Quantum circuits are collections of quantum gates interconnected by quantum wires. They are building blocks of computers that use mechanical effects to perform tasks.

However, no quantum circuit is entirely error-free. Scientists around the globe are keen to optimize the efficiency of quantum circuits.

In a new study, scientists at the Indian Institute of Science (IISc) used mathematical analog and devised an algorithm to address this problem. The algorithm counts the number of computing resources necessary and optimizes them to obtain maximum efficiency.

Aninda Sinha, Associate Professor at the Centre for High Energy Physics, IISc, and corresponding author of the study said, *“We were able to [theoretically] build the most efficient circuit and bring down the number of resources needed by a huge factor.”*

Pratik Nandy, Sinha’s Ph.D. student and a co-author of the paper, said, “*Analogously, there are universal quantum gates for making quantum circuits. In reality, the gates are not 100 percent efficient; there is always an error associated with the output of each gate. And that error cannot be removed; it merely keeps on adding for every gate used in the circuit.”*

*“The most efficient circuit does not minimize the error in the output; rather, it minimizes the resources required for obtaining that same output. So the question boils down to given net error tolerance, what is the minimum number of gates needed to build a quantum circuit?”*

In 2006, a study by the University of Queensland had suggested that the counting the number of gates to achieve maximum efficiency is equivalent to finding the path with the shortest distance between two points in some mathematical space with volume V. A separate 2016 study argued that this number should vary directly with V.

Scientists in this study went back to Queensland’s original study and found that the total counting number of gates won’t result in variation with V, somewhat it varies with V2.

By generalizing the study’s assumptions and later introducing a few modifications, scientists found that the minimum number of gates indeed varies directly with the volume.

Surprisingly, the results of the study appear to link the efficiency optimization problem with string theory, a famous idea that tries to combine gravity and quantum physics to explain how the universe works.

According to scientists, this link can prove to be instrumental in helping scientists interpret theories that involve gravity. They also aim to develop methods that describe a collection of quantum circuits to calculate specific experimental quantities that cannot be theoretically simulated using existing methods.

##### Journal Reference:

- Renormalized Circuit Complexity. DOI: 10.1103/PhysRevLett.124.101602
- Quantum Computation as Geometry. DOI: 10.1126/science.1121541
- Holographic Complexity Equals Bulk Action? DOI: 10.1103/PhysRevLett.116.191301