Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

Questions tagged [unitary]

14 questions
6
votes
2 answers

Is it possible to have a trace fidelity of 1 even if two unitary operations are different?

The gate fidelity of two quantum unitary operations is often described using $\frac{1}{2^n}|\text{tr}(U^\dagger V)|$. Is it ever possible that $U^\dagger V \ne I$ however $\frac{1}{2^n}|\text{tr}(U^\dagger V)| = 1$? Specifically, is it possible to…
smi
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4
votes
2 answers

Is any multi-qubit unitary operation a rotation about a specific unit vector?

I understand that any single qubit unitary operation can be expressed as a rotation around a three dimensional unit vector. Is it possible to do the same for multi-qubit unitaries? Can I express an $n$-qubit unitary operation as a rotation about…
smi
  • 163
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3
votes
1 answer

How to select the embedded matrix in a unitary encoding?

I embed a matrix M in a U unitary, where $M$ is $2^n \times 2^n$, and $$U = \begin{bmatrix}M & *\\ * &*\end{bmatrix}$$ with twice as many rows and columns.. I prepare a state vector with the first qubit being $|0\rangle$, that is $$ |0\rangle…
Matyas
  • 135
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2
votes
0 answers

Expectation value of an ensemble composed of multiplying the same Haar random unitaries

Let $U$ be an $n$ qubit Haar random unitary and $\mathbb{I}_n$ is the $n$ qubit identity operator. I want to find the density matrix corresponding to the following: $$ \rho = \underset{U}{\mathbb{E}}\left[ (\mathbb{I}_{n-1} \otimes U \otimes…
BlackHat18
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2
votes
1 answer

When performing a projective measurement on a subsystem X entangled with another system Y, can the evolution of Y be unitary?

I am interested in the evolution of a subsystem Y entangled with another subsystem X. X and Y are initially in a pure product state. They undergo some global joint evolution E (not necessarily unitary), after which they are entangled with each…
Bidule
  • 21
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2
votes
1 answer

Unitary Transformation for QFT with 2 base states is giving the columns in the wrong order

I'm trying to reproduce in Qiskit the multiplicative form of the QFT for two qubits. It is similar to what is asked in Nielsen's QCQI book in Exercise 5.2 and Box 5.1. To check the results I'm printing the unitary transformation for the Qiskit…
Gustavo Mirapalheta
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1
vote
1 answer

Proof of Monotonicity and Invariance Under Local Unitary Operations for Summed Measures

Suppose we have a set of measures $A_1, A_2, ..., A_n$ that individually satisfy the following properties: 1-Monotonicity under Local Operations and Classical Communication (LOCC) 2-Invariance under Local Unitary Operations I want a prove that…
reza
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1
vote
1 answer

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: Simulation failed and returned the following error message: ERROR: [Experiment 0]…
LukeTheWalker
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1
vote
0 answers

Implementation of the CSD Decomposition for a 4x4 matrix

I am currently reading Volume I of "Principles of Quantum Computation and Information" by Benenti-Casati-Strini. There is a section in chapter 3 which covers the decomposition of any arbitrary $2^n \times 2^n $ unitary matrix into simpler 2x2…
Malaik Kabir
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1
vote
1 answer

Why does the Solovay-Kitaev theorem use the operator norm?

In this review explaining the Solovay-Kitaev theorem, it is stated that the theorem uses the operator norm to define closeness between unitaries. This is then used to determine if a particular set of gates is universal. That is, we require the…
user290109
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0
votes
0 answers

How to see successive contraction of gates in a DAG Circuit

I have a circuit and I want to see the DAG graph at each step of a series of contraction until I get to the unitary matrix of the circuit, I put together some code that should accomplish this, but clearly I made some mistakes as I cannot understand…
LukeTheWalker
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0
votes
2 answers

How to generate a unitary matrix given a permutation of the qubits

The title explains it all, let's say that I have a unitary matrix whose effect is defined when applied to qubits 0 and 1 in order, how can I create its unitary for when it is applied to 1, 0? For two qubit gate it's trivial as that's the…
LukeTheWalker
  • 55
  • 4
0
votes
1 answer

Is it possible to exactly compile Toffoli using H and CSWAP gates and ancilla qubits?

Question: Given controlled-SWAP (CSWAP) and Hadamard (H) gates, is it possible to exactly compile the Toffoli (CCX) gate? Note that I'm not looking for an encoded Toffoli gate. The answer should implement Toffoli exactly on three physical qubits.…
Jonas Anderson
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-1
votes
0 answers

Quantum circuit decomposition

I have a 4x4 unitary matrix. This should be decomposable using elementary one-qubit rotations and a maximum of 3 CNOT gates. However, when I use different qiskit codes, none of them decompose my unitary correctly. What code could I use?"?
Luci Toth
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