# Reducing the CNOT count for Clifford+T circuits on NISQ architectures

@article{Gheorghiu2020ReducingTC, title={Reducing the CNOT count for Clifford+T circuits on NISQ architectures}, author={Vlad Gheorghiu and Jiaxin Huang and Sarah Meng Li and Michele Mosca and Priyanka Mukhopadhyay}, journal={IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems}, year={2020} }

While mapping a quantum circuit to the physical layer one has to consider the numerous constraints imposed by the underlying hardware architecture. Connectivity of the physical qubits is one such constraint that restricts two-qubit operations such as CNOT to "connected" qubits. SWAP gates can be used to place the logical qubits on admissible physical qubits, but they entail a significant increase in CNOT-count, considering the fact that each SWAP gate can be implemented by 3 CNOT gates.
In…

## 17 Citations

### Dynamic qubit allocation and routing for constrained topologies by CNOT circuit re-synthesis

- Physics
- 2022

Many quantum computers have constraints regarding which two-qubit operations are locally allowed. To run a quantum circuit under those constraints, qubits need to be allocated to diﬀerent quantum…

### Hypergraphic partitioning of quantum circuits for distributed quantum computing

- Computer Science
- 2023

,

### Predicting the Optimizability for Workflow Decisions

- Computer Science2022 IEEE/ACM Third International Workshop on Quantum Computing Software (QCS)
- 2022

This work proposes a novel approach to predict the optimizability of any circuit using a Machine Learning-based algorithm within the decision workflow that optimizes the most suitable circuits thereby increasing efficiency of the optimization process itself.

### Synthesizing efficient circuits for Hamiltonian simulation

- PhysicsArXiv
- 2022

We provide a new approach for compiling quantum simulation circuits that appear in Trotter, qDRIFT and multi-product formulas to Clifford and non-Clifford operations that can reduce the number of…

### Optimizing quantum circuit synthesis for permutations using recursion

- Computer ScienceDAC
- 2022

A family of recursive methods for the synthesis of qubit permutations on quantum computers with limited qubit connectivity is described, which combines a scalable heuristic with a non-scalable, yet exact, synthesis.

### Wasserstein Complexity of Quantum Circuits

- Physics, Computer ScienceArXiv
- 2022

This letter obtains a new lower bound for the quantum circuit complexity in terms of a novel complexity measure that is based on the quantum Wasserstein distance, a metric on the space of quantum states, which implies a quantum limit on converting quantum resources to computational resources.

### Recursive Methods for Synthesizing Permutations on Limited-Connectivity Quantum Computers

- Computer Science
- 2022

The utility of this family of recursive methods for the synthesis of qubit permutations on quantum computers with limited qubit connectivity is demonstrated by optimizing the compilation of Quantum Volume circuits, and an old conjecture on reversals being the hardest permutation on a path is disproved.

### Reducing the complexity of the Quantum Fourier Transform implementation

- Physics
- 2022

The quantum Fourier transform (QFT) is one of the most important quantum operations with wide range of application from integer factoring, quantum simulation, quantum Monte Carlo simulation for the…

### Compilation and scaling strategies for a silicon quantum processor with sparse two-dimensional connectivity

- Computer Science
- 2022

This work investigates compilation strategies for sparsely-connected 2d qubit arrangements and proposes a spin-qubit architecture with minimal compilation overhead that allows for compilation strategies which outperform the bestin-class compilation strategy for 1d chains, not only asymptotically, but also down to the minimal structure of a single square.

### T-count and T-depth of any multi-qubit unitary

- Materials Sciencenpj Quantum Information
- 2022

We design an algorithm to determine the (minimum) T-count of any n-qubit (n ≥ 1) unitary W of size 2n × 2n, over the Clifford+T gate set. The space and time complexity of our algorithm are…

## References

SHOWING 1-10 OF 73 REFERENCES

### CNOT circuit extraction for topologically-constrained quantum memories

- Computer ScienceQuantum Inf. Comput.
- 2020

A new technique for quantum circuit mapping, based on Gaussian elimination constrained to certain optimal spanning trees called Steiner trees, is given, which significantly out-performs general-purpose routines on CNOT circuits.

### Optimal synthesis of linear reversible circuits

- Computer ScienceQuantum Inf. Comput.
- 2008

Simulation results show that even for relatively small n the authors' algorithm is faster and yields smaller circuits than the standard method, and can be interpreted as a matrix decomposition algorithm, yielding an asymptotically efficient decomposition of a binary matrix into a product of elementary matrices.

### Quantum circuit optimizations for NISQ architectures

- Computer Science, PhysicsQuantum Science and Technology
- 2020

This work constructs a circuit synthesis scheme that takes as input the qubit connectivity graph and a quantum circuit over the gate set generated by { CNOT, R Z } and outputs a circuit that respects the connectivity of the device.

### On the controlled-NOT complexity of controlled-NOT–phase circuits

- Computer ScienceQuantum Science and Technology
- 2018

It is proved that CNOT minimization over CNOT and phase gates is at least as hard as synthesizing a CNOT -optimal circuit computing a set of parities of its inputs, and presented an efficient heuristic algorithm for synthesizing circuits over C NOT and Z-basis rotations with small CNOT cost.

### 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.

### An efficient conversion of quantum circuits to a linear nearest neighbor architecture

- Computer Science
- 2011

Several promising implementations of quantum computation rely on a Linear NearestNeighbor (LNN) architecture, which arranges quantum bits on a line, and allows neighborinteractions only. Therefore,...

### Efficient CNOT Synthesis for NISQ Devices

- Computer Science
- 2020

This study proposes a CNOT synthesis method called the token reduction method, which works for all quantum computers whose architecture is represented by connected graphs and consistently outperforms the best publicly accessible algorithm for all of the tested quantum architectures.

### NISQ circuit compilation is the travelling salesman problem on a torus

- Computer Science
- 2020

This work bridges a theoretical and practical gap between classical circuit design automation and the emerging field of quantum circuit optimisation with a novel approach to quantum circuit compilation (QCC).

### Quantum CNOT Circuits Synthesis for NISQ Architectures Using the Syndrome Decoding Problem

- Computer ScienceRC
- 2020

A new algorithm for the synthesis of CNOT circuits based on the solution of the syndrome decoding problem is presented, which addresses the case of ideal hardware with an all-to-all qubit connectivity and the cases of near-term quantum devices with restricted connectivity.

### t|ket⟩: a retargetable compiler for NISQ devices

- Computer ScienceQuantum Science and Technology
- 2020

The heart of t|ket⟩ is a language-agnostic optimising compiler designed to generate code for a variety of NISQ devices, which has several features designed to minimise the influence of device error.