Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

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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Why does one need a non-commuting Hamiltonian for an algorithm to exhibit "quantumness"

In two places so far, I've heard statements of the sort "... and we need the Hamiltonian to be non-commuting. If not, the algorithm is classical, and we get no benefit from using a quantum computer." For reference, here are two timestamped youtube…
Alexander Soare
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What does Qubitization mean?

I was listening to an advanced lecture about quantum computing, when the professor introduced a chapter called "Qubitization and the quantum singular value transform", but never really cared to define what qubitization means. After some research I…
Lagrange
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Simulating $e^{iX_1\otimes X_2t}$

I'm trying to figure out the quantum circuit to simulate the time-evolution of a 2-qubit Hamiltonian $e^{iX_1\otimes X_2t}$, where $X$ is a Pauli gate. From this answer, the quantum circuit performs $e^{iZ_1\otimes Z_2t}$ could be constructed as an…
IGY
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Sign problem and stoquastic Hamiltonians

What is the sign problem in quantum simulations and how do stoquastic Hamiltonians solve it? I tried searching for a good reference that explains this but explanations regarding what the sign problem is are very hand-wavy. A related question, for…
BlackHat18
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Hamiltonian simulation in quantum computation

What is the goal of Hamiltonian simulation? Is it going to simulate a quantum system on a classical computer or quantum computer or none of them? What is the relationship between a quantum algorithm and the Hamiltonian simulation?
Ramin Fakhimi
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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).
user21384
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Hamiltonian simulation for 2 qubit gates

I have been reading this paper, and at the end they have given exact decomposition of Hamiltonian simulation step, where they have decomposed a matrix $A$ into pauli matrices and done the operation $e^{iAt}$. The decomposition of A is as follows:…
Jaimin
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Is there a way to express the general 4X4 Hamiltonian in some block diagonal form of 2X2 matrices that I can solve, knowing the exact solution of 2X2?

Is there a way to express the general $4 \times 4$ Hamiltonian in some block diagonal form of $2 \times 2$ matrices that I can solve, knowing the exact solution of $2\times 2$? This is necessary for the treatment I am going to perform later, as I…
Siddhant Singh
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Time-derivatives of Observables over Hamiltonian evolution

I am reading about algorithms to simulate Hamiltonian evolution by means of quantum computers, e.g. a transverse field Ising model. As far as I see one is interested in getting expectation values of observables of interest. Generally, for an…
Josu Etxezarreta Martinez
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time evolution of Hamiltonian and observables

I am given the following Hamiltonian on 4 qubits. $$ H = - J_x (X_0 X_1 + X_2 X_3) - J_z (Z_0 Z_2 + Z_1 Z_3) - h\sum_{j=0}^3 X_j + Z_j $$ I have already implemented the time evolution of this Hamiltonian. Now I wish to use this to calculate $\langle…
Ruebli
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How to model the transtition part of dispersive frequency shift in dispersive readout?

The phenomenon of interest is the resonance frequency shift and the larger noise in the measurements inside the intermediate-powered region as shown below (from Fig. 3.3 of Characterisation of Transmon qubit chips, L. M. Janssen. If I understand…
Ziyuan
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Question on Aharanov and Ta-Shma (ATS)'s Sparse Hamiltonian Simulation notation

In the equations in section 3.4.2 of Aharonov and Ta-Shma's paper (pdf, arxiv abstract), they define the operator: $$T_1:|k,0\rangle\rightarrow|b_k,m_k,M_k,\tilde{A_k},\tilde{U_k},k\rangle,$$ where $b_k,m_k,M_k,$ and $k$ are all integers and…
Hmecher
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How to construct a Hamiltonian for an ensemble of atoms interacting with each other?

How to construct a Hamiltonian for an ensemble of atoms interacting with each other? For example if the one atom hamiltonian can be written…
AQFarouk
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What work has been done on hamiltonian simulation of operators that are integrals instead of sums?

I'm looking at a problem where I want to do hamiltonian simulation of an operator integral. That is, I want to implement the unitary $$\mathrm U = \exp[-i \mathrm H t]$$ where $\mathrm H$ is of the form $$\mathrm H = \int_a^b d\tau \, \mathrm…
Dyon J Don Kiwi van Vreumingen
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