Entanglement forging for quantum simulations
Techniques for quantum entanglement forging for quantum simulations are presented. A decomposer component can decompose a weakly entangled variational state into respective local components of the weakly entangled variational state, wherein the respective local components describe respective tensor product states. A quantum computing simulator component can perform respective quantum simulations of the respective local components of the weakly entangled variational state, and can determine respective portions of variational energy contributed by the respective tensor product states associated with the respective local components based on the respective quantum simulations of the respective local components of the weakly entangled variational state. An energy determination component can determine a variational energy associated with the weakly entangled variational state based on the respective portions of the variational energy contributed by the respective tensor product states.
1 . A computer-implemented method, comprising:
decomposing, by a processor, using a Schmidt decomposition and Schmidt coefficients, a non-maximally entangled variational state into respective local components of the non-maximally entangled variational state for respective simulation on a quantum computing system comprising a quantum processor comprising a set of qubits, wherein the set of qubits consists of a first quantity of qubits that is less than a second quantity of qubits needed to perform a full simulation of the non-maximally entangled variational state, wherein the respective local components describe respective tensor product states, wherein the decomposing comprises rejecting one or more bit strings associated with the respective tensor product states in response to the one or more bit strings differing from a defined reference bit string by a defined number of bits, and wherein the decomposing further comprises rejecting updates of respective Schmidt coefficients of the local components that exceed a defined fixed upper bound;
individually performing, by the quantum processor, using the set of qubits, respective quantum simulations of the respective local components to generate respective variational energy contributions of the respective tensor product states; and
determining, by the processor, a variational energy associated with the non-maximally entangled variational state based on a combination of the respective variational energy contributions of the respective tensor product states.
2 . The computer-implemented method of claim 1 , wherein the respective quantum simulations comprise a variational quantum eigensolver simulation.
3 . The computer-implemented method of claim 1 , wherein the respective tensor product states comprise a first tensor product state and a second tensor product state, wherein the respective local components of the non-maximally entangled variational state comprise a first local component associated with the first tensor product state and a second local component associated with the second tensor product state, and wherein the individually performing the respective quantum simulations comprises:
performing, by the quantum processor, a first quantum simulation of the first tensor product state using a first quantum circuit; and
performing, by the quantum processor, a second quantum simulation of the second tensor product state using a second quantum circuit.
4 . The computer-implemented method of claim 3 , the determining the variational energy comprises:
estimating, by the processor, a first portion of the variational energy based on a first variational energy contribution generated by the first quantum simulation of the first tensor product state; and
estimating, by the processor, a second portion of the variational energy based on a second variational energy contribution generated by the second quantum simulation of the second tensor product state.
5 . The computer-implemented method of claim 1 , wherein the combination is a linear combination of the respective variational energy contributions.
6 . The computer-implemented method of claim 1 , wherein the determining the variational energy comprises performing a non-quantum computing calculation of the variational energy based on the combination of the respective variational energy contributions.
7 . The computer-implemented method of claim 1 , wherein the respective local components comprise a first local component of the non-maximally entangled variational state and a Hamiltonian, and a second local component of the non-maximally entangled variational state and the Hamiltonian, and wherein the computer-implemented method further comprises:
creating, by the quantum processor, a first entangled state among a first subset of the set of qubits associated with first quantum circuitry based on a first quantum simulation relating to the first local component;
creating, by the quantum processor, a second entangled state among a second subset of the set of qubits associated with second quantum circuitry based on a second quantum simulation relating to the second local component, wherein the first subset is different from the second subset;
performing, by the processor, a non-quantum computing simulation of a third entangled state among a third subset of the set of qubits, wherein the third subset comprises qubits from the first subset and the second subset; and
determining, by the processor, an entanglement entropy relating to the third subset of qubits based on the non-quantum computing simulation.
8 . A system, comprising:
a memory that stores computer-executable components; and
a processor, operatively coupled to the memory, that executes at least one of the computer-executable components that:
decomposes, using a Schmidt decomposition and Schmidt coefficients, a non-maximally entangled variational state into respective local components of the non-maximally entangled variational state for respective simulation on a quantum computing system comprising a quantum processor comprising a set of qubits, wherein the set of qubits consists of a first quantity of qubits that is less than a second quantity of qubits needed to perform a full simulation of the non-maximally entangled variational state, wherein the respective local components describe respective tensor product states, wherein the decomposing comprises rejecting one or more bit strings associated with the respective tensor product states in response to the one or more bit strings differing from a defined reference bit string by a defined number of bits, and wherein the decomposing further comprises rejecting updates of respective Schmidt coefficients of the local components that exceed a defined fixed upper bound;
individually performs, by the quantum processor, using the set of qubits, respective quantum simulations of the respective local components to generate respective variational energy contributions of the respective tensor product states; and
determines a variational energy associated with the non-maximally entangled variational state based on a combination of the respective variational energy contributions of the respective tensor product states.
9 . The system of claim 8 , wherein the respective quantum simulations comprise a variational quantum eigensolver simulation.
