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Penalty formulation regarding inequalitties

Unfortunately, your penalty term is not correct. When working with QUBO, penalties should be equal to zero for all feasible solutions to the problem. The proper way express $x_i + x_j \leq 1$ as a ...
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Is D-Wave advantage a noisier hardware compared to the older D-Wave 2000?

Because of higher qubit counts and greater connectivity, the Advantage QPU can hold inputs that are typically between 2 and 4 times larger than those that fit on the 2000Q QPU. Chain lengths on ...
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Penalty formulation regarding inequalitties

Multiply your penalty function with a lagrange multiplier $x_i A x_j + \alpha(x_i + x_j - 1)$ ,where $\alpha$ is the lagrange parameter, and can be set depending on the constraint, whether its a hard ...
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How are IBM's 127 qubits more potent than the 5760 qubits D-Wave - Advantage_system6.1?

The D-Wave machine is a quantum annealer running adiabatic quantum computing algorithms. This is great for optimizing solutions to problems by quickly searching over a space and finding a minimum (or “...
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Can D-Wave machines be applied to simulate Hamiltonians arising in quantum physics?

The D-Wave quantum computer leverages quantum dynamics to accelerate and enable new methods for solving complex problems. People are building quantum applications for a broad spectrum of industries ...
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How to declare non-binary decision variables in an optimization problem?

What do you mean by "declare"? Mathematically or in some programming language? Perhaps what you really want to know is how to represent integral or rational variables using binary variables. ...
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Can D-Wave machines be applied to simulate Hamiltonians arising in quantum physics?

Adiabatic quantum computation, the principle on which quantum annealing is based, is universal, so theory quantum annealing with arbitrary Hamiltonians could be used for simulation (up to the error ...
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Why is quantum annealing often associated with the Ising model?

Quantum annealing is a principle that applies to arbitrary Hamiltonians, and isn't fundamentally tied to Ising model; as you said, the underlying Hamiltonians of D-Wave's devices are Ising ...
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Is there any rigorous proof that Quantum Annealing provides a quantum advantage?

Currently, there is no proof that QA offers any advantage. According to Preskill (see below) there is even a little hope that it will be ever found. Therefore, QA algorithms (QAOA and VQE) or D-Wave ...
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