Newest Questions
12,410 questions
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Why can't "oblivious carry runways" be fully removed from Gidney's implementation of Shor's algorithm?
Hoping that @CraigGidney can hop in here.
I'm trying to understand oblivious carry runways and how it interplays with the rest of the windowed arithmetic implementation of Shor's algorithm as ...
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0
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15
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Removing ancilla qubits in Qiskit circuit
I want to remove the ancilla qubits from my quantum circuit in Qiskit. My MWE below contains four qubits: psi0, psi1, ...
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2
answers
40
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How can contantenated codes help qubits be robust to ionizing radiation?
In Quantum error correction below the surface code threshold, it was discovered that correlated errors set a noise floor of $10^{-10}$ for Willow. In Beyond NISQ: The Megaquop Machine, Preskill's ...
- 1,993
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16
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dynamically updating the states of individual qubits in a composite \( n \)-qubit system
Here’s the scenario:
I am working with a 6-qubit composite state, where the first three qubits $( e_1, e_2, e_3 )$ represent electron spin qubits, and the last three $( n_1, n_2, n_3 $) represent ...
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1
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43
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Showing $H(B)_\omega \leq H(B)_\rho$ via concavity of von Neumann entropy
Denoting in the following $\phi$
with a pure state and $\tau$ as the maximally mixed state, furthermore $p\in[0,1]$.
In Wilde's quantum information theory book, according to eq. 20.111,
by the ...
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19
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What systems might be modeled by an Ising model Hamiltonian with interactions $J_{ij}=\frac{(i^d+j^d)(1-\delta_{ij})}{N^d}$?
I’m considering a fully connected Ising model with a Hamiltonian of the form
$$ H = \sum_{i<j} J_{ij} S_i S_j ,$$
where $ S_i = \pm 1 $ represents the spin of each particle, and the sum is over all ...
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38
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How is fault tolerance possible when external environment can become entangled with your qubits destroying any possible interference?
How is fault tolerance possible when external environment can become entangled with your qubits destroying any possible interference. How are these kind of errors corrected?
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2
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21
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Determining Transformations Between Stabilizer Generators for Large Qubit Systems
I’m currently exploring stabilizer states in quantum computing and have a specific question regarding the transformation of stabilizer generators.
For example, consider the initial stabilizer ...
- 101
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15
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VQE for Max-Cut: Low Approximation Ratio (0.2 - 0.5) Instead of Expected 0.7 - 0.9
I am working on implementing a Variational Quantum Eigensolver (VQE) to solve the Max-Cut problem. I am using the approximation ratio (AR) as the metric to quantify the results, which is typically ...
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83
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Can a quantum state be prepared to encode two pieces of information, allowing a choice of which to read?
Can I prepare a quantum state encoded with, let's say, two bits, but it's only possible to read only one of the bits? But the catch is that it's possible to choose which bit you want to read; after ...
- 139
2
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1
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181
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What is wrong with this argument that we only need to consider Z stabilizers?
Pardon the basic question but I am unable to wrap my head around why this argument is wrong.
Consider a single qubit $\alpha\vert 0\rangle + \beta\vert 1\rangle$. I want to track its evolution under ...
- 23
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40
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How to use Qiskit translation pass manager with Clifford + T gate basis?
Context
In qiskit, the translation stage of the transpilation "translates (or unrolls) the gates specified in a circuit to the native basis gates of a specified backend." (cf doc)
For that, ...
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1
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68
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Prove the expression $\|A\|_p=\max_{\|B\|_q\le 1} {\rm tr}(A^{\dagger}B)$ for the $p$-norm in terms of its Hölder dual $q$-norm
I'm trying to prove
\begin{align}
\|A\|_p = \max_{\|B\|_q\leq 1} {\rm tr}\{A^{\dagger}B\},
\end{align}
where $\|\cdot\|_p$ is the Schatten p-norm, and p and q are Hölder conjugates.
What I have now is
...
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20
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Procedure for constructing magic state gate injection gadgets
I have a quantum computer that cannot implement the gate $U$ by itself, and needs help in the form of a magic state $|U\rangle$ held in another register. Is there a general-purpose procedure for ...
4
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1
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181
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Prove that spectral decomposition is the minimal ensemble decomposition
I understand that the spectral decomposition of a density matrix
$\rho$ expresses it in terms of its eigenvalues and eigenvectors:
$$\rho=\sum_i\lambda_i\left|\psi_i\middle\rangle\!\middle\langle\psi\...
