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Constant-Cost Implementations of Clifford Operations and Multiply-Controlled Gates Using Global Interactions.
Sergey Bravyi1, Dmitri Maslov1, Yunseong Nam2
1IBM Quantum, IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA.
Physical Review Letters
|December 23, 2022
Summary
This study demonstrates that quantum circuits using global entangling gates can implement essential quantum operations efficiently. These circuits offer a significant advantage for quantum algorithms by reducing the number of required entangling gates.
Area of Science:
- Quantum Computing
- Quantum Information Science
Background:
- Quantum circuits are fundamental to quantum computation.
- Efficient implementation of unitary operators is crucial for developing practical quantum algorithms.
Purpose of the Study:
- To investigate the efficiency of quantum circuits utilizing global entangling gates.
- To determine the cost of implementing common quantum operations using these circuits.
Main Methods:
- Considered quantum circuits with single-qubit operations and global entangling gates derived from Ising-type Hamiltonians.
- Analyzed the gate complexity for implementing various unitary operators.
Main Results:
- Achieved constant-cost implementations of Clifford operations (with/without ancillae).
- Developed a constant-cost implementation for multiply-controlled gates using linear ancillae.
- Showcased an O(log*n) cost implementation for n-controlled single-target gates with logarithmic ancillae.
Conclusions:
- Circuits with global entangling gates offer a significant asymptotic advantage in terms of gate cost.
- This approach enables highly efficient execution of key quantum operations, advancing quantum algorithm design.
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