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Questions tagged [adiabatic-model]

Adiabatic quantum computation (AQC) is a form of quantum computing which relies on the adiabatic theorem to do calculations and is closely related to and may be regarded as a subclass of, quantum annealing. (Wikipedia)

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Adiabatic evolution vs QAOA

Attempting to understand some basics here before developing an quantum algorithm. Would of you be able to help clarify the following definitions I attempted to construct which compare the two ...
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How to approximate the time-dependent Hamiltonian in quantum adiabatic theory by the non time-dependent Hamiltonian?

Recently, I am learning how to solve the linear equation $A\left | x \right \rangle =\left | b \right \rangle $ using quantum adiabatic theory. In the solving process, people usually need to set the ...
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How to actually solve for the eigenstates in the adiabatic version of Grover's algorithm

The adiabatic version of Grover's algorithm says that the eigenstates of the Hamiltonian $H(t)=(1-\frac{t}{T})H_0+\frac{t}{T}H_m$ (equation 10 in the linked paper) can be used to solve the eigenvalue ...
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Derivation of energy gap formula for adiabatic Grover algorithm

I am having a difficulty in finding the full derivation for local search energy gap, as described in In the adiabatic version of Grover's algorithm, how is the Hamiltonian constructed?. I looked ...
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Can adiabatic quantum computing be used to find local minimum instead of ground states?

We know that with unfriendly energy gap circumstances, adiabatic quantum computing takes exponential time to find a ground state of some hamiltonian. But if some local minimum state is all we look for,...
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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, ...
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Does the D-Wave hardware show any advantage for academic use-cases, for example in condensed matter physics?

The D-Wave team put out a few papers (like this one and this one) in the last few years describing how their methods can find ground states of certain spin-glass Hamiltonians faster than classical ...
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Did D-Wave show quantum advantage in 2023?

I would like to know your thoughts on whether or not D-Wave has shown a a smoking-gun example of quantum advantage this year. I am genuinely not quite sure what to think, but I believe the answer to ...
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Python code for D-Wave Annealer

In the below screenshot, I am aware of resolving the issue by reducing num_reads as the annealing time is exceeding my allowance. Although it works, my question ...
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Adiabatic state preparation for quantum phase estimation

I'm trying to understand the problem of state preparation for quantum phase estimation (QPE). Specifically how states are prepared adiabatically. I have a couple of questions: 1). Typically when one ...
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Compiling pulses with time dependent $\sigma_x$ and $\sigma_y$ control

I have a Hamiltonian of the form: $$ H = c_x(t) \sigma_x + c_y(t) \sigma_y$$ and I want to compile a pulse "P" that has both $\sigma_x$ and $\sigma_y$ control, with different time dependent ...
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Implementing Adiabatic Grover Search via QAOA

I am reading the paper Grover Search Inspired Alternating Operator Ansatz of Quantum Approximate Optimization Algorithm for Search Problems. The paper proposes running the Adiabatic Grover Search ...
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Is there a quantum algorithm for the closest vector problem on a 2-dimensional lattice?

Is there a standard quantum algorithm (adiabatic or density matrix based) that can output the answer to a 2-dimensional closest vector problem: ie. find the closest lattice point (the blue one) that ...
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Link between AQC and QAOA

I try to understand precisely the link between AQC and QAOA, through the Trotter-Suzuki formula. A similar question is Derivation of QAOA from AQC, but I was asked by moderators to post my question ...
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Computational complexity of the circuit model vs adiabatic model?

I'm trying to understand how computational complexity is quantified in adiabatic quantum computing. With the circuit model, computational complexity is simple: count the number of times you queried ...
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Can Shor's algorithm be done with the same efficiency on an adiabatic quantum computer as on a circuit-based one?

