Method for driving starting quantum state to target one
OwnerRobert R. Tucciinventor
Life of this patent
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Abstract
We describe a method for using a classical computer to generate a sequence of elementary operations (SEO) that can be used to operate a quantum computer. The SEO drives as near as desired, in an efficient way, a starting quantum state to a target one.
Claims20
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 drive a starting unit vector |s′> towards a target unit vector |t>, said method comprising the steps of:
- storing in said classical computer a data trove comprising a positive number ε, and a data-set sufficient to determine |<s′|t>|,
- calculating using said classical computer and using said data trove, a sequence of unitary operators U0,U1,U2, . . . , UM, wherein M depends on ε, wherein there are unit vectors |Φ1> and |Φ2> such that if ERR=∥v1>−|v2>|2 where |v1>=UM . . . U1U0|s′>|Φ1> and |v2>=|t>|Φ2>, then ERR≦ε,
- calculating using said classical computer for each j=0,1,2, . . . M, a SEO corresponding to Uj, wherein said total SEO equals the product ΣM . . . Σ1Σ0,
- wherein for a multiplicity of j, Uj is approximately equal to an operator of the special form
- Aj†{exp(λj|tj><tj|)Bj}Aj
- for some real number λj not in the set {π/3,−π/3,π,−π}, some unit vector |tj>, and some unitary operators Aj and Bj.
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 drive a starting unit vector |s′> towards a target unit vector |t>, said device comprising:
- a memory arranged to store a data trove comprising a positive number ε, and a data-set sufficient to determine |<s′|t>|,
- a processor arranged to calculate using said data trove stored in said memory, a sequence of unitary operators U0,U1,U2, . . . , UM, wherein M depends on ε, and arranged to calculate for each j=0,1,2, . . . M, a SEO Σj corresponding to Uj, wherein there are unit vectors |Φ1> and |Φ2> such that if ERR=∥v1>−|v2>|2 where |v1>=UM . . . U1U0|s′>|Φ1> and |v2>=|t>|Φ2>, then ERR≦ε, wherein said total SEO equals the product ΣM . . . Σ1Σ0,
- wherein for a multiplicity of j, Uj is approximately equal to an operator of the special form
- Aj†{exp(λj|tj><tj|)Bj}Aj
- for some real number λj not in the set {π/3,−π/3,π,−π}, some unit vector |tj>, and some unitary operators Aj and Bj.
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 drive a starting unit vector |s′> towards a target unit vector |t>, said method comprising the steps of:
- storing in said classical computer a data trove comprising a positive number ε, and a data-set sufficient to determine |<s′|t>|,
- calculating using said classical computer and using said data trove, a sequence of unitary operators U0,U1,U2, . . . , UM, wherein M depends on ε, wherein there are unit vectors |Φ1> and |Φ2> such that if ERR=∥v1>−|v2>|2 where |v1>=UM . . . U1U0|s′>|Φ1> and |v2>=|t>|Φ2>, then ERR≦ε,
- calculating using said classical computer for each j=0,1,2, . . . M, a SEO Σj corresponding to Uj, wherein said total SEO equals the product ΣM . . . Σ1Σ0,
- wherein if A is the subset of {0,1,2, . . . M} such that for all j in A, Uj has only two distinct eigenvalues λ1j and λ2j, and the product λ1jλ*2j is not in the set {eiπ/3,e−iπ/3,−1}, then A has 3 or more elements.
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 drive a starting unit vector |s′> towards a target unit vector |t>, said device comprising:
- a memory arranged to store a data trove comprising a positive number ε, and a data-set sufficient to determine |<s′|t>|,
- a processor arranged to calculate using said data trove stored in said memory, a sequence of unitary operators U0,U1,U2, . . . , UM, wherein M depends on ε, and arranged to calculate for each j=0,1,2, . . . M, a SEO Σj corresponding to Uj, wherein there are unit vectors |Φ1> and |Φ2> such that if ERR=∥v1>−|v2>|2 where |v1>=UM . . . U1U0|s′>|Φ1> and |v2>=|t>|Φ2>, then ERR≦ε, wherein said total SEO equals the product ΣM . . . Σ1Σ0,
- wherein if A is the subset of {0,1,2, . . . M} such that for all j in A, Uj has only two distinct eigenvalues λ1j and λ2j, and the product λ1jλ*2j is not in the set {eiπ/3,e−iπ/3,−1}, then A has 3 or more elements.
Dependencies are inferred from the claim text.