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Questions tagged [unitarity]

For questions related to the unitarity (unitary evolution) of quantum systems, as applicable to quantum computing or quantum information.

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Implementing “Classical AND Gate” and “Classical OR Gate” with a quantum circuit

Quantum cNOT Gate (Classical XOR Gate) A "Controlled NOT (cNOT) Gate" flips the 2nd qubit if the 1st qubit is $\left|1\right>$, and returns the 2nd qubit as-is if the 1st qubit is $\left|0\right&...
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2answers
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How to prove that the query oracle is unitary?

The query oracle: $O_{x}|i\rangle|b\rangle = |i\rangle|b \oplus x_{i}\rangle$ used in algorithms like Deutsch Jozsa is unitary. How do I prove it is unitary?
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1answer
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Differentiate between local and global unitaries

Just like we have the PPT, NPT criteria for checking if states can be written in tensor form or not, is there any criteria, given the matrix of a unitary acting on 2 qubits, to check if it is local or ...
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3answers
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Is it correct to say that we need controlled gates because unitary matrices are reversible?

I am new to quantum computing and saw this argument on this site but I don't understand it. First of all, I don't understand what is exactly meant by 'reversible'. Because even if you had a unitary ...
6
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1answer
534 views

Decomposition of a unitary matrix

Following is an excerpt from QCQI: I can understand that this matrix satisfies a unitary matrix. Also, intuitively, I am able to understand it. However, what is the proof that any given Unitary ...
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0answers
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What do you specify when you physically apply a unitary?

In the Environment and Quantum Operations in Nielsen and Chuang, section 8.2.2, they say that when you apply a unitary on a state, you expect the output as the just the state transformed by the ...
4
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1answer
167 views

Extending a square matrix to a unitary matrix

Suppose we have a square matrix $M$ of size $n\times n$. It is given that any element $M_{ij}$ of $M$ is a real number and satisfies $0 \leq M_{ij} \leq 1$, $\forall$ $i,j$. No other property for $M$ ...
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1answer
100 views

Understanding why the modular function part of Shor's algorithm is unitary

I've been struggling to understand the modular exponent bit of Shor's algorithm. My understanding is that it takes a register in the state $\frac{1}{\sqrt{Q}}\sum_{k=1}^{Q-1} |k\rangle |0\rangle$ to ...
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1answer
101 views

Unitary gate(s) from product of exponent

Often unitary gates are defined as a product of exponentials, with some parameter in the power-term. However, often it is not clear how to construct unitary gates from it, at least not for me that is. ...
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2answers
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Unitary acting on standard qubit basis properties

If we have a $U$ (unitary with all real entries) such that: $U|0\rangle =a|0\rangle +b|1\rangle$ What is $U|1\rangle=?$ I know: the definition of what it means to be unitary ie. $U^\dagger U=UU^\...
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What do they mean by “qubit can't be copied”?

What does it mean by ''qubit can't be copied'' ? In a note, it is saying that: Copying a qubit means $$U|\psi\rangle_A|0\rangle_B=|\psi\rangle_A|\psi\rangle_B$$ i.e; applying a unitary ...
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2answers
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What is the smallest quantum circuit to produce two-qubit state (a,b,b,b)?

How can I synthesis a two-qubit quantum state of the state vector (a,b,b,b) using basic quantum-gate circuit (arbitrary single-qubit rotation and controlled $Z$ gate)? And further, can I know a given ...
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6answers
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Quantum states are unit vectors… with respect to which norm?

The most general definition of a quantum state I found is (rephrasing the definition from Wikipedia) Quantum states are represented by a ray in a finite- or infinite-dimensional Hilbert space over ...
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4answers
765 views

Why are quantum gates unitary and not special unitary?

Given that the global phases of states cannot be physically discerned, why is it that quantum circuits are phrased in terms of unitaries and not special unitaries? One answer I got was that it is just ...
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7answers
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If all quantum gates must be unitary, what about measurement?

All quantum operations must be unitary to allow reversibility, but what about measurement? Measurement can be represented as a matrix, and that matrix is applied to qubits, so that seems equivalent to ...
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1answer
492 views

If quantum gates are reversible how can they possibly perform irreversible classical AND and OR operations?

Quantum gates are said to be unitary and reversible. However, classical gates can be irreversible, like the logical AND and logical OR gates. Then, how is it possible to model irreversible classical ...