All Questions
Tagged with quantum-gate hamiltonian-simulation
30 questions
0
votes
1
answer
62
views
Coding a hamiltonian in qiskit
I have a hamiltonian of the form:
$H=\sum_{i=1}^N Z_i Z_{i+1}-Z_NZ_1$
And another one as:
$H=-\sum_{i=1}^N X_i$
I need it to it for N terms.
I am a bit lost can anybody help. I tried looking for ...
- 123
0
votes
0
answers
26
views
Particle number expectation value in QuTip
I am learning now to use QuTiP by going through their documentation site. I am trying to understand what does the argument - particle number expectation value in thermal density matrix do? How does it ...
- 33
0
votes
0
answers
30
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Spin Hamiltonian to Quantum Circuits and are there any group theory associated with the quantum circuits?
Can we think of Quantum Circuits as another representation to describe the dynamics of a system other than its Hamiltonian? How can we go from the spin Hamiltonian version (for eg: SSH Model ...
- 33
1
vote
0
answers
555
views
Applying Trotterization to a Hamiltonian for Time Evolution in Qiskit
I'm currently working on a project where I need to simulate the time evolution of a quantum system using Qiskit. The Hamiltonian of my system is given by:
$$H = -J \sum_{j=1}^{N-1} (\sigma_j^x \...
- 131
0
votes
1
answer
73
views
Creating a parameterized Operator in Qiskit that cannot be decomposed into Qiskit supported gates
I am trying to create a custom ansatz to use the built-in Qiskit VQE() function. My ansatz is composed of single qubit gates and a hamiltonian gate which cannot be decomposed into Qiskit supported ...
- 95
0
votes
3
answers
588
views
How to represent Beam-Splitter and Kerr gates as basic quantum logic gates?
I want to know how to convert these exponential forms to tensor products of well known logic gates (like the ones built into Qiskit). My goal is to program the Beam-splitter-Kerr ansatz circuit for ...
- 95
2
votes
0
answers
45
views
Can we show that a quantum circuit with Poly(n) gates has a Hamitonian with Poly(n) terms?
It is already known that if the Hamiltonian is a sum of Poly(N) Pauli terms, it has an efficient implementation as a quantum circuit. This should mean that the circuit can be implemented with Poly(N) ...
- 21
1
vote
0
answers
576
views
Pauli decomposed Hamiltonian as Diagonal U gate
While trying to implement a quantum circuit, I had to apply Hadamard gates to all qubits to achieve equal superposition. Done.
The next operation is decomposing the Hamiltonian into a sum of tensor ...
- 283
0
votes
0
answers
52
views
How to calculate weight matrix of Hamiltonian for logic gate?
How can we find the $J$ matrix representing a logic gate truth table?
$$H=-\sum_i h_im_i-\sum_{i\lt j}J_{ij}m_im_j,$$
with
$$J=\begin{bmatrix}0 & -1 & +2 \\-1 & 0 & +2\\+2 & +2 &...
- 1
2
votes
2
answers
275
views
How to find a circuit for a unitary operator $e^{-i s |v \rangle \langle v| t }$?
Let $|v \rangle$ be an eigenstate of an $n$-qubit and $2$-local Hamiltonian
$$H = \sum_{i=1}^n \left (X_i + a_i Z_i \right) + \sum_{(i,j)} b_{i,j} Z_i Z_j,$$
where $\sigma_i = I \otimes \cdots \...
- 3,284
1
vote
1
answer
720
views
Understanding Hamiltonian's of the Single Qubit Gates and Toffoli gate
As a most general shape, we can write our unitary(unitary here single qubit gates and toffoli gates) in that shape:
$U = \exp({iHt})$
H is the hamiltonian. However single qubit gates does not reqire ...
- 624
6
votes
2
answers
952
views
How is Quantum Phase Estimation useful for simulating dynamics of a many-body system?
I am quite aware of the Quantum Fourier Transform (QFT) as well as the very closely related topic of Quantum Phase Estimation (QPE). The latter is usually motivated as follows:
Given a unitary $U$ and ...
- 645
3
votes
1
answer
297
views
Is the square-root-of-SWAP for a pair of 4-dimensional qudits isomorphic to two square-root-of-SWAPS for two pairs of qubits?
This may be a very naïve question indicative of a lot of confusion, but I am trying to understand more about Hamiltonian simulation. I'm starting to intuit that the $n^{th}$-root-of-SWAP acting on a ...
- 14.4k
3
votes
3
answers
611
views
Are these two circuits equivalent in performing controlled time-evolution?
I want to perform the controlled time-evolution of some 2 or 3-qubit Hamiltonian. Say we have this example:
$$
H= Z_0\otimes Z_1 + Z_1\otimes Z_2
$$
The circuit performing the time-evolution ...
- 2,408
6
votes
2
answers
2k
views
How to construct the two qubit gate generated by the Hamiltonian $H= X\otimes X + Y \otimes Y + Z \otimes Z $?