1
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1
answer
44
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CNOT gate on an entangled target qubit
When the target qubit of the CNOT gate is in an entangled state, it is understood that the CNOT gate affects that one only and not the qubit entangled with target one. This follows from a recent reply ...
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50
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Does quantum algorithm guarantee to solve a combinatorial problem?
One of the applications of quantum computing is to solve practical problems faced in other fields, such as combinatorial problems. One route is encoding the problem into a Hamiltonian and then finding ...
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1
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1
answer
36
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Qiskit simulation failed and returned the following error message
I am trying to compute some unitary matrix for some big circuit on GPU using qiskit-aer, specifically a 11 qubits circuit with the following error:
...
2
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35
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Much as we have Recursive Bernstein-Vazirani, can we construct Recursive Wordle?
Initially when I first saw an old question about using a quantum computer to solve Wordle, I had dismissed it as nothing but a cute gimmicky mashup. But upon further consideration, the Bernstein-...
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2
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2
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663
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A proof that 4 ≥ ∞ when using the Quantum One-Time Pad
A cryptographic scheme using a $n$-bit key to hide a $m$-bit plaintext is said to be perfectly secret when, without this key, we cannot get any information about the plaintext from the ciphertext. ...
1
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2
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87
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Why is an operator unitary if and only if its matrix representation is unitary?
I am currently reading Nielsen & Chuang's "Quantum Computation and Quantum Information". In it, for an operator (= a linear function) $f\colon V \to W$, the linear operator $f^\dagger$ ...
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59
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CNOT gate when the target qubit is in entangled state
I want to understand how to derive the result of applying a CNOT gate to a state where the target qubit is in an entangled or Bell state. I have read that the first qubit remains the same, as expected ...
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43
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Operation 'sx' is not defined for this system
Any one knows how to resolve the below error:Operation 'sx' is not defined for this system. The below code works really well with ...
- 219
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0
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28
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Stabilizer states entanglement entropy
I am trying to calculate the entanglement entropy of N qubits of stabilizer states. I have seen the following QCSE post: Measuring entanglement entropy using a stabilizer circuit simulator, where it ...
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6
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3
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280
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Does the matrix representation of quantum gates depend on the basis?
I have read that I can chose any orthonormal basis $\{|0⟩, |1⟩\}$ of $\mathbb{C}^2$ as my basis states for a single qubit. Usually $|0⟩ = \begin{pmatrix}1\\0\end{pmatrix}$ and $|1⟩ = \begin{pmatrix}0\\...
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1
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59
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Why does the error is always logical NOT when MWPM fails?
Consider the decoding of noisy syndrome using pymatching (as shown here) for the repetition code. The logical operator in this case is simply identity matrix. One could write the python code as
...
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44
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Compiling logical operators from joint measurements
Lattice surgery on surface codes, and recent generalisations to QLDPC codes, perform computation via sequences of joint logical measurements.
A lot of work has gone into reducing the space-time ...
- 143
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Periodic electric field link operator in QuSpin
I am trying to implement a truncated bosonic Hilbert space as described in Eqs. (15) and (16) of this paper on simulating the Schwinger model. However, I am unable to implement the "periodic ...
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76
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How to obtain the set of stabilizer generator of a code, from stabilizer of its circuit tableau simulation
What is the relationship between the stabilizer generator of a quantum stabilizer code, and the stabilizer generator of its circuit tableau? I notice some difference for cases.
I use Stim to simulate ...
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21
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What is the difference between `HighLevelSynthesis` and `UnrollCustomDefinitions` qiskit transpilation passes?
The doc for UnrollCustomDefinitions indicates :
...
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1
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1
answer
129
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What does the inequality $\sum_k A_k^* A_k \leq I$ represent in Kraus' theorem?
Nielsen and Chuang's statement of Kraus' Theorem includes the inequality
$$ \sum_k A_k^* A_k \leq I.$$
What does this inequality represent? What quantities are being compared by this symbol?
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21
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VibrationalStructureProblem in Qiskit with PySCF
I am looking for some example code that solves the Vibrational Structure Problem in Qiskit using PySCF driver (not Gaussian) using a recent version of Qiskit (1.2 or 1.3), preferably with UCCSD ansatz....
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42
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Trying to run a VQE problem on Qiskit runtime
I am trying to find the ground state of a LiH molecule using qiskit runtime instead of the Estimator primitive. I am basically using the exact code given in the documentation here as a trial. But ...
2
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0
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39
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Does correcting a density matrix to be positive semi-definite affect its concurrence?
