Device and method for continuous time quantum computing

A quantum computing device, comprising:

• a quantum system providing a computational Hilbert space having a first subspace of dimension D1 and a second subspace of dimension D2,
• a number K≥1 of control field generators, each control field generator capable of generating a semi-classical control field, wherein a Hamiltonian applied to the quantum system depends on the control fields, and
• a classical control system controlling the control field generators, wherein the classical control system is able to:
• by means of a first sequence of control field settings, apply to the quantum system a first effective Hamiltonian (Heff) having, in computational bases of the first and second subspace, a matrix representation with an off-diagonal block corresponding to an input matrix A of shape D1×D2 having a singular value decomposition
• A
• =
• ∑
• j
• =
• 1
• J
• ⁢
• σ
• j
• ❘
• "\[LeftBracketingBar]"
• i
• j
• 〉〈
• r
• j
• ❘
• "\[RightBracketingBar]"
• with a number J of non-zero singular values σj, left singular vectors |lj from the first subspace and right singular vectors rj| from the second subspace, and
• by means of a second sequence of control field settings, apply to the quantum system a second effective Hamiltonian having a matrix representation of the form
• Z
• =
• I
• 1
• -
• I
• 2
• ⁢
• where
• ⁢
• I
• 1
• =
• ∑
• j
• =
• 1
• J
• ❘
• "\[LeftBracketingBar]"
• l
• j
• 〉〈
• l
• f
• ❘
• "\[RightBracketingBar]"
• 1
• and
• I
• 2
• =
• ∑
• j
• =
• 1
• J
• ❘
• "\[LeftBracketingBar]"
• r
• j
• 〉〈
• r
• j
• ❘
• "\[RightBracketingBar]"
• 1
• ,
• such that the second effective Hamiltonian (Z) induces a phase rotation in two dimensional subspaces spanned by two computational Hilbert space vectors, where one of the vectors is taken from the first subspace and the other is taken from the second subspace, wherein, in order to obtain unitary evolution of the quantum system having, in a matrix representation in the computational bases of the first and second subspace, an off-diagonal block corresponding to a given function f (A) of the input matrix A, the classical control system is configured to perform the steps:
• (a) apply the second effective Hamiltonian for a first phase rotation time corresponding to a phase rotation by a first angle (Φ1), then
• (b) apply the first effective Hamiltonian for a first time (t1), and then
• (c) apply again the second effective Hamiltonian for a phase rotation time corresponding to a phase rotation by the negative of the first angle or apply the negative of the second effective Hamiltonian for the first phase rotation time, thereby effecting a unitary transformation e−iGΦ1t1:=eiΦ1Ze−i Heff t1e−iΦ1Z,
• wherein the classical control system is further configured to repeat the steps a-c for a second, third and so on up to a L-th angle ΦL and a second, third and so on up to a L-th time tL thereby effecting a unitary transformation UHOSVT=e−iGΦLtL e−iGΦL-1tL-1 . . . e−iGΦ1t1,
• a classical preprocessing system that carries out an optimization of the first, second third and so on rotation angles ΦL and times tL, wherein the classical preprocessing system comprises a neural network, in particular a generative neural network, wherein the optimization involves a gradient descent on weights of the neural network, wherein the optimization involves feeding the function f(A) or its singular value decomposition to an input layer of the neural network.