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Application US20190258757
Published 2019-08-22
Optimal Fault-tolerant Implementations Of Heisenberg Interactions And Controlled-zª Gates
The disclosure describes various aspects of techniques for optimal fault-tolerant implementations of controlled-Za gates and Heisenberg interactions. Improvements in the implementation of the controlled-Za gate can be made by using a clean ancilla and in-circuit measurement. Various examples are described that depend on whether the implementation is with or without measurement and feedforward. The implementation of the Heisenberg interaction can leverage the improved controlled-Za gate implementation. These implementations can cut down significantly the implementation costs associated with fault-tolerant quantum computing systems.
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- 1. A method for performing a quantum algorithm, comprising:
identifying use of a controlled-Za gate as part of the quantum algorithm, wherein a is a parameter and a∈[−1, 1]; implementing the controlled-Za gate for a fault-tolerant quantum information processing (QIP) system, wherein the implementation of the controlled-Za gate includes multiple elements with only six (6) of the elements being controlled-NOT (CNOT) gates; mapping the implementation of the controlled-Za gate into a physical representation in the fault-tolerant QIP system; and performing the quantum algorithm based at least in part on the physical representation.
- 8. A fault-tolerant quantum information processing (QIP) system for performing a quantum algorithm, comprising:
an implementation component configured to:
identify use of a controlled-Za gate as part of the quantum algorithm, wherein a is a parameter and a∈[−1, 1],
implement the controlled-Za gate for the fault-tolerant QIP system, wherein the implementation of the controlled-Za gate includes multiple elements with only six (6) of the elements being controlled-NOT (CNOT) gates, and
map the implementation of the controlled-Za gate into a physical representation in the fault-tolerant QIP system; and
an algorithms component configured to perform the quantum algorithm based at least in part on the physical representation.
- 9. A non-transitory computer-readable medium storing code with instructions executable by a processor for performing a quantum algorithm, comprising:
code for identifying use of a controlled-Za gate as part of the quantum algorithm, wherein a is a parameter and a∈[−1, 1]; code for implementing the controlled-Za gate for a fault-tolerant quantum information processing (QIP) system, wherein the implementation of the controlled-Za gate includes multiple elements with only six (6) of the elements being controlled-NOT (CNOT) gates; code for mapping the implementation of the controlled-Za gate into a physical representation in the fault-tolerant QIP system; and code for performing the quantum algorithm based at least in part on the physical representation.
- 10. A method for performing a quantum algorithm, comprising:
identifying use of a controlled-Za gate as part of the quantum algorithm, wherein a is a parameter and a∈[−1, 1]; implementing the controlled-Za gate for a fault-tolerant quantum information processing (QIP) system, wherein the implementation of the controlled-Za gate includes multiple elements with only four (4) of the elements being T gates, only three (3) of the elements being controlled-NOT (CNOT) gates, and only three (3) of the elements being Hadamard (H) gates; mapping the implementation of the controlled-Za gate into a physical representation in the fault-tolerant QIP system; and performing the quantum algorithm based at least in part on the physical representation.
- 17. A fault-tolerant quantum information processing (QIP) system for performing a quantum algorithm, comprising:
an implementation component configured to:
identify use of a controlled-Za gate as part of the quantum algorithm, wherein a is a parameter and a∈[−1, 1],
implement the controlled-Za gate for the fault-tolerant QIP system, wherein the implementation of the controlled-Za gate includes multiple elements with only four (4) of the elements being T gates, only three (3) of the elements being controlled-NOT (CNOT) gates, and only three (3) of the elements being Hadamard (H) gates, and
map the implementation of the controlled-Za gate into a physical representation in the fault-tolerant QIP system; and
an algorithms component configured to perform the quantum algorithm based at least in part on the physical representation.
