Efficient quantum simulation with quantum information compression and multiple fermion-to-qubit basis transformations
View Patent ↗Aspects of the present disclosure describe a method including compressing and uncompressing redundant quantum information encoded in quantum computers; processing quantum information in the compressed space; and computing, in response to determining the ansatz terms, a set of optimal transformations.
1 . A method of using a quantum information processing system comprising a plurality of trapped ions, each trapped ion defining a qubit, the method comprising:
performing a dynamic simulation of a Fermionic system, comprising:
computing, by a processor, first quantum circuits that implement one-body Trotter terms and second quantum circuits that implement two-body Trotter terms of a time evolution operator of the Fermionic system on a plurality of qubits;
compressing, by the processor, the second quantum circuits, each of which implements a two-body Trotter term on a first qubit, a second qubit, a third qubit, and a fourth qubit of the plurality of qubits in a selected state, wherein in the selected state, the first and second qubits are in a first qubit state, and the third and fourth qubits are in a second qubit state;
implementing, by an optical controller, the computed first quantum circuits and the compressed second quantum circuits on the plurality of qubits; and
measuring, by an imaging system, a qubit state of each of the plurality of qubits at a first time; and
outputting, by the processor, an indication of the measured qubit state of each of the plurality of qubits at the first time, the indication illustrating a time evolution of the Fermionic system at the first time.
2 . The method of claim 1 , wherein each of the first quantum circuits comprises a singly-controlled X gate and a controlled-NOT gate on the pair of qubits of the plurality of qubits.
3 . The method of claim 1 , wherein each of the second quantum circuits comprises a triply-controlled-X and controlled-NOT gates on the first, second, third, and fourth qubits.
4 . The method of claim 3 , wherein each of the compressed second quantum circuit comprises a quantum circuit that implements a one-body Trotter term on the first and third qubits, a controlled-NOT gate on the first and second qubits, and a controlled-NOT gate on the second and fourth qubits.
5 . The method of claim 1 , further comprising:
computing, by the processor, third quantum circuits that implement hybrid Trotter terms between one-body Trotter terms and two-body Trotter terms, each of the third quantum circuits comprising a doubly-controlled X gate.
6 . A method of performing an estimation of a ground state energy of a Fermionic system using a quantum information processing system comprising a plurality of trapped ions, each trapped ion defining a qubit, the method comprising:
performing a dynamic simulation of a Fermionic system, comprising:
preparing, by an optical controller, a plurality of qubits in a first ansatz state;
computing, by a processor, first quantum circuits that implement one-body Trotter terms and second quantum circuits that implement two-body Trotter terms of a parametrized unitary ansatz evolution operator of a Fermionic system, on the plurality of qubits;
compressing, by the processor, the second quantum circuits, each of which implements a two-body Trotter term on a first qubit, a second qubit, a third qubit, and a fourth qubit of the plurality of qubits in a selected state, wherein in the selected state, the first and second qubits are in a first qubit state, and the third and fourth qubits are in the same a second qubit state;
implementing, by the optical controller, the computed first quantum circuits and the compressed second quantum circuits on the plurality of qubits; and
measuring, by an imaging system, a qubit state of each of the plurality of qubits; and
outputting, by the processor, an indication of the measured qubit state of each of the plurality of qubits, the indication illustrating a first energy of the Fermionic system.
7 . The method of claim 6 , further comprising:
modifying, by the processor, the parametrized unitary ansatz evolution operator; and
repeating the preparing of the plurality of qubits, the computing of the first quantum circuits and the second quantum circuits, the compressing of the second quantum circuits, the measuring of the qubit state of each of the plurality of qubits, and the outputting of an indication of the measured qubit state of each of the plurality of qubits, the indication illustrating a second energy of the Fermionic system, wherein the second energy is less than the first energy.
8 . The method of claim 6 , wherein each of the first quantum circuits comprises a singly-controlled X gate and a controlled-NOT gate on the pair of qubits of the plurality of qubits.
9 . The method of claim 6 , wherein each of the second quantum circuits comprises 13 controlled-NOT gates on the first, second, third, and fourth qubits.
10 . The method of claim 9 , wherein the compressed second quantum circuits comprises a quantum circuit that implements a one-body Trotter term on the first and third qubits, a controlled-NOT gate on the first and second qubits, and a controlled-NOT gate on the second and fourth qubits.
11 . The method of claim 6 , further comprising:
computing, by the processor, third quantum circuits that implement hybrid Trotter terms between one-body Trotter terms and two-body Trotter terms, each of the third quantum circuits comprising 30 controlled-NOT gates; and
compressing, by the processor, the third quantum circuits.
12 . A non-transitory computer readable medium having instructions stored therein that, when executed by a processor, cause the processor to:
simulate a dynamic simulation of a Fermionic system by:
computing, by a processor, first quantum circuits that implement one-body Trotter terms and second quantum circuits that implement two-body Trotter terms of an evolution operator of a Fermionic system, on a plurality of qubits, each qubit comprising a trapped ion;
compressing, by the processor, the second quantum circuits, each of which implements a two-body Trotter term on a first qubit, a second qubit, a third qubit, and a fourth qubit of the plurality of qubits in a selected state, wherein in the selected state, the first and second qubits are in a first qubit state, and the third and fourth qubits are in a second qubit state;
implementing, by an optical controller, the computed first quantum circuits and the compressed second quantum circuits on the plurality of qubits; and
measuring, by an imaging system, a qubit state of each of the plurality of qubits; and
output, by the processor, an indication of the measured qubit state of each of the plurality of qubits.
13 . The non-transitory computer readable medium of claim 12 , wherein
the evolution operator of the Fermionic system is a time evolution operator of the Fermionic system, and
the indication of the measured qubit state of each of the plurality of qubits is a time evolution of the Fermionic system.
14 . The non-transitory computer readable medium of claim 12 , wherein
the evolution operator of the Fermionic system is a parametrized unitary ansatz evolution operator of the Fermionic system, and
the indication of the measured qubit state of each of the plurality of qubits is a first energy of the Fermionic system.
15 . The non-transitory computer readable medium of claim 14 , further comprising instructions for preparing, by the optical controller, the plurality of qubits in a first ansatz state.
16 . The non-transitory computer readable medium of claim 15 , further comprising instructions for
modifying, by the processor, the parametrized unitary ansatz evolution operator; and
repeating the preparing of the plurality of qubits, the computing of the first quantum circuits and the second quantum circuits, the compressing of the second quantum circuits, the measuring of the qubit state of each of the plurality of qubits, and the outputting of an indication of the measured qubit state of each of the plurality of qubits, the indication illustrating a second energy of the Fermionic system, wherein the second energy is less than the first energy.
17 . The non-transitory computer readable medium of claim 12 , wherein each of the first quantum circuits comprises a singly-controlled X gate and a controlled-NOT gate on the pair of qubits of the plurality of qubits.
18 . The non-transitory computer readable medium of claim 12 , wherein each of the second quantum circuits comprises controlled-NOT gates on the first, second, third, and fourth qubits.
19 . The non-transitory computer readable medium of claim 18 , wherein the compressed second quantum circuit comprises a quantum circuit that implements a one-body Trotter term on the first and third qubits, a controlled-NOT gate on the first and second qubits, and a controlled-NOT gate on the second and fourth qubits.
20 . The non-transitory computer readable medium of claim 15 , further comprising instructions for
computing, by the processor, the third quantum circuits.