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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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 ...
1 vote
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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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1 vote
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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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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 \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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