OPTIMAL FAULT-TOLERANT IMPLEMENTATIONS OF HEISENBERG INTERACTIONS AND CONTROLLED-Z^a GATES
The disclosure describes various aspects of techniques for optimal fault-tolerant implementations of controlled-Z α gates and Heisenberg interactions. Improvements in the implementation of the controlled-Z α 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-Z α gate implementation. These implementations can cut down significantly the implementation costs associated with fault-tolerant quantum computing systems.
1 . A method for performing a quantum algorithm, comprising:
identifying use of a controlled-Z α gate for the quantum algorithm, wherein α is a parameter and αϵ[−1, 1], wherein the quantum algorithm includes a Heisenberg interaction and is based on projecting a real-valued degree of freedom in the Heisenberg interaction onto a R z α rotation;
implementing the controlled-Z α gate for a fault-tolerant quantum information processing (QIP) system, wherein the controlled-Z α gate includes multiple elements with only six (6) of the multiple elements being controlled-NOT (CNOT) gates;
mapping the implemented controlled-Z α gate into a physical representation in the fault-tolerant QIP system; and
performing the quantum algorithm that includes the Heisenberg interaction based at least in part on the physical representation.
2 . The method of claim 1 , wherein the implementing of the controlled-Z α gate includes implementing the controlled-Z α gate with an ancilla qubit for the fault-tolerant QIP system.
3 . The method of claim 2 , wherein the multiple elements of the controlled-Z α gate include a single parametrized Z α gate, only four (4) Hadamard gates, only four (4) T gates, only four (4) T † gates, and the six (6) controlled-NOT (CNOT) gates.
4 . The method of claim 1 , wherein the quantum algorithm is a quantum Fourier transform (QFT).
5 . The method of claim 1 , further comprising implementing the controlled-Z α gate without measurement and feedforward.
6 . The method of claim 1 , wherein:
the fault-tolerant QIP system is a trapped-ion QIP system, and
the mapping of the implemented controlled-Z α gate uses multiple qubits in the trapped-ion QIP system.
7 . The method of claim 1 , wherein:
the fault-tolerant QIP system is a superconducting QIP system, and
the mapping of the implemented controlled-Z α gate uses multiple superconducting-based qubits in the superconducting QIP system.
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-Z α gate as part of the quantum algorithm, wherein α is a parameter and αϵ[−1, 1], wherein the quantum algorithm includes a Heisenberg interaction and is based on projecting a real-valued degree of freedom in the Heisenberg interaction onto a R z α rotation,
implement the controlled-Z α gate for the fault-tolerant quantum information processing (QIP) system, wherein the controlled-Z α gate includes multiple elements with only six (6) of the multiple elements being controlled-NOT (CNOT) gates;
map the implemented controlled-Z α gate into a physical representation in the fault-tolerant QIP system; and
an algorithms component configured to perform the quantum algorithm that includes the Heisenberg interaction based at least in part on the physical representation.
9 . The fault-tolerant QIP system of claim 8 , wherein the implementation component is further configured to implement the controlled-Z α gate with an ancilla qubit for the fault-tolerant QIP system.
10 . The fault-tolerant QIP system of claim 9 , wherein the multiple elements of the controlled-Z α gate include a single parametrized Z α gate, only four (4) Hadamard gates, only four (4) T gates, only four (4) T † gates, and the six (6) controlled-NOT (CNOT) gates.
11 . The fault-tolerant QIP system of claim 8 , wherein the quantum algorithm is a quantum Fourier transform (QFT).
12 . The fault-tolerant QIP system of claim 8 , wherein the implementation component is further configured to implement the controlled-Z α gate without measurement and feedforward.
13 . The fault-tolerant QIP system of claim 8 , wherein:
the fault-tolerant QIP system is a trapped-ion QIP system, and
the implementation component is further configured to map the implemented controlled-Z α gate using multiple qubits in the trapped-ion QIP system.
14 . The fault-tolerant QIP system of claim 8 , wherein:
the fault-tolerant QIP system is a superconducting QIP system, and
the implementation component is further configured to map the implemented controlled-Z α gate using multiple superconducting-based qubits in the superconducting QIP system.
15 . A fault-tolerant quantum information processing (QIP) system comprising:
electronic memory configured to store code for performing a quantum algorithm; and
a processor that, when executing the code stored on the electronic memory, is configured to:
identify use of a controlled-Z α gate for the quantum algorithm, wherein α is a parameter and αϵ[−1, 1], wherein the quantum algorithm includes a Heisenberg interaction and is based on projecting a real-valued degree of freedom in the Heisenberg interaction onto a R z α rotation,
implement the controlled-Z α gate for a fault-tolerant quantum information processing (QIP) system, wherein the controlled-Z α gate includes multiple elements with only six (6) of the multiple elements being controlled-NOT (CNOT) gates,
map the implemented controlled-Z α gate into a physical representation in the fault-tolerant QIP system, and
perform the quantum algorithm that includes the Heisenberg interaction based at least in part on the physical representation.
16 . The fault-tolerant QIP system of claim 15 ,
wherein the processor is further configured to implement the controlled-Z α gate with an ancilla qubit for the fault-tolerant QIP system, and
wherein the multiple elements of the controlled-Z α gate include a single parametrized Z α gate, only four (4) Hadamard gates, only four (4) T gates, only four (4) T † gates, and the six (6) controlled-NOT (CNOT) gates.
17 . The fault-tolerant QIP system of claim 15 , wherein the quantum algorithm is a quantum Fourier transform (QFT).
18 . The fault-tolerant QIP system of claim 15 , wherein the processor is further configured to implement the controlled-Z α gate without measurement and feedforward.
19 . The fault-tolerant QIP system of claim 8 , wherein:
the fault-tolerant QIP system is a trapped-ion QIP system, and
the processor is further configured to map the implemented controlled-Z α gate using multiple qubits in the trapped-ion QIP system.
20 . The fault-tolerant QIP system of claim 8 , wherein:
the fault-tolerant QIP system is a superconducting QIP system, and
the processor is further configured to map the implemented controlled-Z α gate using multiple superconducting-based qubits in the superconducting QIP system.