Hamiltonian simulation in the interaction picture
AssigneeMicrosoft Technology Licensing, LLC
InventorsGuang Hao Low, Nathan O. Wiebe
Life of this patent
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Abstract
In this disclosure, quantum algorithms are presented for simulating Hamiltonian time-evolution e−i(A+B)t in the interaction picture of quantum mechanics on a quantum computer. The interaction picture is a known analytical tool for separating dynamical effects due to trivial free-evolution A from those due to interactions B. This is especially useful when the energy-scale of the trivial component is dominant, but of little interest. Whereas state-of-art simulation algorithms scale with the energy ∥A+B∥≤∥A∥+∥B∥ of the full Hamiltonian, embodiments of the disclosed approach generally scale linearly with the sum of the Hamiltonian coefficients from the low-energy component B and poly-logarithmically with those from A.
Claims15
A method, comprising:
- configuring a quantum computer to simulate time-evolution of a quantum system represented by a time-independent Hamiltonian of the form H=A+B, wherein A and B are two non-commuting parts, a free particle theory part A and a part describing interactions B by:
- transforming the time-independent Hamiltonian to a time-dependent Hamiltonian, wherein the time-dependent Hamiltonian has the form H(t)=eiAtBe−iAt;
- approximating a truncation and discretization of a Dyson series for the time-dependent Hamiltonian H(t) with a spectral norm α=maxt∥H(t)∥ and average rate-of change
- 〈
-
- H
- .
-
- 〉
- =
- 1
- t
-
- ∫
- 0
- t
-
- H
- .
- (
- s
- )
-
-
- ds
- ;
- and
- performing a simulation of the quantum system using the quantum computer by implementing a circuit of quantum gates.
A computing system, comprising:
- a classical computer configured to:
- transform a time-independent Hamiltonian of the form H=A+B wherein A and B are two non-commuting parts, a free-particle theory part, A, and a part describing interactions, B, to a time-dependent Hamiltonian in the interaction picture wherein the time-dependent Hamiltonian has the form H(t)=eiAtBe−iAt;
- approximate a truncation and discretization of a Dyson series for the time-dependent Hamiltonian, H(t), with a spectral-norm α=maxt ∥H(t)∥ and an average rate-of-change and
- 〈
-
- H
- .
-
- 〉
- =
- 1
- t
-
- ∫
- 0
- t
-
- H
- .
- (
- s
- )
-
-
- ds
- ;
- compile a circuit of quantum gates representing the approximated truncated and discretized Dyson series;
- and
- a quantum computer configured to perform a simulation of the quantum system by implementing the circuit of quantum gates.
A method, comprising:
- implementing a quantum algorithm on a quantum computer for simulating a general sparse time-dependent quantum system represented by a time-dependent Hamiltonian H(t), wherein the quantum algorithm does not use graph decomposition techniques by:
- approximating a truncation and discretization of a Dyson series for the time-dependent Hamiltonian, H(t), with a spectral-norm α=maxt∥h(t)∥ and average rate-of-change
- 〈
-
- H
- .
-
- 〉
- =
- 1
- t
-
- ∫
- 0
- t
-
- H
- .
- (
- s
- )
-
-
- ds
- ;
- compiling a circuit of quantum gates representing the approximated truncated and discretized Dyson series;
- and
- implementing the quantum algorithm on the quantum computer by implementing the circuit of quantum gates.
Dependencies are inferred from the claim text.