Harrow-Hassidim-Lloyd Algorithm
About Many people say that quantum computers can perform calculations faster. But what specific calculations become faster? In reality, quantum…
Quantum
kevin-tofu The difference between Eigen Decomposition and Spectral Decomposition
Spectral decomposition and eigendecomposition are both fundamental concepts in linear algebra, used to break down matrices into simpler components. While…
SU(4) is represented as direct product of pauli matrices in SU(2)
About The SU(4) denotes a special unitary transformation of 4-dimensional complex vector space and has 15 independent generators, which must…
Why quantum gates are represented as Unitary
Quantum Gate is represented as Unitary When we think back on normalize condition of quantum state, For this normalization condition…
Why Unitary is represented using Hermite
The Representation of Unitary An unitary matrix U is represented as (1), but why is it possible? The Hermite and…
Pure State Representation using density matrix
As we can see here (https://eye.kohei-kevin.com/2023/07/01/note-machine-learning-with-quantum-computers-2/), a pure state vector is represented as following But, if we use density matrix…
Note : Optimal Quantum Circuits for General Two-Qubit Gates
About Optimal Quantum Circuits for General Two-Qubit Gates Magic Basis Theorem 1 Theorem 3 Every two-qubit quantum gate in SO(4)…
Distinguish Unitary U and Special Unitary SU
The difference The effect to Quantum Bit It causes global phase on qubit The representation using Hermite As we can…
Special Unitary Group SU(n)
About Special Unitary Group of degree (n) SU(n) refers to the n-dimensional case of the special unitary group, which plays…
Parameter-Shift Rule
About To optimize parameters, estimating gradients is quite important. Since the optimization is highly depending on gradient descent methods. In…