Unfortunately, I cannot find any information on this, so I am asking in this forum if anyone knows, and if so, why this is the case?
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Adiabatic computing basics

I am reading about adiabatic quantum computing- specifically, about how it can find the lowest energy configuration of the Ising model. It is said that the initial state is a superposition of all the ...
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Derivation of QAOA from AQC

In adiabatic quantum optimization we start with an initial Hamiltonian $H_0$ and then adiabatically evolve from $H_0$ to $H_P$ (problem hamiltonian) for a time $T$ according to \begin{equation}\label{...
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AQC definition modifications costs and pay-offs

I was wondering if one can think of a more general relation between alleviating conditions for the state in which the evolution takes palce in AQC paradigm and constraining the structure of the ...
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How to compare Quantum Annealing and Adiabatic Quantum Computing?

I'm still unsure on the difference between adiabatic quantum computing (AQC) and quantum annealing (QA). Please critique these interpretations: AQC: Define a Hamiltonian with an easy-to-prepare ...
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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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What arguments point towards D-Wave devices being potentially useful?

I'm looking for any evidence pointing towards D-Wave's approach to quantum computation being promising to achieve any sort of computational advantage with respect to classical devices. Note that I'm ...
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Error analysis on the approximation of an adiabatic evolution operator by a QAOA circuit

I would like to know what would be the approximation error of a QAOA circuit. Suppose we have time-dependent Hamiltonian $H(t) = (1 - s(t))H_{init} + s(t)H_{prob}$ where $H_{init}$ in an initial ...
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Is there any rigorous proof that Quantum Annealing provides a quantum advantage?

Is there any rigorous proof that Quantum Annealing (QA) is of any benefit (e.g. in terms of time to optimal solution, convergence rate, etc.) for a specific problem? Or any empirical evidence for the ...
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Is digital quantum computing more powerful than the analog one?

What I get so far: Analog quantum computing: The Hamiltonian is implemented on the QC, solution is found by e.g. quantum annealing. The whole state is changing continuously. Digital quantum computing: ...
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Computational Complexity of random Transverse-Ising Chain

It is well known that many NP-hard classical problems can be mapped to a spin-configuration Ising problem (see for example https://arxiv.org/pdf/1302.5843.pdf) However, what I would like to know is ...
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The energy levels crossover problem in Quantum Annealing

How to avoid energy levels crossover in quantum annealing by Kibble-Zurek mechanism? Any detailed references?
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Understanding QAOA from Basics/scratch

Recently after working on QAOA with finance and graph coloring problems. I have started exploring the QAOA from scratch. I would like to understand the QAOA derivation mathematically and have started ...
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Why does QAOA's performance monotonically increase as p increases?

From A Quantum Approximate Optimization Algorithm - Farhi et al. The Quantum Approximate Optimization Algorithm has the key feature that as p increases the approximation improves. We contrast this to ...
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Quantum Adiabatic algorithm and Hardness of ExactCover

It was numerically shown in this paper that the ExactCover problem, given the unique satisfying assignment (USA) assumption, could be solved by an adiabatic quantum algorithm (AQC) in time polynomial ...
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How to formulate QUBO as summation quadratic and linear parts of K-graph coloring problem?

While trying to understand the graph coloring problem with VQE using the QUBO Formulation mentioned section "5.2 Graph Coloring". Mentioned article prepared the QUBO directly in to matrix ...
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Any simulator packages for quantum annealing/adiabatic quantum computation?

Are there any simulator packages for quantum annealing/adiabatic quantum computation, like Qiskit Aer but for quantum annealing? There seems to be only classical heuristics in D-Wave Ocean package, ...
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Example of lower bound on spectral gap for adiabatic quantum computing

is there a list of reference for which the authors prove a lower bound of the spectral gap for an adiabatic quantum algorithm? I.e. I am searching for examples where the authors solve a problem with ...
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How is eigendecomposition of a Hamiltonian equivalent to finding the minimum of an energy function?

