🔧 Gate Decomposition
Break down complex gates into universal building blocks
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Building Quantum Circuits
Why Decompose Quantum Gates?
Gate decomposition is the process of expressing complex quantum gates as sequences of simpler, physically implementable gates. Real quantum hardware can only execute a limited set of native gates—decomposition bridges the gap between algorithms and hardware.
🎯The Problem
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Infinite Gate Set
Algorithms use arbitrary rotations
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Hardware Limits
Quantum processors have 5-10 native gates
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Multi-Qubit Gates
Complex gates like Toffoli need decomposition
✓The Solution
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Universal Sets
Small sets that approximate any gate
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Systematic Methods
Proven decomposition algorithms
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Hardware Compatibility
Circuits run on real quantum computers
Key Concepts
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Universal Gate Set
A finite set of gates that can approximate any quantum operation to arbitrary precision
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Gate Equivalence
Different gate sequences that produce the same quantum state transformation
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Circuit Depth
Number of sequential gate layers—shorter is better for minimizing errors
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Approximation Error
Difference between ideal gate and decomposed approximation
💡Real-World Impact
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IBM Quantum:Automatically decomposes circuits to native {CX, ID, RZ, SX, X} gates
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Google Sycamore:Uses {√X, √Y, CZ} native gates—all others decomposed
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IonQ:Native arbitrary single-qubit rotations reduce decomposition overhead