- 18. A non-transitory computer-readable medium storing code with instructions executable by a processor for performing a quantum algorithm, comprising:
code for identifying use of a controlled-Za gate as part of the quantum algorithm, wherein a is a parameter and a∈[−1, 1]; code for implementing the controlled-Za gate for a fault-tolerant quantum information processing (QIP) system, wherein the implementation of the controlled-Za gate includes multiple elements with only four (4) of the elements being T gates, only three (3) of the elements being controlled-NOT (CNOT) gates, and only three (3) of the elements being Hadamard (H) gates; code for mapping the implementation of the controlled-Za gate into a physical representation in the fault-tolerant QIP system; and code for performing the quantum algorithm based at least in part on the physical representation.
- 19. A method for performing a quantum simulation, comprising:
identifying use of a Heisenberg interaction as part of the quantum simulation; identifying a controlled-Za gate for implementing the Heisenberg interaction, wherein a is a parameter and a∈[−1, 1]; implementing the Heisenberg interaction for a fault-tolerant quantum information processing (QIP) system, wherein the implementation of the Heisenberg interaction is based on an implementation of the controlled-Za gate and includes multiple elements with only one (1) of the elements being a parametrized Za gate; mapping the implementation of the Heisenberg interaction into a physical representation in the fault-tolerant QIP system; performing the quantum simulation based at least in part on the physical representation; and providing results from the quantum simulation.
- 28. A fault-tolerant quantum information processing (QIP) system for performing a quantum simulation, comprising:
an implementation component configured to:
identify use of a Heisenberg interaction as part of the quantum simulation,
identify a controlled-Za gate for implementing the Heisenberg interaction, wherein a is a parameter and a∈[−1, 1],
implement the Heisenberg interaction for the fault-tolerant QIP system, wherein the implementation of the Heisenberg interaction is based on an implementation of the controlled-Za gate and includes multiple elements with only one (1) of the elements being a parametrized Za gate,
map the implementation of the Heisenberg interaction into a physical representation in the fault-tolerant QIP system; and
an algorithms component configured to:
perform the quantum algorithm based at least in part on the physical representation, and
provide results from the quantum simulation.
- 29. A non-transitory computer-readable medium storing code with instructions executable by a processor for performing a quantum simulation, comprising:
code for identifying use of a Heisenberg interaction as part of the quantum simulation; code for identifying a controlled-Za gate for implementing the Heisenberg interaction, wherein a is a parameter and a∈[−1, 1]; code for implementing the Heisenberg interaction for a fault-tolerant quantum information processing (QIP) system, wherein the implementation of the Heisenberg interaction is based on an implementation of the controlled-Za gate and includes multiple elements with only one (1) of the elements being a parametrized Za gate; code for mapping the implementation of the Heisenberg interaction into a physical representation in the fault-tolerant QIP system; code for performing the quantum simulation based at least in part on the physical representation; and code for providing results from the quantum simulation.
- 30. A method for performing a quantum simulation, comprising:
identifying use of a Heisenberg interaction as part of the quantum simulation; implementing a pre-fault tolerant implementation of the Heisenberg interaction, wherein the pre-fault tolerant implementation of the Heisenberg interaction includes multiple elements with only three (3) of the elements being controlled-NOT (CNOT) gates; mapping the pre-fault tolerant implementation of the Heisenberg interaction into a physical representation in a quantum information processing (QIP) system; performing the quantum simulation based at least in part on the physical representation; and providing results from the quantum simulation.
- 33. A quantum information processing (QIP) system for performing a quantum simulation, comprising:
an implementation component configured to:
identify use of a Heisenberg interaction as part of the quantum simulation;
implement a pre-fault tolerant implementation of the Heisenberg interaction, wherein the pre-fault tolerant implementation of the Heisenberg interaction includes multiple elements with only three (3) of the elements being controlled-NOT (CNOT) gates;
map the pre-fault tolerant implementation of the Heisenberg interaction into a physical representation in the QIP system; and
an algorithms component configured to:
perform the quantum algorithm based at least in part on the physical representation, and
provide results from the quantum simulation.
