# 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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### How to tell if the ground states of two Hamiltonians are solutions of the same optimization problem?

Let's say, that we have an optimization problem in the form: $$\min_x f(x) \\ g_i(x) \leq 0, i = 1, ..., m \\ h_j(x) = 0, j = 1, ..., p,$$ where $f(x)$ is an objective function, $g_i(x)$ are ...
1answer
82 views

### Is there a general method of expressing optimization problem as a Hamiltonian?

Let's say, that we have an optimization problem in the form: $$\min_x f(x) \\ g_i(x) \leq 0, i = 1, ..., m \\ h_j(x) = 0, j = 1, ..., p,$$ where $f(x)$ is an objective function, $g_i(x)$ are ...
2answers
372 views

### How to recognize if a paper is talking about quantum annealing or gate logic?

I am currently reading various survey papers in Quantum Machine Learning, such as "Quantum Machine Learning" by Biamonte, Wittek, Pancotti, Rebentrost, Wiebe, and Lloyd. To me, it is not clear when ...
1answer
64 views

### How to understand Deutsch-Jozsa algorithm from an adiabatic perspective?

I'm trying to understand the Deutsch-Josza algorithm from an adiabatic perspective as presented in Adiabatic quantum computing A: Review of modern physics, vol 90, (2018) pp 015002-1 (arXiv version). ...
2answers
102 views

### What is the correspondence between adiabatic phase and a topological phase?

In the adiabatic model, we have a system acquiring a Berry phase due to cyclic slow periodic evolution under a Hamiltonian. While in the topological phases, we talk about systems such as anyons which ...
1answer
152 views

### What are XX, YY, YZ etc. couplings?

The D-wave quantum computer allows us to be able to minimize Ising models. In reading other questions and responses, particularly What would be the simplest addition that would make the D-Wave ...
0answers
35 views

### Numerical approximation to eigenstates and their differentials

I am working in Adiabatic Quantum Computing and I have a $6\times6$ Hamiltonian. I have only the symbolic expression for its eigenstates which have complicated expressions in solutions of degree $6$ ...
1answer
98 views

### Problem with approximating adiabatic evolution with quantum circuit

I am reading on how to approximate adiabatic evolution with quantum circuit and I had some trouble following the arguments given in the early papers which proves this results. I am mainly following ...
1answer
54 views

### Proof on approximating adiabatic evolution by quantum circuit

I am reading on how the adiabatic evolution can be approximated by a quantum circuit of size poly(nT) and I am trying to follow the derivation in the paper W. van Dam, M. Mosca, and U. Vazirani, “...
1answer
46 views

### What is the “TRIAD” graph and where can I find more information about it?

I was looking up how to program for a D-Wave machine and I came across this image which says it's the "optimal hardware graph" for a D-Wave machine: Unfortunately the image seems to have come from ...
3answers
126 views

### Can we do adiabatic quantum computing with a quantum circuit model and how?

This is a question that must be asked a lot but is it possible? And if in theory possible, what are the challenges to do it, and what are the drawbacks?
1answer
263 views

### Does the D-Wave 2000Q satisfy DiVincenzo's criteria?

DiVincenzo's criteria for quantum computation are the following: A scalable physical system with well characterized qubits. The ability to initialize the state of the qubits to a simple fiducial ...
0answers
174 views

### In D-Wave's universal quantum computer, why does the YY term have to be driven along with the linear X term?

D-Wave has a new prototype annealer that uses a Hamiltonian which, if there was enough qubits and sufficient control, would be able to simulate any universal circuit-based quantum computer with at ...
4answers
1k views

### Are quantum computers just a variant on Analog computers of the 50's & 60's that many have never seen nor used?

In the recent Question "Is Quantum Computing just Pie in the Sky" there are many responses regarding the improvements in quantum capabilities, however all are focussed on the current 'digital' ...
2answers
289 views

### Can adiabatic quantum computing be faster than Grover's algorithm?

It has been proven that adiabatic quantum computing is equivalent to "standard", or gate-model quantum computing. Adiabatic computing, however, shows promises for optimisation problems, where the ...
1answer
97 views

### Can quantum annealing find excited states?

If we start with a Hamiltonian $H(t_i)$, and with our qubits prepared in the ground state of this, and then slowly change this to a Hamiltonian $H(t_i)$, the final state of our qubits should be the ...
1answer
185 views

### Adiabatic Quantum Computing vs Adiabatic Quantum Optimization vs Quantum Annealing

I am aware that of the difference of Adiabatic Quantum Computing (AQC) and Quantum Annealing (QA) as explained here. However, another term which came up in some papers was Adiabatic Quantum ...
2answers
601 views

### What precisely is Reverse Annealing?

Quantum Annealing, (related questions Quantum Annealing, or hamiltonian related) is the process used in D-Waves' Quantum Annealer, in which the energy landscapes are explored, for different solutions, ...
4answers
1k views

### Why is it crucial that the initial Hamiltonian does not commute with the final Hamiltonian in adiabatic quantum computation?

I've read in many sources and books on adiabatic quantum computation (AQC) that it is crucial for the initial Hamiltonian $\hat{H}_i$ to not commute with the final Hamiltonian $\hat{H}_f$, i.e. \$\left[...
1answer
993 views

### What precisely is quantum annealing?

Many people are interested in the subject of quantum annealing, as an application of quantum technologies, not least because of D-WAVE's work on the subject. The Wikipedia article on quantum annealing ...
1answer
1k views

### What is the difference between quantum annealing and adiabatic quantum computation models?

From what I understood, there seems to be a difference between quantum annealing and adiabatic quantum computation models but the only thing I found on this subject implies some strange results (see ...