Questions tagged [hamiltonian-simulation]
Hamiltonian simulation is a class of algorithms that, given a Hermitian matrix A, output a quantum circuit implementing an approximation to the unitary exp[iAt].
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How to benchmark approximate random unitary sampling
I'm currently studying a specific sampling "quantum advantage" (sorry for the buzzword) protocol wich consist of periodically driving a random Ising chain (https://iopscience.iop.org/article/...
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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 ...
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How does edge-coloring help for quantum walks?
Reviewing Childs, Cleve, Deotto, Farhi, Gutmann, and Spielman's famous 2002 welded-trees problem, (quantum) Theseus can find his way out of a labyrinth having an exponential number of rooms (vertices),...
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Excplicit Description of Hamiltonians?
The wikipedia article for Hamiltonian simulation lists two complexities: gate and query complexity.
These two types of complexity refer to two different things; gate complexity is the asymptotic ...
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What are the entries in the 2x2 $W$ gate used for walking along the welded-trees graph of Childs et al.?
As an extension of a famous description of non-local Hamiltonian simulation in section 4.7.3 of Nielsen and Chuang, the welded-trees paper of Childs, et al. provides the following circuit for use in ...
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The approximation of the time evolution operator U, using Trotter formula, can't hold anymore taking a time step of $\Delta t = \pi$
The problems arises from a consideration written on the book "Quantum computation and quantum information" from Michael A. Nielsen and Isaac L. Chuang on page 259.
In this chapter it's ...
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Can a Hamiltonian of a tripartite system map an product state into a product state?
Suppose we have a finite dimensional Hilbert space $\mathcal{H}_A \otimes \mathcal{H}_B \otimes \mathcal{H}_C$ and a Hamiltonian has the following form:
$$H = H_A \otimes I \otimes I + I \otimes H_B \...
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How to perfrom a time-dependent Hamiltonian simultation using the Trotter-Suzuki formula?
I would like to know how to perform trotterization of a time-dependent operator (such as a Hamiltonian) on a gate-based quantum computer? I've seen examples for time-independent Hamiltonians, but I ...
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circuit for quantum simulation?
What would be the circuit for operation exp(iθZ⊗Z⊗Z⊗X) by only using CNOTs and single-qubit gates. And How we can improve the circuit to implement the operation exp(iφZ⊗Z⊗X⊗Z ).exp(iθZ⊗Z⊗Z⊗X).Are ...
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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 ...
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Do the following circuits violate the principle of "no fast-forwarding"?
The no fast-forwarding principle states roughly that, given that we can simulate a Hamiltonian for time $t$ using $r$ gates, in order to perform the Hamiltonian simulation for time $2t$, we must in ...
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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) ...
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Questions about ActiveSpaceTransformer code implementation
Could anyone explain how dipole moment and 2-body integrals mathematically relate to DFT embeddings ?
How is ActiveSpaceTransformer different from ECP (Effective Core Potentials) ?
If ...
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Why do Hamiltonian simulation algorithms not depend on the size of the Hamiltonian for the gate complexity?
The wikipedia page for Hamiltonian simulation mentions the gate and query complexities for different algorithms used for the problem (Trotter-Suzuki, Taylor Series, Quantum Walks, and QSP).
They ...
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Is Hamiltonian simulation with only real entries BQP-complete?
It is often asserted that Hamiltonian simulation (given some Hermitian matrix, $H$) is BQP-complete.
I don't see how the input to such an algorithm is done without the use of some block-encoding or ...
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Qiskit - Approximation of Hamiltonian energy via QPE
I'm trying to study QPE with the motivation of obtaining eigenvalues of Hamiltonian, i.e. energies of a system. My problem is, that while np.linalg.eig and VQE are agreeing on the lowest energy, ...
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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 ...
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time evolution of Hamiltonian to generate the Bell pair
Consider two different Hamiltonians: $H_1(t) = ZZ + \alpha(t)X_1 + \beta(t)X_2$ and $H_2(t) = XX + \alpha(t)Z_1 + \beta(t)Z_2$, where $\alpha(t)$ and $\beta(t)$ are time-dependent functions. Starting ...
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Solving a linear optimization problem with inequality constraints in qiskit? is it possible?
This is an easy optimization problem that can be classically solved. My question is that, in qiskit, how can we solve this optimization problem using IBM real machines? Is it even possible to do that?
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Block encoding for a sum of Pauli terms
Given a qubit Hamiltonian with polynomially many local Pauli terms, what is the most natural way of constructing its block encoding? I know there are multiple ways of doing so, but I am looking for ...
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Is it possible to implement any random Hamiltonian using quantum circuit
Are there any restrictions on implementing the evolution of any random Hamiltonian? Suppose I want to implement Rabi oscillations using a quantum circuit, I initialize the state and the Hamiltonian ...
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Can superoperators work in Monte Carlo solver in QuTip?
The Monte Carlo solver works with kets instead of density matrices. And it doesn't allow a superoperator (which acts on density matrices or superkets) as a collapse operator. Since my master equation ...
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How to implement the cross term (multi-qubit) in the square of the finite difference operator?
I am trying to simulate the Hamiltonian evolution of the 1+1D $\lambda\phi^4$ scalar field theory by digitising it and encoding on a quantum computer. The process of digitising is taken from this ...
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What is the difference between Trotter, Lie-Trotter and Trotter-Suzuki approximations?
