Quantum Circuit Depth Calculator
The number of time steps required to execute a circuit.
Formula first
Overview
Quantum circuit depth represents the longest path of gates from any input to any output. In high-performance quantum computing, minimizing depth is essential for reducing the total execution time and mitigating the impact of decoherence before the computation completes.
Symbols
Variables
D = Depth
Apply it well
When To Use
When to use: Apply this metric when analyzing the parallelizability of a quantum algorithm. It is used to estimate the time-cost of a circuit on a specific hardware backend, assuming gates in the same 'layer' can be executed simultaneously.
Why it matters: Circuit depth is a primary constraint in the NISQ era because each additional layer of gates increases the probability of error due to qubit relaxation and dephasing. Algorithms with lower depth are generally more robust and have a higher success rate on near-term devices.
One free problem
Practice Problem
A quantum circuit consists of 10 sequential Hadamard gates applied to the same qubit. What is the depth of this circuit?
Solve for:
Hint: Since each gate depends on the previous one being completed, the depth is equal to the total number of gates.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Quantum Computation and Quantum Information by Michael A. Nielsen and Isaac L. Chuang
- Wikipedia: Quantum circuit
- Nielsen & Chuang, Quantum Computation and Quantum Information
- IBM Qiskit Documentation: Glossary
- Nielsen and Chuang Quantum Computation and Quantum Information
- Arute et al. Quantum supremacy using a programmable superconducting processor
- Preskill Quantum Computing in the NISQ era and beyond
- University Quantum Computing — Circuit Complexity