Quantum computing Sample Clauses

Quantum computing. The state of a quantum system is described by a unit vector|ψ⟩(called a ‘ket’ vector) in a Xxxxxxx spaceHoverC, for quantum computing purposes offinite 2. Preliminaries α1 dimensiond. Elements from the dual spaceH ∗ of linear functionalsH→C are denoted by ‘bra’ vectors⟨ϕ|. 8 For every vector|χ⟩ ∈Hthere is a unique vector⟨χ|∈H ∗ such that⟨χ|ψ⟩:=⟨χ||ψ⟩= (|χ⟩,|ψ⟩), where(·,·)is the inner product on the Hilbert space. If wefix an orthonormal basis{|e i⟩}i∈I ofH, we can express a ket vector|ψ⟩and the corresponding bra vector⟨ψ|as |ψ⟩= α2 ∈C d and⟨ψ|= ¯α ¯α. . .¯α ∈ Cd ∗   . 1 2 d . αd | ⟩ with theα i being the vector coefficients of ψ with respect to this basis, also known as its amplitudes. Given the properties above, the inner product is then pinned down to (|ψ⟩,|ϕ⟩) = ¯αiβi p | ⟩ | ⟩ (where ψ is as above and theβ i are the coefficients of ϕ ). The inner product induces a norm: |ψ⟩2 := ⟨ψ|ψ⟩(2-norm). p P The2-norm is also called theEuclideannorm, and we sometimes drop the subscript2if it is clear from the context which norm we use. In the case of unit vectors, we have by definition1 = |ψ⟩ 2 = ⟨ψ|ψ⟩ 2 = squared moduli of a state’s amplitudes must sum to1. i |αi|2, hence the {| ⟩ | ⟩} | ⟩ | ⟩ | ⟩ Ifd= 2, the quantum system is called a ‘qubit’ (quantum bit), and the canonical basis is often written as 0 , 1 and referred to as thecomputational basis. Each of the two basis states then represents the bit taking the classical value0or1. An arbitrary qubit state ψ =α 0 0 +α 1 1 however can be any linear combination of the basis states, and we say that the qubit is in a superposition of0and1if both coefficientsα 0 andα 1 are non-zero. H Given two systems (e.g. two electrons) with respective state spaces 1 and N

Quantum computing. This use case will include Quantum Computing applications to High Energy Physics. Its aim is to recast relevant High Energy Physics computational problems into quantum algorithms and explore new applications such as direct simulation of quantum systems. It is expected that the work will initially be done on quantum simulators and, when available on quantum hardware.