Questions tagged [hadamard-test]
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14
questions
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Modified hadamard test with $O(\frac{1}{\epsilon})$ samples using amplitude estimation
On the wikipedia entry for the Hadamard test, it mentions the test can be used with amplitude estimation to only require $O(\frac{1}{\epsilon})$ samples, rather than $O(\frac{1}{\epsilon^2})$ samples. ...
0
votes
1
answer
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views
Realization of the gate $(I\pm U)/2$
The state after applying the Hadamard test (before measurement)
is $$\newcommand{\ket}[1]{|#1\rangle}\newcommand{\bra}[1]{\langle#1|}\ket{0}\frac{I+U}{2}\ket{\psi} + \ket{1}\frac{I-U}{2}\ket{\psi}.$$
...
- 311
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Removing ancilla qubit from circuit with Hadamard test controlled-Z gate
I want to remove the ancilla qubit from the following quantum circuit:
Is this possible?
The final state of $\newcommand{\ket}[1]{\vert#1\rangle}\newcommand{\bra}[1]{\langle#1\vert}\ket{\psi_1}$ is $\...
- 311
2
votes
0
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Efficient way to compute the $L^1$ norm of quantum state
We all know that the $L^2$ norm
$$
||\psi||_2 = \sqrt{\sum_i |c_i|^2}
$$
of a quantum state $|\psi\rangle = \sum_i c_i |i\rangle$ is always equal to $1$. It is possible to compute the $L^1$ norm
$$
||\...
- 181
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votes
1
answer
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Generalized version of the Hadamard test for $\text{Re} \langle \phi | U | \psi \rangle$
I am wondering if it is possible to generalize the Hadamard test for computing $\text{Re} \langle \phi | U | \psi \rangle$ (different states for left and right operands).
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1
vote
1
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Was Deutsch contemplating a positive-operator valued measurement to distinguish balancedness from constancy?
This is a follow up to a couple of questions on Deutsch's foundational paper on quantum Turing machines. In it, he determines $f(0)\oplus f(1)$ with a single query by measuring a state prepared as $\...
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Given three quantum states, how to compute the triple product of amplitudes $\sum_i u_i v_i w_i$?
Assume I have three quantum states $|u\rangle$, $|v\rangle$ and $|w\rangle$ which can be obtained with three quantum circuits $U$, $V$ and $W$.
We know that we can easily estimate the inner product $\...
- 181
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What is a Hadamard test?
What is a Hadamard test? I have seen this term at many places in video lectures and on various weblinks.
A detailed answer on this would be a great help. This is what Wikipedia says, but I really ...
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How to modify the Hadamard test for a non-unitary operator
Assuming I am doing statevector simulations, I need to compute an inner product of the type
$$
X_b = \langle\psi | I_0^{\otimes (n-1)} \otimes X | \psi \rangle,
$$
where $\psi$ is a generic input ...
- 181
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votes
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Compute the inner product with an operator given by the tensor product of two tensors
Assume I have a quantum register made of $N$ qubits.
Assume I want to compute the inner product
$$
\langle \psi|I_{n_y} \otimes A_{n_x}| \psi \rangle .
$$
Note that I am using statevetor ...
- 181
-1
votes
1
answer
97
views
Help in understanding the algebra of hadamard test
I am new to quantum computing and was looking through the jupyter notebook of Variational Quantum Linear Solver by Qiskit. I came across the hadamard test and was not understanding how it works.
It is ...
- 27
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votes
1
answer
465
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Fidelity (overlap) test over reduced density matrices on quantum circuit
The inner product between two quantum states
$\rho(x_1) = U(x_1)|0\rangle\langle 0| U^\dagger(x_1)$ and
$\rho(x_2) = U(x_2)|0\rangle\langle 0| U^\dagger(x_2)$ can be calculated analytically with $Tr[\...
- 795
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2
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How to transform an Hamiltonian operator to a controlled gate (Hadamard test) in Pennylane?
I would like to perform an Hadamard test on a given Hamiltonian operator $\hat{H}$ acting on a 2-qubits system. For instance, suppose $\hat{H}$ can be decomposed into a ...
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votes
1
answer
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What is the original reference for the Hadamard test?
The Hadamard test is a widely used routine in quantum computing to compute the real and imaginary part of expectation values of unitary operators. However, all papers I have come across in the ...
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