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9 views

SWAP test and density matrix distinguishability

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 ...
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0answers
20 views

how to simulate toric and surface codes with stim + PyMatching

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 ...
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0answers
9 views

ATS Sparse Hamiltonian Simulation notation

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 $k$ ...
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0answers
23 views

What is the best way to get started on quantum finance?

What is the best way to get started on quantum finance? Any books, websites or learning material you can advice?
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0answers
19 views

Two body integral calculation taking too long

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: ...
0
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1answer
30 views

Is it possible to collapse a superposition into a preset state such that all entangled qubits collapse to the same state?

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 (...
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0answers
34 views

In quantum error correction using repetition codes, how would I decode an even # of repetitions with errors on half the qubits using majority voting? [closed]

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?
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1answer
34 views

How is transformation for measurement in an arbitrary basis derived?

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 ...
2
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1answer
29 views

How to write the covariance matrix of a quantum gaussian state as a function of photon numbers?

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 = \...
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0answers
15 views

$E(U_j,V_j)\leq\Delta/(2m)$ if probabilities of outcomes obtained from the approximate circuit is within a tolerance $Δ>0$

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 ...
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0answers
18 views

What exactly happens in a quantum annealing process?

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 ...
2
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1answer
55 views

Computing expectation value of a Pauli string on stabilizer states

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 ...
1
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0answers
12 views

How to take 3-point or more correlators into edge probability computation in surface code decoding?

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 ...
1
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0answers
20 views

Why we need real-time feedback of Surface Code Decoding results?

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 ...
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1answer
23 views

Knill Laflamme conditon

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 $|\psi\rangle \otimes |0\rangle_E$. ...
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2answers
58 views

How to perform encoding and syndrome measurement in stim

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

Why does quantum distinguishability ensure no faster-than-light communication?

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 $|0\rangle$, $|1\rangle$, $|+\rangle$, $|−\rangle$ ...
3
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2answers
568 views

Why is there there an infinite number of possible bases but only a finite number of measurement outcomes

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 ...
4
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1answer
72 views

What is the structure of coefficients of $2^N\times 2^N$ unitary matrices decomposed in terms of the Pauli basis?

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\...
1
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1answer
37 views

In Schumacher’s noiseless channel coding theorem, how do we get the exponents in $|0\rangle ^{\otimes n(1−p)/2}|1\rangle ^{\otimes n(1−p)/2}$?

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 ^{\...
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0answers
25 views

How can I get fidelity of a gate from randomized benchmarking?

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 ...
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0answers
20 views

Notation to Replace the Input to a Function [closed]

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 ...
2
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0answers
63 views

How to show that Werner states produce correlations explainable via local hidden variable models?

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 ...
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0answers
26 views

How to write a code to made envelope function equal to $\pi$ to result in an X gate?

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

How does quantum metrology realized in experiment now?

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 ...
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0answers
21 views

How do you access stored Ramsey experiment frequency?

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?
6
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0answers
58 views

Review paper on depth, qubits and $T$ gates number on Clifford+T decomposition for various "typical" algorithms

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 ...
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1answer
36 views

Compute expectation value of an operator in openfermion

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 ...
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0answers
28 views

How to determining whether certain dynamical processes are elementary? [closed]

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 ...
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1answer
45 views

Decomposition of U1 gate $U_1(\lambda)$ , Phase Shift gate $\phi(\delta) $, and Swap gate [closed]

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{...
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1answer
18 views

Q#/VS: No namespace with the name "Microsoft.Quantum.Canon" exists

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 ...
1
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0answers
32 views

How to understand picking a random subcube in the Aaronson/Ambainis spatial search algorithm?

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 ...
1
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1answer
58 views

How to compute the measurement probabilities of $|\phi\rangle=\sum_k c_k |k\rangle$ in a rotated basis $V|k\rangle$?

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 $\{|k\rangle,k=0,1,...N-1\}$. ...
1
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1answer
41 views

What is the syntax for general control gate in stim

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,...
5
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1answer
249 views

What is the motivation for using dual lattice in the surface code?

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 ...
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0answers
20 views

Working with higher energy states in Qiskit Experiments

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 ...
4
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2answers
54 views

Can error correction for a classical algorithm with bit flips be easier than for a general quantum circuit?

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 ...
3
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1answer
37 views

Using Classical Shadow to predict quantum state's fidelity has nothing to do with the dimension of the density matrix?

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)*...
1
vote
1answer
23 views

how to know the appropriate time to know the SWAP gate operation in dipole interaction

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 ...
6
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3answers
647 views

Quantum advantage with only Clifford gates (Gottesman Knill theorem)

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 ...
4
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0answers
72 views

Can changing reference frames generate entanglement in identical particles?

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 ...
2
votes
1answer
60 views

How to import a generic stabilizer code in stim

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 ...
2
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2answers
47 views

How does the formula for the parameter shift rule change if we measure in the $X$ basis?

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}{...
3
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0answers
57 views
+150

Conditional lower bound on approximate stabilizer rank of magic states

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 ...
3
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0answers
38 views

What does the $I$ mean when measuring ${\rm Tr}(\rho (I\otimes\sigma\otimes\cdots))$ in quantum tomography?

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,\...
5
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2answers
305 views

What is the computational complexity in initializing a quantum register?

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 ...
0
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0answers
13 views

Confusion about Mitiq folding for zero noise extrapolation

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 ...
0
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1answer
39 views

Random circuits with google cirq

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 ...
2
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2answers
36 views

Optimal decompositions of some standard multi-qubit gates

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 ...
0
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1answer
21 views

have to process 512×512 pixel image will it be possible in Qiskit. what hardware requirement will be?

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 ...

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