This question is in regards to Dwave's quantum computer which is tailored to solve QUBO problems using quantum annealing. QM tells us that the ground state of a quantum system is given by the ...
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Comparing complexity of digital and analog quantum computation

The complexity of an algorithm run on a digital quantum computer is quantified, roughly, by the number of elementary gates in the corresponding circuit. Can one similarly quantify the complexity of an ...
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Question about the counter diabatic(CD) term in Digitized Adiabatic Quantum Computing

Recently I have read two articles about the Digitized Adiabatic Quantum Computing(DAQC), and tried to factorize $35=5\times7$ and $2479=67\times37$. But some problems came when trying to solve the ...
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Standard to select base hamiltonaian for Adiabatic quantum computing

I'm learning about connection between QUBO and The Ising Model. It says Take the base Hamiltonian of an adiabatic process as $\sum_i \big(\frac{1-\sigma_i^x}{2}\big)$ to implement Hamiltonian for ...
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The Adiabatic Theorem - How to derive Schrödinger equation in the "s" variable

I'm studying Adiabatic Quantum computing from the book "Adiabatic Quantum Computation and Quantum Annealing: Theory and Practice" by Catherine C. McGeoch at D-Wave. The section THE ...
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Penalty Function for XOR gate

I was reading a paper on Gates for Adiabatic Quantum Computer. In the paper, there were different penalty functions already given in the form of the following table: I do not quite understand the ...
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Relationship of Adiabatic Quantum Computing speedup to Quantum Random Walk hit time

Considering the following two phenomena: Adiabatic quantum computing in general exhibits a quadratic speedup over classical simulated annealing, though for some Hamiltonians it may be faster (while ...
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Why is it so important to have uniform chain lengths in a minor embedding?

Very brief background In quantum annealing, the discrete optimization problem we wish to solve (such as finding the minimum of $b_1b_2 - 3b_1 + 5b_3b_4$ for binary variables $b_i$) may have a ...
user1271772 No more free time's user avatar
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Why do I get this extra factor when working out the dynamics of an adiabatic quantum computation?

I was trying to revise my understanding of adiabatic quantum computation via a simple example. I'm familiar with the overall concept -- that you have an overall Hamiltonian $$ H(s)=(1-s)H_0+s H_f $$ ...
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Why is the time ordering omitted in the trotterised version of the time-dependent evolution operator?

The unitary evolution of a time-dependent hamiltonian is given by the time-ordered matrix exponential $$\begin{aligned} U(t)&=\mathcal T\exp\left[-i\int_0^tH(\tau)d\tau\right]\\ &=I-i\int_0^td\...
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In the adiabatic version of Grover's algorithm, how is the Hamiltonian constructed?

X-posted on physics.stackexchange In quantum computation, there is a famous algorithm to search a marked item in an unstructured database called Grover's algorithm. It achieves a quadratic speedup ...
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Adiabatic Quantum Computer e intermediate Hamiltonian evolves the state within the manifold

The Adiabatic Quantum Computer is implemented by slowly increasing the parameter s from 0 to 1 in the intermediate Hamiltonian $[\hat{H}(s) = \hat{H}_{input} + (1-s)\hat{H}_{init} + s\hat{H}_{circuit}]...
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Types of Quantum Computer [duplicate]

I am confused of all that different Quantum computers. please correct me if I say something wrong. There are two main different types of quantum computing: Quantum Gates based computing quantum ...
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Is the problem Hamiltonian in QAOA and AQC always a phase Hamiltonian?

In QAOA and AQC the problem Hamiltonian is always a Phase Hamiltonian (meaning only phases are added) Is that part of the QAOA and AQC definition or it is only used because it is convenient and work? ...
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What is the computational complexity of quantum annealing?

Quantum annealing can be thought of as a black box solver that can find approximate solutions to hard optimization problems. For example, D-Wave quantum annealers can approximately solve quadratic ...
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Why QAOA with $p \rightarrow \infty $ gives the optimal solution?

In the QAOA paper, it is shown that the optimal value of the p-ansatz $M_p$ converges to $\max_z C(z)$ as $p \rightarrow \infty$ on page 10. The proof is to relate to QAOA by considering the time-...
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Why does the problem Hamiltonian of QAOA always consist of $Z$ and $I$ gates?

I noticed that in QAOA the problem hamiltonian always consists of $Z$ and $I$ gates. But isn't QAOA a form of Adiabatic Programming? Where the idea is just to go from one ground state to another? Does ...
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