Method for sampling probability distributions using a quantum computer
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 operation (SEO) that can be used to operate a quantum computer, thereby inducing the quantum computer to sample an arbitrary probability distribution. The probability distribution being sampled is specified in the form of a Bayesian network.
Claims25
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 approximately sample a probability distribution π(x) defined for all x∈{0,1}NB, said method comprising the steps of:
- storing in said classical computer a data trove comprising a positive number ε, a point x0∈{0,1}NB such that π(x0) is nonzero, and a data-set that specifies said probability distribution π(x),
- 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(x) such that if ERR=∥v1−|2|2 where |v1=UM . . . U1U0|x0|Φ1 and |v2=Σx√{square root over (π(x))}|x|Φ2(x), 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.
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 approximately sample a probability distribution π(x) defined for all x∈{0,1}NB, said device comprising:
- a memory arranged to store a data trove comprising a positive number ε, a point x0∈{0,1}NB such that π(x0) is nonzero, and a data-set that specifies said probability distribution π(x),
- 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(x) such that if ERR=∥v1−|v2|2 where |v1=UM . . . U1U0|x0|Φ1 and |v2=Σx√{square root over (π(x))}|x|Φ2(x), then ERR≦ε, wherein said total SEO equals the product ΣM . . . Σ1Σ0.
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 approximately sample a probability distribution π(x) defined for all x∈{0,1}NB, said method comprising the steps of:
- storing in said classical computer a data trove comprising a positive number ε, and a data-set that specifies a multiplicity of conditional probabilities of said π(x),
- 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(x) such that if ERR=∥v1−|v2|2 where |v1=UM . . . U1U0|Φ1 and |v2=Σx√{square root over (π(x))}|x|Φ2(x), 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.
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 approximately sample a probability distribution π(x) defined for all x∈{0,1}NB said device comprising:
- a memory arranged to store a data trove comprising a positive number ε, and a data-set that specifies a multiplicity of conditional probabilities of said π(x),
- 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 said total SEO equals the product ΣM . . . Σ1Σ0, wherein there are unit vectors |Φ1 and |Φ2(x) such that if ERR=∥v1−|v2|2 where |v1=UM . . . U1U0|Φ1 and |v2=Σx√{square root over (π(x))}|x|Φ2(x), then ERR≦ε.
Dependencies are inferred from the claim text.