All Questions

Let us either be given the density matrix \begin{equation} |\psi\rangle\langle \psi| \otimes |\psi\rangle\langle \psi| , \end{equation} for an $n$ qubit pure state $|\psi \rangle$ or the maximally ...

According to PyMatching's github page the package can be decode toric and surface codes. Stim's example uses stim + PyMatching combination to get logical error rate vs physical error rate curves for ...

In the equations in section 3.4.2 of Aharonov and Ta-Shma's paper, they define the operator $$T_1:|k,0\rangle\rightarrow|b_k,m_k,M_k,\tilde{A_k},\tilde{U_k},k\rangle,$$ where $b_k,m_k,M_k,$ and $k$ ...

What is the best way to get started on quantum finance? Any books, websites or learning material you can advice?

I'm running the most recent version of qiskit and am trying to run H2 in the cc-pvtz basis. However, it is taking an incredibly long time. This is what my code looks like: ...

Ideally, I'd be able to apply an operation to qubit 0 that would collapse the superposition to a set state (say 1) on qubit 0 & 1. The operation applied to qubit 0 would be a one qubit operation (...

For example its easy to see that $101\rightarrow 1$, because it's an odd number of repetitions. But what would, for example, $1100$ be decoded to?

I started with Qiskit today and find it very exciting. As a first question I want to understand how to measure an arbitrary state $|\Psi\rangle$ not in the basis of ...

Assume having a one-mode quantum Gaussian state with quadrature observable vector $\hat r = [\hat q , \hat p ] $ and covariance matrix $\sigma$. According to definition [1]: \begin{equation} \sigma = \...

Suppose we wish to perform a quantum circuit containing $m$ gates, $U_1$ through $U_m$. Unfortunately, we are only able to approximate the gate $U_j$ by the gate $V_j$ . In order that the ...

I recently began to learn about quantum annealing, with focus on d-waves quantum annealers and QUBO optimization problems. By now I more or less understood the basic idea of quantum annealing. But ...

I need some help on stim, where I'm trying to compute expectation values of Pauli strings. Hopefully I did not overlook on the documentation an implementation of ...

In Google's work of repetition code (Exponential suppression of bit or phase errors with cyclic error correction), they use the method of Correlation Matrix to ...

When we use surface code to detect and correct errors, we can track the errors in software and change the computation results accordingly. So why do we need real-time feedback on decoding results? Are ...

In Preskill's notes on quantum error correcting codes in Section 7.2, there seems to be no condition on the environment part of the state, i.e. $|0\rangle_E$ in $|\psi\rangle \otimes |0\rangle_E$. ...

I can generate the encoding circuit of a stabilizer code and can read it into stim. For example for the $[[5,1,3]]$ code : ...

On page 56-57 in Nielsen and Chuang, for a proposed scenario, it's said that: if Bob had access to a device that could distinguish the four states $|0\rangle$, $|1\rangle$, $|+\rangle$, $|−\rangle$ ...

The statement in the question comes from the answer to the following question on Reddit, if more context is needed: And how does a perfect quantum computer ensure that we know for sure that the state ...

Any square $2^N\times 2^N$ matrix can be written as a sum of tensor products of pauli matrices. Eg a $8\times 8$ matrix can be written as $$U=\sum_{i_1,i_2,i_3}u_{i_1,i_2,i_3}\sigma_{i_1}\otimes\...

On pg. 55 in Nielsen and Chuang, it's said that: the $|0\rangle + |1\rangle$ product can be well approximated by a superposition of states of the form $|0\rangle ^{\otimes n(1−p)/2}|1\rangle ^{\...

I found (page 33) the method of finding fidelity from fit by "interleaved and reference decay" according to the sequence fidelity formula: $$F_{ref}=Ap_{ref}^{m}+B,$$ where $p_{ref}^{m}$ is ...

On pg. 54 in Nielsen and Chuang, it's said that: it is not surprising that similar techniques can be used to compress the source so that only $H(p, 1 − p)$ qubits are required to store the compressed ...

Werner states can be written as $$\rho_W= p\frac{\Pi_+}{\binom{n+1}{2}} +(1-p)\frac{\Pi_-}{\binom{n}{2}}, $$ with $\Pi_\pm\equiv\frac12(I\pm\mathrm{SWAP})$ projectors onto the $\pm1$ eigenspaces of ...

$$ \hat U_d = \exp\Big( -i\underbrace{\frac{Q}{2}\int_0^T A(t^\prime)\mathop{dt^\prime}}_{\Theta(t)} \hat\sigma_x \Big) $$ This equation is a Unitary transformation applied to a qubit from time $t = 0$...

