Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

Questions tagged [hamiltonian]

61 questions
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Efficient method to find square root of a Hamiltonian

I'm working with a Hamiltonian $H$ represented as a linear combination of Pauli strings: $$H = \sum_j \alpha_j P_j,$$ where $P_j \in \{I, X, Y, Z\}^{\otimes n}$ are tensor products of Pauli matrices and $n$ is the number of qubits. I'm looking for…
Kushagra Garg
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Is there an efficient algorithm for decomposing an arbitrary Hamiltonian into Pauli strings?

Basically the title. If I have a $2^N\times 2^N$ Hamiltonian $H$ of random numbers (we can take the Hamiltonian as normalized if we want) and $N$ is an integer, is there an efficient way of writing $$ H = \sum_{i}{\beta_iP_i} $$ where $\beta_i \in…
Physics Penguin
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How to splice Hamiltonians corresponding to channels $\Phi_1$ and $\Phi_2$ so as to obtain a Hamiltonian corresponding to $\Phi_2\circ\Phi_1$?

Suppose I have two quantum channels $\Phi_1:B(\mathcal{H}_1)\rightarrow B(\mathcal{H}_2)$ and $\Phi_2:B(\mathcal{H}_2)\rightarrow B(\mathcal{H}_3)$, and let $\Phi=\Phi_2\circ \Phi_1$. Stinespring Dilation says there are two auxiliary systems…
Sam Jaques
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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 evolution is implemented in the quantum circuit…
FearlessVirgo
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Implement a hamiltonian simulation on a diagonal matrix?

I'm trying to implement a Hamiltonian simulation of a diagonal matrix explained on A.M. Childs. Quantum information processing in continuous time (Rule 1.6 in Ref. 10). Briefly, the operations are: $$ |a,0\rangle \rightarrow |a, d(a)\rangle …
Lucas Amaral Dos Santos Barros
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Source reference for QMA-completeness of the following pairwise product of Pauli matrices

The following pairwise Pauli matrices are sufficient to capture the power of QMA complexity class. $\{I,\ I\otimes X,\ I\otimes Z,\ X\otimes I,\ Z\otimes I,\ X\otimes X,\ X\otimes Z,\ Z\otimes X, \ Z\otimes Z \}$ as mentioned in equation 10 of…
108_mk
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Is there any mathematical technique to find the exact solution of a QUBO problem?

Suppose I am given a QUBO problem consisting in the minimization of a quadratic function $\vec{x}^T Q \vec{x}$ over a binary-valued vector $\vec{x} \in \{0, 1\}^n$, with $Q$ a symmetric indefinite real matrix. Is it possible to compute analytically…
SimoneGasperini
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Analysis of error propagation in time-independent Hamiltonian computations

With a Feynman-Kitaev Hamiltonian, quantum computation does not need to apply any gates; you construct the Hamiltonian, initialize the system, and let it propagate on its own. However, the Hamiltonian you can actually construct is probably not…
Sam Jaques
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Does optimization via Hamiltonian evolution have an analogy like gradient descent?

I'm trying to find out, if there is a simplified concept to understand what is occuring during quantum annealing/ Falqon/ Hamiltonian evolution like algorithms. During classical gradient descent algorithms, one can imagine a marble that rolls along…
Ethan Davies
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The support of the ground state of stoquastic Hamiltonian is connected

A Hamiltonian $H$ is stoquastic in the standard basis if all the off-diagonal terms of the Hamiltonian are non-positive. If we choose $\beta$ small enough, all entries of $I-\beta H$ are non-negative. By the Perron-Frobenius Theorem, the eigenvector…
qmww987
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Underlying Hamiltonians and pulse level controls of different commercially available quantum computers

My research area is in quantum state transfer, and I am trying to perform a 'proof of principle' that requires the underlying Hamiltonians of quantum systems and the control I can have on these systems using pulse-level controls. For example, for an…
ZacB
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I would like to know the textbook/paper on hamiltonian for rf-SQUID

I am a graduate student in the Department of Computer Engineering, and I am currently doing research on superconducting quantum computers. In particular, I am focusing on quantum annealing machines and working on building a simulation environment…
Aki
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How can one use QAOA to obtain parameters that approximate the first excited state of the target Hamiltonian?

One can use QAOA to find the ground state and its energy by minimizing the expectation value of a target Hamiltonian (say, $H_T$) with respect to the QAOA ansatz and obtaining optimal parameters associated with the ground state of the target…
Pratham Hullamballi
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Understanding circuit to Hamiltonian embedding where we do not have a separate clock register

I am trying to understand the clock construction given in this paper, to embed a circuit to a Hamiltonian, which doesn't need to access a separate clock register. The construction, at a high level, comprises of using a complicated sequence of flag…
BlackHat18
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How does a quantum system identify hermitian and unitary matrices?

I am a beginner in quantum computing. I know that multiplying a state $|u\rangle$ with a hermitian matrix $M$ yields spectral decomposition and multiplying $|u\rangle$ with a unitary matrix yield an evolved state, say $|v\rangle$. My doubt is how…
Jayakumar
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