All Questions

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 ...

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 ...

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 ...

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^{-...

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 ...

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 ...

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 ...

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: ...

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, ...

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 $...

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 ...

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 ...

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 ...

I have recently started with quantum computing and created a quantum teleportation circuit to transmit a qubit state from q_0 to ...

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

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\...

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\...

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 ...

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 ...

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||...

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

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 ...

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 ...

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 ...

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 ...

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

Executing the following: ...

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: ...

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

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 ...

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

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? ...

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. ...

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 $m$ ...

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?

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

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 $\...

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 ...

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-...

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 ...

If I from qiskit.quantum_info import random_unitary and then random_unitary(2**number_of_qubits) What returns is a unitary ...

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 ...

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 ...

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 ...

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 ...

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 \...

I have been trying to execute the quantum circuit in the backend of the IBM 16 qubit Melbourne machine. I end up getting ...

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....

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 ...

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. ...