Are there some lists of the method to realize quantum metrology, or rather, utilizing quantum resources to enhance the precision of parameter estimation. The experimental method I've know is listed as ...

What is the stored frequency for the Ramsey experiment and how can this stored frequency be accessed? Is there a backend.get(frequency) command for this frequency?

I am looking for some review paper providing concrete numbers about the depth, number of qubits and number of $T$ gates required on the Clifford+T basis for various quantum algorithms (quantum Fourier ...

I am trying to compute the 2-electron reduced-density matrix (2-RDM) for a given quantum state with openfermion. The code is as follow ...

In the introduction of 1.6 Quantum information in Nielsen and Chuang's textbook, it is said that one of the fundamental goals uniting work on quantum information theory is Identify elementary classes ...

Can we express U1 gate $U_1(\lambda)$ , Phase Shift gate $\phi(\delta) $, and Swap gate $$ U_1(\lambda) = \begin{pmatrix}1 & 0 \\ 0 & e^{i\lambda}\end{pmatrix}$$ $$ \phi(\delta) = \begin{...

I am trying to run a simple "Hello World" project in Q#, following this tutorial. I have completed the following steps (Step #s from tutorial link): Step 1: Installed the latest version of ...

I am referring to the Quantum Search of Spatial Regions paper. I must confess that the paper itself is a bit heavy for my level of mathematical fluency. Trying to understand it nevertheless and having ...

I came across the following question and have some conceptual questions. Consider a general quantum state $|\phi\rangle$ of dimension $N$ spanned by some standard basis $\{|k\rangle,k=0,1,...N-1\}$. ...

For a stabilizer code with the stabilizers in canonical form, an encoding circuit has the form that's a product of hadamard gates and general control gates : $H_i C_i(U_i)$. For example for the $[[5,1,...

I'm learning surface codes from a theoretical perspective. In all the literature I read, they just introduced the dual lattice for working with $Z$ strings without many words addressing why we need to ...

I'm looking at the source code for the Qiskit Experiments module and see that the EFRabi class subclasses the Rabi class with the intent of calibrating rotations between the 1 and 2 states instead of ...

Assume one runs a purely classical algorithm on $n$ logical qubits on a physical device with some bit flip probability. Can implementing error correction in this case be any easier than in the case of ...

Using classical shadow(or refer to this post for basic things about classical shadow), we can predict linear functions like $Tr(O\hat{\rho})$ with number of copies(referred paper): $$ 2\log(2M/\delta)*...

Consider dipole-dipole interaction between two qubits,$H_{int} = g \boldsymbol\sigma_{1}\cdot\boldsymbol\sigma_{2}=g(X_1X_2+Y_1Y_2+Z_1Z_2)$. How can I show that by turning on this interaction for an ...

Let's say I want to solve a computational task which input can be encoded in $n$ bits of information. The look for a quantum advantage is (usually) asking to find a quantum algorithm in which there ...

Suppose we have a pair of qubits, physically realised as two spin-half particles in some separable pure state $|\psi\rangle$, separated by a distance '$l$', large enough to be regarded as ...

I just started using stim to simulate the performance of quantum error correcting codes. I hope this is the right place to ask questions about the subject. The example code with the repetition code ...

I'm studying the parameter shift rule and got stuck when improving an example with Pauli operators in https://arxiv.org/abs/1803.00745. This paper shows up $\partial_\mu f=\frac{1}{2}(f(\mu+\frac{\pi}{...

I am currently reading about the approximate stabilizer rank and properties of the same. I will quote the definitions from this paper. The stabilizer rank of a quantum state $|\psi\rangle$ is the ...

In Nielsen and Chuang's QCQI, I learned that the quantum tomography for n qubit can be described easily in math as we need to measure $Tr(\rho W_k),\forall k$ where $W_k\in\{I,\sigma_x,\sigma_y,\...

I'm trying to figure out what is the computational complexity of initializing a quantum register of N qubits. For my research, I have used the initialize method of qiskit, in which you set the ...

I'm reading the mitiq zero noise extrapolation documentation and I just can't make sense of how the scale_factor for folding work. "The minimum scale factor is one (which corresponds to folding ...

For my dissertation I need to simulate random circuits and I have been trying to use google Cirq for that. Looking at the documentation I have seen how to create my own circuit and simulate it, but it ...

To have a concrete example in mind: 3-qubit Toffoli gate can be decomposed into 6 $CNOT$s as shown here I believe this is the most economic decomposition in terms of the number of $CNOT$s used. My ...

I'm working on Quantum image processing of satellite images. I'm completely a beginner also I'm learning it by my own that's why I need help. Can you please help me out I want to process the image of ...