# Experimental Superposition of Orders of Quantum Gates

**Authors:** Lorenzo M. Procopio, Amir Moqanaki, Mateus Araújo, Fabio Costa, Irati A. Calafell, Emma G. Dowd, Deny R. Hamel, Lee A. Rozema, Časlav Brukner, Philip Walther  
**arXiv:** [1412.4006](https://arxiv.org/abs/1412.4006)  
**Date:** 2014-12-12  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/1412.4006v1/

## Key points

- Quantum computing utilizes qubits in superpositions of different states to potentially outperform classical computers
- Research titled "Experimental Superposition of Orders of Quantum Gates" explores unconventional computational strategies
- Implementation of superimposing quantum circuits with unique gate orders shows promise for advancements in quantum computing paradigms
- Determination of gate commutation or anti-commutation can be made with just one use of each gate, unlike traditional circuits requiring at least two uses
- Scaling up to involve N gates could provide exponential edge over classical algorithms and linear advantage over fixed-gate-order-based quantum algorithms
- Resource leveraged in experiments enables "superposition of causal orders," enhancing efficiency levels for certain quantum algorithms

## Summary

In the realm of quantum computing, the manipulation of quantum bits (qubits) in superpositions of different states has shown promise for outperforming classical computers. This groundbreaking research, titled "Experimental Superposition of Orders of Quantum Gates" and conducted by researchers Lorenzo M. Procopio, Amir Moqanaki, Mateus Araújo, Fabio Costa, Irati A. Calafell, Emma G. Dowd, Deny R. Hamel, Lee A. Rozema, Časlav Brukner, and Philip Walther and published in Nature Communications (2015), showcases the potential for significant advancements in quantum computing paradigms through the exploration of unconventional computational strategies. One such strategy is the concept of superimposing quantum circuits with unique gate orders. Recent experimental efforts have validated this theory by implementing a scenario where two quantum gates are applied in a superposition of both possible orders to determine if they commute or anti-commute. Surprisingly, this determination can be made with just one use of each gate - a stark contrast to traditional quantum circuits that require at least two uses of one gate. As this approach is scaled up to involve N gates, creating a superposition of quantum circuits appears poised to deliver an exponential edge over classical algorithms and a linear advantage over fixed-gate-order-based quantum algorithms. The innovative resource leveraged in these experiments can be interpreted as a "superposition of causal orders," showcasing its potential to enable certain quantum algorithms to operate with efficiency levels that may prove unattainable on conventional fixed-gate-sequence-constrained quantum computers. , , , , and  are all key concepts in this groundbreaking study, highlighting the transformative capabilities offered by superpositions of quantum circuits and the potential for significant advancements in quantum computing paradigms through the exploration of unconventional computational strategies.