I know that the two qubit gate generated by $H=X\otimes X$ is $\exp\{-\text{i}\theta X\otimes X\}=\cos{\theta} \mathbb1 \otimes \mathbb1 - \text{i} \sin{\theta} X \otimes X$, where $X$ is the $\...
- 81
3
votes
1
answer
75
views
Distant quantum gates between uncoupled qubits
Is there any formalism to perform quantum gates between two qubits (let's say in a superconducting quantum network) to perform a quantum gate between two qubits which are not directly coupled? I want ...
- 1,795
3
votes
1
answer
873
views
XY Hamiltonian in a 1D Heisenberg Chain
I've been trying to implement the 1D Heisenberg chain (i.e. the XXZ model) on Qiskit but have been having trouble. To recap, the Heisenberg hamiltonian is as follows:
$$H_{XXZ} = \sum^{N}_{i = 1} [J(S^...
4
votes
1
answer
124
views
Definitions of $D_y$ gate in Hamiltonian simulation: are they the same?
I'm reading a Hamiltonian simulation example proposed in this paper. From their notation, the operator $D_y$ (sometimes it's called $H_y$) serves the function to diagonalize the Pauli matrix $\sigma_y(...
- 2,408
6
votes
1
answer
2k
views
How can I simulate Hamiltonians composed of Pauli matrices?
Suppose I want to perform the time-evolution simulation on the following Hamiltonians:
$$
H_{1} = X_1+ Y_2 + Z_1\otimes Z_2
\\
H_{2} = X_1\otimes Y_2 + Z_1\otimes Z_2
$$
Where $X,Y,Z$ are Pauli ...
- 2,408
2
votes
1
answer
146
views
Is there a tool to get the quantum circuit corresponding to a sparse matrix?
If I know a sparse matrix, is there any tool that allows me to get the corresponding quantum circuit directly?
If not what should I do?
For example，I want to try hamilton simulation and I have the ...
- 35
3
votes
1
answer
147
views
What do coupling coefficients mean in terms of Pauli gates, and why are they time dependent?
I am reading this error mitigation paper by the IBM team and I am slightly confused about the meaning of "coupling coefficients" when describing multi-qubit Hamiltonian.
I have only seen ...
- 401
3
votes
1
answer
629
views
Question Regarding Simulating Hamiltonian With Quantum Circuit
There have been a few other questions about this section of Nielsen and Chuang, but when working through the output of the circuit, there are some inconsistencies that are probably due to some mistep/...
- 529
7
votes
3
answers
2k
views
Quantum circuit to implement matrix exponential
I want to build a circuit which will implement $e^{iAt}$, where $ A=
\begin{pmatrix}
1.5 & 0.5\\
0.5 & 1.5\\
\end{pmatrix}
$ and $t= \pi/2 $.
We see that $A$ can be written as, $A=1.5I+0.5X$. ...
- 341
1
vote
2
answers
129
views
Constructing a time evolution operator $e^{it H}$ for $H^2=I$
Consider a Hamiltonian $H = \sigma_x \otimes \sigma_z$
Construct the time evolution operator $U(t) = \mathrm{e}^{-\frac{iHt}{\frac{h}{2\pi}}}$ [Hint:Write down the expansion of $\mathrm{e}^x$ and use ...
2
votes
2
answers
222
views
Circuit of a very trivial thing
I am writing to double check that if have a hamiltonian of the form $H = I_1 \otimes I_2$, when I seek to find the unitary, $e^{-i\gamma I_1 \otimes I_2}$, there really is no need to convert this into ...
- 1,003
8
votes
1
answer
1k
views
Practical implementation of Hamiltonian Evolution
Following from this question, I tried to look at the cited article in order to simulate and solve that same problem... without success. Mainly, I still fail to understand how the authors managed to ...
- 879
4
votes
1
answer
180
views
How are two different registers being used as "control"?
On page 2 of the paper Quantum Circuit Design for Solving Linear Systems of Equations (Cao et al.,2012) there's this circuit:
It further says:
After the inverse Fourier transform is executed on ...
- 17.8k
13
votes
1
answer
3k
views
How to implement a matrix exponential in a quantum circuit?
Maybe it is a naive question, but I cannot figure out how to actually exponentiate a matrix in a quantum circuit.
Assuming to have a generic square matrix A, if I want to obtain its exponential, $e^{A}...
- 879
17
votes
1
answer
1k
views
Obtaining gate $e^{-i\Delta t Z}$ from elementary gates
I am currently reading "Quantum Computation and Quantum Information" by Nielsen and Chuang. In the section about Quantum Simulation, they give an illustrative example (section 4.7.3), which I don't ...
- 1,049
12
votes
2
answers
729
views
How are elementary quantum gates realised?
When expressing computations in terms of a quantum circuit, one makes use of gates, that is, (typically) unitary evolutions.
In some sense, these are rather mysterious objects, in that they perform "...
glS♦
- 26.9k