# Asymptotic Improvements to Quantum Circuits via Qutrits

@article{Gokhale2019AsymptoticIT, title={Asymptotic Improvements to Quantum Circuits via Qutrits}, author={Pranav Gokhale and Jonathan M. Baker and Casey Duckering and Natalie C. Brown and Kenneth R. Brown and Frederic T. Chong}, journal={2019 ACM/IEEE 46th Annual International Symposium on Computer Architecture (ISCA)}, year={2019}, pages={554-566} }

Quantum computation is traditionally expressed in terms of quantum bits, or qubits. In this work, we instead consider three-level qutrits. Past work with qutrits has demonstrated only constant factor improvements, owing to the $\log_{2}$ (3) binary-to-ternary compression factor. We present a novel technique using qutrits to achieve a logarithmic depth (runtime) decomposition of the Generalized Toffoli gate using no ancilla-a significant improvement over linear depth for the best qubit-only…

## 68 Citations

### Improved Quantum Circuits via Intermediate Qutrits

- Computer Science
- 2020

This work presents a novel technique, intermediate qutrits, to achieve sublinear depth decompositions of the Generalized Toffoli and other arithmetic circuits using no additional ancilla—a significant improvement over linear depth for the best qubit-only equivalents.

### Towards universal gate synthesis and error correction in transmon qudits

- Physics
- 2022

This work designs a superconducting qudit-based quantum processor wherein the logical space of transmon qubits is extended to higher-excited levels and proposes a universal gate set featuring a two-qudit cross-resonance entangling gate, which concludes that universal qudit control is within reach of current transmon-based architectures.

### Efficient realization of quantum algorithms with qudits

- Physics, Computer Science
- 2021

This work proposes a technique for an e-cient implementation of quantum algorithms with multilevel quantum systems (qudits) by transpilation of a circuit in the standard qubit form, which depends on the parameters of a qudit-based processor, such as their number and the number of accessible levels.

### QuDiet: A Classical Simulation Platform for Qubit-Qudit Hybrid Quantum Systems

- Computer Science
- 2022

Diet is introduced, a state-of-the-art user-friendly python-based higher-dimensional quantum computing simulator that simulates various benchmark quantum circuits by utilizing generalized quantum gates with an abstraction so that any naive user can simulate qudit systems with ease as compared to the existing ones.

### Initial-State Dependent Optimization of Controlled Gate Operations with Quantum Computer

- Computer Science, PhysicsQuantum
- 2022

A new circuit optimizer called AQCEL, which aims to remove redundant controlled operations from controlled gates, depending on initial states of the circuit, and can remove unnecessary qubit controls from multi-controlled gates in polynomial computational resources.

### Moving quantum states without swap via intermediate higher-dimensional qudits

- PhysicsPhysical Review A
- 2022

Quantum algorithms can be realized in the form of a quantum circuit. To map quantum circuit for speciﬁc quantum algorithm to quantum hardware, qubit mapping is an imperative technique based on the…

### Efficient Quantum Circuit Decompositions via Intermediate Qudits

- Computer Science2020 IEEE 50th International Symposium on Multiple-Valued Logic (ISMVL)
- 2020

This work gives a method to generate ancilia out of idle qubits by placing some in higher-value states, called qudits, and shows how to take a circuit with many O(n) ancillas and design an ancilla-free circuit with the same asymptotic depth.

### Realization of two-qutrit quantum algorithms on a programmable superconducting processor

- Physics
- 2022

Processing quantum information using quantum three-level systems or qutrits as the fundamen-tal unit is an alternative to contemporary qubit-based architectures with the potential to provide…

### Numerical gate synthesis for quantum heuristics on bosonic quantum processors

- PhysicsFrontiers in Physics
- 2022

There is a recent surge of interest and insights regarding the interplay of quantum optimal control and variational quantum algorithms. We study the framework in the context of qudits which are, for…

### Constructing All Qutrit Controlled Clifford+T gates in Clifford+T

- MathematicsRC
- 2022

. For a number of useful quantum circuits, qudit constructions have been found which reduce resource requirements compared to the best known or best possible qubit construction. However, many of the…

## References

SHOWING 1-10 OF 76 REFERENCES

### Superconducting qutrit-qubit circuit: A toolbox for efficient quantum gates

- Physics
- 2018

As classical computers struggle to keep up with Moore's law, quantum computing may represent a big step in technology and yield significant improvement over classical computing for many important…

### Quantum computing using shortcuts through higher dimensions

- Physics
- 2008

Quantum computation oﬀers the potential to solve fundamental yet otherwise intractable problems across a range of active ﬁelds of research. Recently, universal quantum-logic gate sets—the building…

### Factoring using $2n+2$ qubits with Toffoli based modular multiplication

- Computer ScienceQuantum Inf. Comput.
- 2017

An implementation of Shor's quantum algorithm to factor n-bit integers using only 2n+2 qubits using a purely Toffoli based modular multiplication circuit that evades most of the cost overheads originating from rotation synthesis and enables testing and localization of some faults in both, the logical level circuit and an actual quantum hardware implementation.

### Simplifying quantum logic using higher-dimensional Hilbert spaces

- Physics
- 2009

Quantum computation promises to solve fundamental, yet otherwise intractable, problems across a range of active fields of research. Recently, universal quantum logic-gate sets—the elemental building…

### Time-efficient implementation of quantum search with qudits

- Computer Science
- 2012

A simpler and more efficient scheme for the implementation of the multivalued Grover’s quantum search, in which the Hadamard gate is replaced by a d-dimensional (complex-valued) unitary matrix F, which can be realized through any physical interaction, which achieves an equal-weight superposition state.

### Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing

- Physics, Computer Science
- 2014

The results demonstrate that Josephson quantum computing is a high-fidelity technology, with a clear path to scaling up to large-scale, fault-tolerant quantum circuits.

### Factoring with Qutrits: Shor's Algorithm on Ternary and Metaplectic Quantum Architectures

- Computer ScienceArXiv
- 2016

The cost of performing Shor's algorithm for integer factorization on a ternary quantum computer is determined using two natural models of universal fault-tolerant computing: a model based on magic state distillation and a modelbased on a metaplectic topological quantum computer.

### Gate scheduling for quantum algorithms

- PhysicsArXiv
- 2017

This work suggests a two-step approach in which logical gates are initially scheduled neglecting the limited connectivity, while routing operations are added at a later step and their number is empirically minimized.

### Optimized Surface Code Communication in Superconducting Quantum Computers

- Physics, Computer Science2017 50th Annual IEEE/ACM International Symposium on Microarchitecture (MICRO)
- 2017

This paper evaluates two established quantum error correction codes-planar and double-defect surface codes-using a set of compilation, scheduling and network simulation tools, and finds that the simpler planar codes are sometimes more favorable for implementation on superconducting quantum computers, especially under conditions of high communication congestion.

### Implementation of a Toffoli gate with superconducting circuits

- PhysicsNature
- 2012

By exploiting the third energy level of the transmon qubits, the number of elementary gates needed for the implementation of the Toffoli gate is significantly reduced, relative to that required in theoretical proposals using only two-level systems.