Method For Projecting Out Irreducible Representations From a Quantum State of n Particles with d Colors
OwnerRobert Ralph Tucciinventor
Life of this patent
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Abstract
We describe a method for using a classical computer to generate a particular sequence of elementary operations (SEO), an instruction set for a quantum computer. Such a SEO will induce a quantum computer to perform a unitary transformation U that we call an Irreps Gen U. This U simultaneously diagonalizes a set of operators Hμ called HYPs (Hermitian Young Projectors) for n particles with d colors or, equivalently, for n qu(d)its. Hμ projects out n particle irrep μ of U(d).
Claims13
A method of operating a classical computer to calculate a total SEO, with the purpose of using said total SEO to operate a quantum computer, and to induce said quantum computer to undergo a unitary transformation U that acts on n qu(d)its, wherein U simultaneously diagonalizes a set of operators Hμ, that satisfies the H-properties, wherein said U can be expressed in the form
- U
- =
- ∑
- μ
-
-
- H
- μ
-
- D
- μ
- ,
- wherein each operator Dμ lives in μ with respect to a set of Jμ operators that satisfies the J-properties, wherein said total SEO comprises a product of unitary operators Λμ554 , wherein each Λμ is designed to diagonalize for the matrix to which it is applied, all rows or columns corresponding to index μ.
A device that calculates a total SEO, with the purpose of using said total SEO to operate a quantum computer, and to induce said quantum computer to undergo a unitary transformation U that acts on n qu(d)its, wherein U simultaneously diagonalizes a set of operators Hμ that satisfies the H-properties, wherein said U can be expressed in the form
- U
- =
- ∑
- μ
-
-
- H
- μ
-
- D
- μ
- ,
- wherein each operator Dμ lives in μ with respect to a set of Jμ operators that satisfies the J-properties, wherein said total SEO comprises a product of unitary operators Λμ554 , wherein each Λμ is designed to diagonalize for the matrix to which it is applied, all rows or columns corresponding to index μ.
A method of operating a classical computer to calculate a total SEO, with the purpose of using said total SEO to operate a quantum computer, and to induce said quantum computer to undergo a transformation
- A
-
-
- Γ
-
- (
- τ
- )
-
- ∏
-
- =
- 1
- L
-
-
- {
- J
- μ
-
-
- (
- κ
-
- n
-
- )
- }
-
- A
- †
- ,
-
- wherein
- A
- =
- ∏
-
- =
- 1
- L
-
-
- {
- U
-
-
- (
- κ
-
- n
-
- )
- }
- ,
- wherein τ is the target qu(d)it and κlnl are nl control qu(dl) its which are different particles for different l, wherein Γ(τ) is an element of U(d) acting on τ, wherein Jμl(κlnl) for all μl with fixed l is a set of operators satisfying the J-properties and acting on κlnl, wherein Uμl(κlnl) is a unitary operator acting on κlnl and satisfying
- Uμ(α)Jμ(α)Uμ(α)†=Hμ(α)
- with μ=μl and α=κlnl, wherein Hμl(κlnl) for all μl with fixed l is a set of operators satisfying the H-properties, wherein said Uμl(κlnl) comprises a product of unitary operators Λμl 554 for all μl at fixed l, wherein each Λμl is designed to diagonalize the Jμl rows or columns of some matrix.
A device that calculates a total SEO, with the purpose of using said total SEO to operate a quantum computer, and to induce said quantum computer to undergo a transformation
- A
-
-
- Γ
-
- (
- τ
- )
-
- ∏
-
- =
- 1
- L
-
-
- {
- J
- μ
-
-
- (
- κ
-
- n
-
- )
- }
-
- A
- †
- ,
-
- wherein
- A
- =
- ∏
-
- =
- 1
- L
-
-
- {
- U
-
-
- (
- κ
-
- n
-
- )
- }
- ,
- wherein τ is the target qu(d)it and κlnl are nl control qu(dl) its which are different particles for different l, wherein Γ(τ) is an element of U(d) acting on τ, wherein Jμl(κlnl) for all μl with fixed l is a set of operators satisfying the J-properties and acting on κlnl, wherein Uμl(κlnl) is a unitary operator acting on κlnl and satisfying
- Uμ(α)Jμ(α)Uμ(α)†=Hμ(α)
- with μ=μl and α=κlnl, wherein Hμl(κlnl) for all p with fixed £ is a set of operators satisfying the H-properties, wherein said Uμl(κlnl) comprises a product of unitary operators Λμ554 for all μl at fixed l, wherein each Λμl, is designed to diagonalize the Jμl rows or columns of some matrix.
Dependencies are inferred from the claim text.