# On the advantages of using relative phase Toffolis with an application to multiple control Toffoli optimization

@article{Maslov2015OnTA, title={On the advantages of using relative phase Toffolis with an application to multiple control Toffoli optimization}, author={Dmitrii L. Maslov}, journal={ArXiv}, year={2015}, volume={abs/1508.03273} }

Various implementations of the Toffoli gate up to a relative phase have been known for years. The advantage over regular Toffoli gate is their smaller circuit size. However, their use has been often limited to a demonstration of quantum control in designs such as those where the Toffoli gate is being applied last or otherwise for some specific reasons the relative phase does not matter. It was commonly believed that the relative phase deviations would prevent the relative phase Toffolis from…

## 69 Citations

### Improved NCV Gate Realization of Arbitrary Size Toffoli Gates

- Engineering2017 30th International Conference on VLSI Design and 2017 16th International Conference on Embedded Systems (VLSID)
- 2017

An efficient heuristic is used for decomposition of the Toffoli gate without using any NCV catalog, after applying a template based optimization step, and the cost of resultant circuit is similar to or sometimes better than the one reported by previous approaches.

### Dynamical Decomposition and Mapping of MPMCT Gates to Nearest Neighbor Architectures

- Computer Science2021 26th Asia and South Pacific Design Automation Conference (ASP-DAC)
- 2021

This paper proposes a method to inserts SWAP gates while decomposing MPMCT gates unlike most of the existing methods, and considers the effect on the latter part of a circuit carefully by considering the qubit layout when composing an MPM CT gate.

### A SAT Encoding for Optimal Clifford Circuit Synthesis

- Computer ScienceASP-DAC
- 2023

An optimal synthesis method for Clifford circuits is proposed based on encoding the task as a satisfiability problem and solving it using a SAT solver in conjunction with a binary search scheme and it is demonstrated to synthesize optimal circuits for up to 26 qubits---more than four times as many as the current state of the art.

### Efficient Construction of a Control Modular Adder on a Carry-Lookahead Adder Using Relative-Phase Toffoli Gates

- Computer ScienceIEEE Transactions on Quantum Engineering
- 2022

This article constructs an efficient control modular adder with small KQ by using relative-phase Toffoli gates in two major types of quantum computers: fault-tolerant quantum computers on the logical layer and noisy intermediate-scale quantum computers (NISQ).

### A polynomial time and space heuristic algorithm for T-count

- Computer ScienceQuantum Science and Technology
- 2021

This work focuses on reducing the physical cost of implementing quantum algorithms when using the state-of-the-art fault-tolerant quantum error correcting codes, in particular, those for which implementing the T gate consumes vastly more resources than the other gates in the gate set.

### Efficient Circuits for Quantum Search over 2D Square Lattice Architecture

- Computer Science2019 56th ACM/IEEE Design Automation Conference (DAC)
- 2019

This work discusses how to efficiently implement MCT gates on 2D Square Lattices (2DSL), suitable for superconducting circuits, by taking advantage of relative-phase Toffoli gates and H-tree layouts to drastically reduce resulting circuits’ depths and the amount of SWAPping required.

### Towards Large-scale Functional Verification of Universal Quantum Circuits

- Computer Science, PhysicsQPL
- 2018

A framework for the formal specification and verification of quantum circuits based on the Feynman path integral is introduced, and the algorithm is shown to give a polynomial-time decision procedure for checking the equivalence of Clifford group circuits.

### Equivalence Checking of Quantum Circuits With the ZX-Calculus

- Computer ScienceIEEE Journal on Emerging and Selected Topics in Circuits and Systems
- 2022

It is demonstrated how the ZX-calculus based approach for equivalence checking can be expanded in order to verify the results of compilation flows and optimizations on quantum circuits.

### Signal processing techniques for efficient compilation of controlled rotations in trapped ions

- PhysicsNew Journal of Physics
- 2020

Quantum logic gates with many control qubits are essential in many quantum algorithms, but remain challenging to perform in current experiments. Trapped ion quantum computers natively feature the…

### Limiting the Search Space in Optimal Quantum Circuit Mapping

- Computer Science2022 27th Asia and South Pacific Design Automation Conference (ASP-DAC)
- 2022

It is shown that the search space of the mapping problem can be limited drastically while still preserving optimality, and optimal solutions can be determined for instances that timeouted before or speed-ups of up to three orders of magnitude can be achieved.

## References

SHOWING 1-10 OF 25 REFERENCES

### On the CNOT-cost of TOFFOLI gates

- PhysicsQuantum Inf. Comput.
- 2009

It is proved that the n-qubit analogue of the TOFFOLI requires at least 2n CNOT gates, and a complete classification of three-qu bit diagonaloperators by their CNOT-cost, which holds even if ancilla qubits are available.

### Polynomial-Time T-Depth Optimization of Clifford+T Circuits Via Matroid Partitioning

- Computer ScienceIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
- 2014

A polynomial-time algorithm for optimizing quantum circuits that takes the actual implementation of fault-tolerant logical gates into consideration, allowing space-time trade-offs to be easily explored.

### Elementary gates for quantum computation.

- MathematicsPhysical review. A, Atomic, molecular, and optical physics
- 1995

U(2) gates are derived, which derive upper and lower bounds on the exact number of elementary gates required to build up a variety of two- and three-bit quantum gates, the asymptotic number required for n-bit Deutsch-Toffoli gates, and make some observations about the number of unitary operations on arbitrarily many bits.

### The simplified Toffoli gate implementation by Margolus is optimal

- Biology
- 2003

It is proved that the simplified Toffoli gate by Margolus, which coincides with the Toffolis gate up to a single change of sign, cannot be realized with less than three controlled-not gates.

### Quantum Circuit Simplification and Level Compaction

- Computer Science, PhysicsIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
- 2008

This paper considers a local optimization technique based on templates to simplify and reduce the depth of nonoptimal quantum circuits and shows how templates can be used to compact the number of levels of a quantum circuit.

### Universal quantum computation with ideal Clifford gates and noisy ancillas (14 pages)

- Physics
- 2005

We consider a model of quantum computation in which the set of elementary operations is limited to Clifford unitaries, the creation of the state |0>, and qubit measurement in the computational basis.…

### Quantum circuits of T-depth one

- MathematicsArXiv
- 2012

A class of circuits whose T- depth can be reduced to 1 by using sufficiently many ancillas is described, and it is shown that the cost of adding an additional control to any controlled gate is at most 8 additional T-gates, and T-depth 2.

### Superconducting Circuits for Quantum Information: An Outlook

- PhysicsScience
- 2013

For the first time, physicists will have to master quantum error correction to design and operate complex active systems that are dissipative in nature, yet remain coherent indefinitely.

### Scaling the Ion Trap Quantum Processor

- PhysicsScience
- 2013

The latest progress and prospects in the scaling of trapped ions to hundreds or thousands of qubits and beyond are reviewed, with the promise of advanced architectures and new technologies, such as microfabricated ion traps and integrated photonics.

### Quantum computation and quantum information

- PhysicsMathematical Structures in Computer Science
- 2007

This special issue of Mathematical Structures in Computer Science contains several contributions related to the modern field of Quantum Information and Quantum Computing. The first two papers deal…