# Optimizing T gates in Clifford+T circuit as $pi/4$ rotations around Paulis

arXiv: Quantum Physics, 2019.

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Abstract:

In this work, we introduce a new circuit optimization technique to reduce the number of T gates in Clifford+T circuits by treating T gates conjugated by Clifford gates as $frac{pi}{4}$-rotations around Pauli operators. The tested benchmarks shows up to $71.43%$ and an average $42.67%$ reduction in T-count, both surpass the best performanc...More

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Introduction

- Much effort has been devoted to build the world’s first meaningful quantum computer, which can deliver the ability to help scientists/engineers to develop new materials from drugs to battery, and to solve optimization problems from finance to logistics.
- Limited connectivity of existing quantum hardwares have a significant impact on the cost of quantum algorithms
- This raise a related problem called qubit allocation or quantum scheduling[1, 2].
- There may be significant variation in the error rate of qubits and links, or system reliability in general, on existing hardwares[3]
- Such variation makes implementing a given circuit on NISQ hardwares to achieve better performance even more complicated

Highlights

- Much effort has been devoted to build the world’s first meaningful quantum computer, which can deliver the ability to help scientists/engineers to develop new materials from drugs to battery, and to solve optimization problems from finance to logistics
- We introduce a new circuit optimization technique to reduce the number of T gates in circuits by treating gates conjugated by
- To understand the ability of these noisy intermediate-scale quantum (NISQ) devices and the capability of future practical quantum computers, it is essential to develop efficient implementations of quantum algorithms, which are typically expressed in terms of quantum circuits
- We present a new optimization technique to reduce the number of T gates in Clifford+T circuits by treating every gate conjugated by
- A unified framework of circuit optimization would be very interesting. Another avenue of work is to start from the original unitary gate U which may not be exactly represented by
- The tested benchmarks shows up to 71.43% and an average 42.67% reduction in T-count, both surpass the best performance reported
- For quantum algorithms based on phase estimations, phase kickback tricks will introduce ancillary qubits to perform phase gates[26]

Results

- The tested benchmarks shows up to 71.43% and an average 42.67% reduction in T-count, both surpass the best performance reported.
- It is worth mentioning that unlike other T-count optimizers which usually cause more than 100% increase in CNOT-count, the optimization procedure will not increase CNOT-count while reducing T-count

Conclusion

**SUMMARY AND FUTURE WORK**

In this work, the authors present a new optimization technique to reduce the number of T gates in Clifford+T circuits by treating every gate conjugated

Clifford operators as π 4 Pauli operators.

For benchmarking circuits like Adder8 and Mod54, T-Optimizer will reduce significantly more T gates than any other circuit optimization software.

As the authors learn through the benchmarking result, all these benchmarked quantum circuit optimizers have “sweet spots” in which their performance has no equal.- A unified framework of circuit optimization would be very interesting
- Another avenue of work is to start from the original unitary gate U which may not be exactly represented by.
- The algorithm runs in O(log2.71(1/ǫ)) time and produce a quantum circuit of size O(log3.97(1/ǫ)) to approximate the desired unitary gate up to accuracy ǫ.
- To efficiently approximate general multi-qubit unitary gates, there is still ample room for improvement in circuit size

Summary

## Introduction:

Much effort has been devoted to build the world’s first meaningful quantum computer, which can deliver the ability to help scientists/engineers to develop new materials from drugs to battery, and to solve optimization problems from finance to logistics.- Limited connectivity of existing quantum hardwares have a significant impact on the cost of quantum algorithms
- This raise a related problem called qubit allocation or quantum scheduling[1, 2].
- There may be significant variation in the error rate of qubits and links, or system reliability in general, on existing hardwares[3]
- Such variation makes implementing a given circuit on NISQ hardwares to achieve better performance even more complicated
## Results:

The tested benchmarks shows up to 71.43% and an average 42.67% reduction in T-count, both surpass the best performance reported.- It is worth mentioning that unlike other T-count optimizers which usually cause more than 100% increase in CNOT-count, the optimization procedure will not increase CNOT-count while reducing T-count
## Conclusion:

**SUMMARY AND FUTURE WORK**

In this work, the authors present a new optimization technique to reduce the number of T gates in Clifford+T circuits by treating every gate conjugated

Clifford operators as π 4 Pauli operators.

For benchmarking circuits like Adder8 and Mod54, T-Optimizer will reduce significantly more T gates than any other circuit optimization software.

As the authors learn through the benchmarking result, all these benchmarked quantum circuit optimizers have “sweet spots” in which their performance has no equal.- A unified framework of circuit optimization would be very interesting
- Another avenue of work is to start from the original unitary gate U which may not be exactly represented by.
- The algorithm runs in O(log2.71(1/ǫ)) time and produce a quantum circuit of size O(log3.97(1/ǫ)) to approximate the desired unitary gate up to accuracy ǫ.
- To efficiently approximate general multi-qubit unitary gates, there is still ample room for improvement in circuit size

- Table1: We report the CNOT-count and T-count after no optimization (original) and after T-par, TOpt and T-Optimizer optimizations with no ancillae

Funding

- The tested benchmarks shows up to 71.43% and an average 42.67% reduction in T-count, both surpass the best performance reported
- The tested benchmarks shows up to 71.43% and an average 42.67% reduction in T-count, both surpassing the best performance reported
- It is worth mentioning that unlike other T-count optimizers which usually cause more than 100% increase in CNOT-count, our optimization procedure will not increase CNOT-count while reducing T-count

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