Multi-Controlled NOT Quantum Circuit With Reduced Gate Depth
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Solution Overview
Problem
Existing quantum circuits for multi-controlled NOT gates require large circuit depths, leading to prolonged computation times, especially when implementing these gates using basic gates and varying auxiliary qubit and gate arrangements.
Innovation Solution
A quantum circuit design that minimizes circuit depth by utilizing a first auxiliary circuit, a quantum gate group, and a second auxiliary circuit, employing Toffoli gates or alternative quantum logic gates like CH, CZ, and CS gates to perform controlled NOT operations on target and auxiliary qubits, allowing for parallel operations and reduced depth.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If basic gates and auxiliary qubits are used to implement multi-controlled NOT gate, then the gate can be implemented on hardware platform, but circuit depth increases leading to longer computation time
Solution Approach 1:
The patent segments the multi-controlled NOT gate implementation into multiple layers (first auxiliary circuit, quantum gate group, second auxiliary circuit) that can be executed in parallel. This segmentation allows the circuit to be divided into independent operational stages, reducing the sequential depth and enabling parallel execution to decrease computation time while remaining compatible with hardware platforms.
Solution Approach 2:
The patent introduces auxiliary qubits as an additional dimension resource to reduce circuit depth. By adding these auxiliary quantum bits, the implementation can distribute control logic across multiple qubits simultaneously, enabling parallel operations that reduce the temporal dimension (computation time) while maintaining hardware compatibility.
2Productivity
If circuit depth is reduced for faster computation, then computation speed improves, but implementation complexity may increase
Solution Approach 1:
The patent uses auxiliary qubits as intermediary elements that facilitate the reduced-depth implementation. These intermediary qubits act as mediators between control qubits and the target qubit, enabling parallel controlled operations that reduce circuit depth and increase computation speed, while the structured use of these intermediaries keeps the overall complexity manageable through systematic gate grouping.
3Loss of time
If more auxiliary qubits are used to reduce circuit depth, then computation time decreases, but device resource consumption increases
Solution Approach 1:
The patent optimizes the number of auxiliary qubits by changing the structural parameters of the circuit implementation. Through careful parameter selection in the gate group configuration and layer structure, the patent achieves the minimum necessary auxiliary qubits to enable parallel operations that reduce computation time, balancing resource consumption with performance improvement.
Data Source
AI summary
Disclosed is a quantum circuit for implementing multi-controlled NOT gates with N control qubits. A quantum circuit for implementing multi-controlled NOT gates with N control qubits according to one embodiment of the present disclosure may include a first auxiliary circuit that corresponds to one or more initial layers of a plurality of layers and performs a controlled NOT operation on a target qubit based on an Nth control qubit from among the N control qubits and a first auxiliary qubit initialized to a |+> state, a quantum gate group that corresponds to the plurality of layers and performs controlled NOT operation on the first auxiliary qubit based on first to (N−1)th control qubits, and a second auxiliary circuit that corresponds one or more last layers of the plurality of layers and performs controlled NOT operation on the target qubit based on the Nth control qubit and the first auxiliary qubit.