10 . The system of claim 8 , wherein the respective tensor product states comprise a first tensor product state and a second tensor product state, wherein the respective local components of the non-maximally entangled variational state comprise a first local component associated with the first tensor product state and a second local component associated with the second tensor product state, and wherein the individually performing the respective quantum simulations comprises:
performing, by the quantum processor, a first quantum simulation of the first tensor product state using a first quantum circuit, and
performing, by the quantum processor, a second quantum simulation of the second tensor product state using a second quantum circuit.
11 . The system of claim 10 , wherein the determining the variational energy comprises:
estimating a first portion of the variational energy based on a first variational energy contribution generated by the first quantum simulation of the first tensor product state, and
estimating a second portion of the variational energy based on a second variational energy contribution generated by the second quantum simulation of the second tensor product state.
12 . The system of claim 8 , wherein the combination is a linear combination of the respective variational energy contributions.
13 . The system of claim 8 , wherein the determining the variational energy comprises performing a non-quantum computing calculation of the variational energy based on the combination of the respective variational energy contributions.
14 . The system of claim 8 , wherein the respective local components comprise a first local component of the non-maximally entangled variational state and a Hamiltonian, and a second local component of the non-maximally entangled variational state and the Hamiltonian, and wherein the at least one of the computer-executable components further:
creates, by the quantum processor, a first entangled state among a first subset of the set of qubits associated with first quantum circuitry based on a first quantum simulation relating to the first local component;
creates, by the quantum processor, a second entangled state among a second subset of the set of qubits associated with second quantum circuitry based on a second quantum simulation relating to the second local component, wherein the first subset is different from the second subset;
performs a non-quantum computing simulation of a third entangled state among a third subset of the set of qubits, wherein the third subset comprises qubits from the first subset and the second subset; and
an entanglement entropy relating to the third subset of qubits based on the non-quantum computing simulation.
15 . A computer program product that facilitates quantum simulations associated with quantum circuitry, the computer program product comprising a non-transitory computer readable medium having program instructions embodied therewith, the program instructions are executable by a processor to cause the processor to:
decompose, using a Schmidt decomposition and Schmidt coefficients, a non-maximally entangled variational state into respective local components of the non-maximally entangled variational state for respective simulation on a quantum computing system comprising a quantum processor comprising a set of qubits, wherein the set of qubits consists of a first quantity of qubits that is less than a second quantity of qubits needed to perform a full simulation of the non-maximally entangled variational state, wherein the respective local components describe respective tensor product states, wherein the decomposing comprises rejecting one or more bit strings associated with the respective tensor product states in response to the one or more bit strings differing from a defined reference bit string by a defined number of bits, and wherein the decomposing further comprises rejecting updates of respective Schmidt coefficients of the local components that exceed a defined fixed upper bound;
individually perform, by the quantum processor, using the set of qubits, respective quantum simulations of the respective local components to generate respective variational energy contributions of the respective tensor product states; and
determine a variational energy associated with the non-maximally entangled variational state based on a combination of the respective variational energy contributions of the respective tensor product states.
16 . The computer program product of claim 15 , wherein the respective tensor product states comprise a first tensor product state and a second tensor product state, wherein the respective local components of the non-maximally entangled variational state comprise a first local component associated with the first tensor product state and a second local component associated with the second tensor product state, individually performing the respective quantum simulations comprises:
performing, by the quantum processor, a first quantum simulation of the first tensor product state using a first quantum circuit;
determine a first portion of the variational energy based on a first variational energy contribution generated by the first quantum simulation of the first tensor product state;
performing, by the quantum processor, a second quantum simulation of the second tensor product state using a second quantum circuit; and
determine a second portion of the variational energy based on a second variational energy contribution generated by the second quantum simulation of the second tensor product state.
17 . The computer program product of claim 15 , wherein the respective quantum simulations comprise a variational quantum eigensolver simulation.
18 . The computer program product of claim 15 , wherein the combination is a linear combination of the respective variational energy contributions.
19 . The computer program product of claim 15 , wherein the determining the variational energy comprises performing a non-quantum computing calculation of the variational energy based on the combination of the respective variational energy contributions.
20 . The computer program product of claim 15 , wherein the respective local components comprise a first local component of the non-maximally entangled variational state and a Hamiltonian, and a second local component of the non-maximally entangled variational state and the Hamiltonian, and wherein the program instructions are executable by the processor to cause the processor to:
create, by the quantum processor, a first entangled state among a first subset of the set of qubits associated with first quantum circuitry based on a first quantum simulation relating to the first local component;
create, by the quantum processor, a second entangled state among a second subset of the set of qubits associated with second quantum circuitry based on a second quantum simulation relating to the second local component, wherein the first subset is different from the second subset;
perform a non-quantum computing simulation of a third entangled state among a third subset of the set of qubits, wherein the third subset comprises qubits from the first subset and the second subset; and
determine an entanglement entropy relating to the third subset of qubits based on the non-quantum computing simulation.