I am working on calculating the concurrence of a two-qubit system, and I encountered an issue where my density matrix occasionally has small negative eigenvalues due to numerical errors in my ...
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24
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equivalent expression of the uncertainty principle in the presence of quantum memory [duplicate]
I'm reading the paper The Uncertainty Principle in the Presence of Quantum Memory. In the appendix the authors say that expression (2) is equivalent to (3). However, R is a mapping performed on system ...
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0
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94
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Is there a name for this complexity class?
Let me use the ad hoc name weak-$BQP$ for the class obtained from $BQP$ by the following modification: Given a problem instance $x$ with correct solution $y\in \{0, 1 \}^n$, the circuit $C_{|x|}$ ...
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84
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Finding solutions to commutation relation
In a Hilbert space of dimension $d$, a positive definite operator $A>0$ is given. I would be interested in the set of operators $B>0$ such that there exists some $C>0$ that satisfies:
$$i[A,B]...
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1
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61
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Pauli Twirling not increasing Circuit depth?
This paper talks about the properties of Pauli twirling a circuit. Pauli twirling is a technique that converts arbitrary quantum noise into Pauli errors by applying random Pauli gates before and after ...
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1
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62
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Linear combination of unitaries with Qiskit circuit
I'm reading the PennyLane tutorial on linear combination of unitaries (LCU) algorithm. Does Qiskit have any in-built functions that let me do the same thing?
Specifically, I want to build a circuit (...
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0
answers
25
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How do I analytically calculate the fidelity of a GHZ state produced by the photonic cluster state generation circuit?
In this paper, a GHZ state may be produced by a circuit where a spin qubit is entangled with N photon qubits by CNOTs.
How would I calculate the fidelity of a GHZ produced by this protocol, where an ...
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3
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136
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Intuition about [8,3,2] code
Is there any intuition why this code would support logical CZ between any two logical qubits and transversal CCZ gate? What intrinsic property supports this? Can we possibly have a family of codes ...
- 426
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255
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Simple successor gate
I want to create a gate that, given a sequence of qbits that encode n, transforms that sequence in n+1, in other words the successor function. I managed to do it in qiskit by writing this:
...
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47
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Reset channels for two-qubit space
In the paper "Unbiased Simulation of Near-Clifford Quantum Circuits" by Ryan S. Bennink et al. (arXiv) the authors define a Pauli reset ("Pauli measurements followed by Clifford ...
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58
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Verifying the eigenvectors of Grover Operation Q in Brassard's Amplitude Amplification and Estimation
This question is regarding Brassard's et al. Quantum Amplitude Amplification and Estimation (arXiv).
Specifically, I fail to understand why $|\Psi_\pm\rangle = \frac{1}{\sqrt{2}}\Bigl( \frac{1}{\sqrt{...
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69
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Eigenvalues of Q operator in Brassard's Amplitude Amplification
Regarding Brassard's et al. Quantum Amplitude Amplification and Estimation (arXiv) in which they define
$$
Q = -AS_0A^{-1}S_x
$$
And say
Consider the orthogonal complement $H^{\perp}_{\psi}$ of $H_\...
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1
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135
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What is the length scale of correlated errors observed on the 72-qubit google chip used in the quantum memory experiment
I would like to have a rough idea of the length-scale over which the correlated errors of unknown origin have been observed in the Google quantum memory experiment.
One possible way to deduce this ...
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37
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How to train QNN on qiskit or ionq simulators
I am trying to train a QNN using qiskit and ionq, the method I use now is to manually feed my input data into quantum circuits:
...
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1
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76
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Applying local unitary operator of one qubit on an entangled state
Suppose I have the following Bell state where
$$|\psi\rangle=\frac{1}{\sqrt{2}}\begin{pmatrix} 1 \\ 0 \\ 0 \\ -1\end{pmatrix}$$
And the following unitary operator
$A(\theta_{1})$ and $B(\theta_{2})$ ...
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11
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Are there any limit in the number of mid-circuit measurements when running a circuit on IBM QPU?
I am struggling to run circuits on IBM quantum hardware. Is it possible that my circuit is overcoming some limits in the number of mid-circuit measurements per qubit? Actually, I am asking for ...
- 11
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53
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Making a superposition proportional to a 1-cosine envelope
Here is a simple circuit that produces a superposition proportional to a sine envelope $\sum_{k=0}^{n-1} \sin(\pi k/n)$:
Is there also a simple circuit to prepare a 1-cosine envelope? A state ...
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