Is Quantum Annealing really limited to QUBO?

Is Quantum Annealing really limited to QUBO? Ask Question Asked today Modified today Viewed 4 times 0 I try to understand the fundamental differences between Adiabatic Quantum Computing (AQC) and Quantum Annealing (QA). Note some related questions : Is the Quantum Annealing model universal? What precisely is quantum annealing? What is the difference between quantum annealing and adiabatic quantum computation models? As far as I could investigate, QA can be viewed as : the quantum counterpart of classical simulated annealing, in which "thermal fluctuations" are replaced by quantum fluctuations and the quantum tunnel effect, a relaxation of AQC as temperature conditions for this latter ro run are difficult to achieve in practice But both QA and AQC originates from the time-dependent Hamiltonian H(s)=A(s) H m +B(s) H c ,s= t T ∈[0,1] 𝐻 ( 𝑠 ) = 𝐴 ( 𝑠 ) 𝐻 𝑚 + 𝐵 ( 𝑠 ) 𝐻 𝑐 , 𝑠 = 𝑡 𝑇 ∈ [ 0 , 1 ] where : A(0)=1 𝐴 ( 0 ) = 1 and A(1)=0 𝐴 ( 1 ) = 0 and B(0)=0 𝐵 ( 0 ) = 0 and B(1)=1 𝐵 ( 1 ) = 1 , and T 𝑇 is the total time duration of the time evolution. For AQC, the initial Hamiltonian H m 𝐻 𝑚 and the final one H c 𝐻 𝑐 are chosen so that the initial state be an (easily preparable) eigenstate of H m 𝐻 𝑚 and the final Hamiltonian encodes the optimization problem to solve, whose solutions are encoded as eigenstates of H c 𝐻 𝑐 and the associated eigenvalue representing the cost of the solution. Usually, in both QA and AQC, the standard choice for H m 𝐻 𝑚 is : H m =− ∑ i=1 n X i ⇒ H m | + n ⟩=−n| + n ⟩ (1) (1) 𝐻 𝑚 = − ∑ 𝑖 = 1 𝑛 𝑋 𝑖 ⇒ 𝐻 𝑚 | + 𝑛 ⟩ = − 𝑛 | + 𝑛 ⟩ which is indeed easy to prepare (wall of Hadamard applied on | 0 n ⟩ | 0 𝑛 ⟩ ). But for AQC, one may choose a different form for H m 𝐻 𝑚 , e.g. for encoding some optimization constraints and thus avoiding unfeasible solutions. In the context of QA, the time-dependent Hamiltonian is often presented as : H(t)=Γ(t) H T + H L (2) (2) 𝐻 ( 𝑡 ) = Γ ( 𝑡 ) 𝐻 𝑇 + 𝐻 𝐿 In article Villanueva, 2023, this form (2) is related to (1) by setting (in page 4) : B=1−AandΓ= A 1−A 𝐵 = 1 − 𝐴 and Γ = 𝐴 1 − 𝐴 I do not understand the underlying reasons for QA to consider (2) instead of (1) but furthermore, in all publications I went through QA seems limited to hamiltonians : H m =− ∑ i=1 n X i 𝐻 𝑚 = − ∑ 𝑖 = 1 𝑛 𝑋 𝑖 and H c = ∑ i=1 n β i Z i + ∑ i,j=1 n β ij Z i Z j 𝐻 𝑐 = ∑ 𝑖 = 1 𝑛 𝛽 𝑖 𝑍 𝑖 + ∑ 𝑖 , 𝑗 = 1 𝑛 𝛽 𝑖 𝑗 𝑍 𝑖 𝑍 𝑗 which means that the problem you want to solve is a Quadratic Unconstrained Binary Optimization Problem (a QUBO). I do not understand why the QA framework would be limited to QUBO problems ? Is it just a convenient choice of e.g. D-Wave to restrict themselves to this type of problem ? given that indeed many problems can be turned into a QUBO. annealingadiabatic-model Share Improve this question Follow asked 50 mins ago deb2014 6013 3 silver badges 8 8 bronze badges Add a comment Know someone who can answer? Share a link to this question via email, Twitter, or Facebook. Your Answer Sign up or log in Sign up using Google Sign up using Email and Password Post as a guest Name Email Required, but never shown Post Your Answer By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy. Start asking to get answers Find the answer to your question by asking. Ask question Explore related questions annealingadiabatic-model See similar questions with these tags. The Overflow Blog Seizing the means of messenger production How can you test your code when you don’t know what’s in it? 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