \rangle \langle a| + |b \rangle \langle b|), $$ where $|a\rangle$ and $|b\rangle$ are quantum states. I saw that ...
1
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1answer
60 views

CSS Code and Fault-tolerant Problem in Nielsen and Isaac Chuang‘s book

Could someone help me with $Problem-10.52$ in Nielsen and Isaac Chuang‘s book? The screenshot is shown below. I have no idea about that. Hope someone can give me some suggestions. By the way, if I ...
0
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1answer
16 views

Why do I get the error name operator is not defined?

I checked this code multiple times, I am trying to reproduce the same code using Grover's algorithm from qiskit summerschool: ...
0
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1answer
18 views

IBMQ: “Credentials are already in use”

Executing the following: ...
0
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2answers
44 views

Creating a parameterized Operator in Qiskit

I'm trying to run a VQE for a specific custom Anzats. The Anzats is built up of an unitary matrix $U_H$, which I'm trying to created in this way: ...
1
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0answers
35 views

Getting Choi-matrix of a subsystem

In Qiskit, for a given QuantumCircuit object, you can computed its Choi-matrix via the corresponding Choi object, for example: <...
2
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2answers
53 views

Is there a quantum processor with physically implemented Toffoli gate?

Recently, I came across the article Realization of efficient quantum gates with a superconducting qubit-qutrit circuit where its authors proposed a physical implementation of three qubits quantum ...
4
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0answers
35 views

Is there a good reason to use T-count minimization for circuits executed on current IBM open quantum systems (real hardware)?

As far as I understood from a series of papers, minimizing the T-count in Clifford+T circuits is essential for fault-tolerant ...
2
votes
2answers
26 views

Creating a resource count unit test in Q#

I want to create a unit test in Q# that runs an operation and asserts that it used at most 10 Toffoli operations. How do I do this? For example, what changes do I have to make to the code below? ...
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0answers
14 views

Correctly configuring a Q# test project in Visual Studio Code

I have some Q# code which I'm editing using visual studio code. The codebase is divided into a src/ folder and a test/ folder. ...
2
votes
1answer
19 views

To find the best angles in QAOA why we do not optimize over a maximum ofall shots instead of a mean?

When finding the best angles for QAOA we optimize over $F_{p}(\beta , \gamma) = \langle \psi_p(\gamma,\beta)|C|\psi_p(\gamma,\beta)\rangle $. In each optimization step we simulate the circuit $m$ ...
2
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1answer
50 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?
0
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1answer
50 views

Quantum Circuit to inverse the probability distribution

I'm using Qiskit and after running the circuit, as we all know, we get a count dictionary such as ...
4
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2answers
108 views

Is the trace distance between multipartite states invariant under permutations?

Consider two multipartite states $\rho_{A_1A_2..A_L}$ and $\sigma_{A_1A_2..A_L}$ in $\mathcal{H}_{A_1} \otimes\mathcal{H}_{A_2} \otimes...\mathcal{H}_{A_L} $. For an arbitrary permutation $\pi$ over $\...
2
votes
2answers
53 views

Does it make sense to sum two Choi operators?

I am very new to the theory of the Choi representation of quantum processes and I am learning it all by myself from research papers (especially this https://arxiv.org/abs/1111.6950) as I didn't find ...
-1
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0answers
25 views

Code keeps running job after job

I'm attempting to to run a electronic ground state energy calculator, when I send a job to the real quantum computer it will wait in the queue, run the job, give me a histogram (on the quantum-...
2
votes
0answers
51 views

Can we characterise how correlated the expectation values associated with a pair of observables are?

Consider a state $\rho$ and two observables $P$ and $Q$. Is there a good way to characterise how correlated the associated expectation values are? Be it in terms of mutual information or something ...
2
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1answer
48 views

Physical implementing random unitary

If I from qiskit.quantum_info import random_unitary and then random_unitary(2**number_of_qubits) What returns is a unitary ...
4
votes
1answer
37 views

In QAOA, why do we pick the initial Hamiltonian $B$ to be $\sigma_x$ applied to each qubit?

In QAOA 1, why do we pick the initial Hamiltonian $B$ to be $\sigma_x$ applied to each qubit? Would it be possible to pick $B$ to be an application of $\sigma_z$'s instead? Then $C$ and $B$ would be ...
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0answers
24 views

What is a “repeat until success quantum circuit” in quantum neural networks?

I am working now on a quantum neural network project and want a deep explanation on the Repeat Until Success circuit. What I know about this circuit is that it allows a nonlinear activation function ...
1
vote
1answer
60 views

Pauli Matrix tolerant and encoding

I'm stumped by these questions in Chuang's book. If I have a state $|ψ\rangle=1/2\sqrt2(1+M_0)(1+M_1)(1+M_2)|0\rangle_7$, where $$M_0=X_0X_4X_5X_6; M_1=X_1X_3X_5X_6; M_2=X_2X_3X_4X_6$$ I rewrite its ...
0
votes
2answers
68 views

Is it correct to say that when a qubit in state $|\psi\rangle$ loses its coherence it collapses to $|0\rangle$ or $|1\rangle$? [closed]

I have few questions about decoherence mechanism. I read that there are different types of decoherence, phase or "bit flip", it is the second one that I will speak about here. Is it correct ...
2
votes
1answer
60 views

Question about quantum error correction and density matrixs

I am now studying QEC and feel confused. If I have a density matrix before the correction: The circuit is: $\rho = p^0(1-p)^3|\varphi\rangle \langle\varphi|+p^1(1-p)^2\sum_{i=1}^3X_i|\varphi\rangle \...
0
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1answer
36 views

Error while trying to execute the Quantum Circuits in IBMQ

I have been trying to execute the quantum circuit in the backend of the IBM 16 qubit Melbourne machine. I end up getting ...
0
votes
1answer
40 views

Cirq.simulate expectation value of a Hamiltonian

I want to simulate the final state of an ansatz in cirq using simulate. Now I want to calculate the expectation value of a Hamiltonian. How do I do this? I can only find simulator.run examples in cirq....
1
vote
2answers
74 views

What is $\sum_{i}\langle i \vert U \vert j\rangle$ for unitary $U$?

The question is basically the title but given a unitary operator $U$ and a computational basis, can we say anything about the complex number below? $$c = \sum_{i}\langle i \vert U \vert j\rangle$$ I ...
2
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1answer
33 views

Two qubit state + Depolarizing channel = Bell diagonal state?

In multiple sources, e.g. RGK, KGR, it is stated (without proof) that if you take any two qubit state and send it through a depolarizing channel, the resulting state would be a Bell-diagonal state. ...

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