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SWAP test and density matrix distinguishability

Let us either be given the density matrix $$|\psi\rangle\langle \psi| \otimes |\psi\rangle\langle \psi| ,$$ for an $n$ qubit pure state $|\psi \rangle$ or the maximally ...
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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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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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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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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: ...
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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 (...
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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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 ...
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]: \sigma = \...
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$E(U_j,V_j)\leq\Delta/(2m)$ 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 ...
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 ...
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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 ...
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 ...
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 ...
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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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 : ...
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 $|0\rangle$, $|1\rangle$, $|+\rangle$, $|−\rangle$ ...
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 ...
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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 ...
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 ...
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 $\{|k\rangle,k=0,1,...N-1\}$. ...
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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 ...