What is the difference between (1) Trotter (2) Lie-Trotter and (3) Trotter-Suzuki approximation? Are they all different? what are the formulas and errors associated in each of these approximations in ...
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Confusing notation in Block-Encoding
I'm reading the lecture notes from Ronald de Wolf and got confused at the part where it introduces Block encoding, specifically by this notation at page 76:
More generally we can define an $a$-qubit ...
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Expectation value of a time evolved circuit in the non-Z basis
I am new to qiskit and have hit a roadblock in my calculation. Given the following circuit:
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How does Quantum Simulation actually solve the problem it poses?
The problem of quantum simulation is below:
Given a Hermitian matrix, $H$, compute the unitary $e^{-iHt}$ for any $t > 0$. Using this computed unitary, calculate $e^{-iHt}\psi$ for any given $\psi$
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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 &...
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Proof of $cos(Ht) = \sum_\sigma cos(\sigma) \left | w_\sigma \right > \left < v_\sigma \right |$ in Quantum Singular Value Transform
I am reading the grand unification of quantum algorithms, and read over the hamiltonian simulation technique.
However, I am a bit confused. They pose that
$
e^{-iHt} = cos(Ht) - isin(Ht)
$
for all ...
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Creating a plot of groundstate energy (for a set distance) against noise
I am trying to create a plot of groundstate energy against noise like mentioned in the title.
I do this in the aim of finding some sort of correlation between the two meaning I can find what the ...
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How is the P function applied in QSVT for the case of Hamiltonian simulation if it only modifies singular values?
I am watching Andras Gilyen's talk on QSVT here.
On one slide he mentions the core of QSVT:
Given $U$--- a block encoding of matrix $A$ that has singular values $\lambda$, left singular vectors, $\...
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How to choose values of phi for Hamiltonian simulation with Quantum Singular Value Transform?
I am reading the review, Grand Unification of Quantum Algorithms, which covers the area known as "Quantum Singular Value Transform (QSVT)."
I am really trying to understand it behind the ...
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unexpected keyword argument in qiskit vqe
I want to find the estimate of the ground state energy of my Hamiltonian H that is implemented as PauliSumOp in my variable <...
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Why does the quantum walk operator only have two eigenvectors?
In Child's paper on the relationship between discrete and continuous quantum walks, he makes the following claim.
Although he provides a proof after this:
I don't understand how the walk operator ...
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Quantum Signal Operator and the unitary state preparation oracle? [closed]
I am looking into IL Chuang and GH Low's Hamiltonian Simulation with Qubitization paper.
I am very confused on the terminology and motivation behind definition 1.
I do not understand what the unitary ...
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Lowest energy problem with additional constraints
Consider the following minimization problem:
\begin{align}
&\min_{\rho} \mathrm{Tr}[\rho H] \\
\text{such that:}& \\
&Tr[\rho A_i] \leq 0 \ \ \forall A_i, \ i \in \{1,2,3,...\}
\end{align}
...
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How do we compute quantum walks for a graph?
I am reading Childs' paper on discrete and continuous quantum walks. I do not really understand why quantum walks are useful--- as implementing the quantum walk operator requires knowing the principal ...
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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 \...
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How does the Active Space Transform work theoretically?
I have a question about the ActiveSpaceTransformer which is used in vqe calculations for a molecule of LiH in Qiskit. In the documentation the inactive Fock operator is defined.I don't understand why ...
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Where can I find a list of Hamiltonians and their decomposition to paulis?
I am trying to grasp insights into how the local terms of real Hamiltonians in the nature might be distributed. And therefore I was wondering if there is a dataset that lists known Hamiltonians and ...
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Ordered Tensoring of Operators
Novice warning: I have a strong feeling I am simply misunderstanding something fundamental!
Setup:
Classically -
I taken in some structured input and assign to each qubit $q_i$ in a register $Q = \{...
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How do you add spin up and spin down fermions to a FermiHubbardModel class in Qiskit?
I've been programming a FermiHubbardModel class with the Qiskit library for a VQE, but the class only shows input options for the U (onsite) and t (hopping) parameters when I construct a LineLattice.
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Reverse mapping from qubit Hamiltonian to fermionic operator
I'm just wondering if there is an algorithm to do reverse mapping of a Hamiltonian on qubit basis to fermionic operator in Fock space, assuming we know the mapping rule (e.g. Jordan-Wigner).
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Hamiltonian Simulation Circuit for Grover's Search
The Hamiltonian in the simulation of Grover Search is given as, $H=|x\rangle\langle x|+|\psi\rangle\langle\psi|$. It is said that in order to simulate $H$ we can simulate the Hamiltonians $H_1=|x\...
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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 ...
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Under what conditions the minimum eigengap is non-zero?
I would like to know sufficient conditions for a non-zero eigengap of a time-dependent Hamiltonian.
Suppose we have a time-dependent Hamiltonian $H(t)$ defined as follows:
$$H(t) = (1-s(t))H_{init} + ...
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qiskit vs dimod: ising matrix in 2 libaries are different
I have a simple QUBO problem in qiskit library:
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Why was Feynman hesitant about simulating fermions with a quantum computer?
Richard Feynman has a number of foundational publications from the early-mid 80's on quantum computing that I continue to read with awe and inspiration. As earlier discussed, the 1985 article "...
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Simulation of non hermitian operators with Qiskit
I am trying to simulate on a quantum computer a wavepaket evolution with a non unitary evolution operator (Hamiltonian with an absorbing (imaginary) potential for instance) and I found this post :
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