Decomposing the generalized Toffoli gate with qutrits

Abstract

The problem of finding efficient decompositions of multi-qubit gates is of importance for quantum computing, especially, in application to existing noisy intermediate-scale quantum devices, whose resources are substantially limited. Here we propose a decomposition scheme for a generalized $N$-qubit Toffoli gate with the use of $2N-3$ two-qutrit gates for arbitrary connectivity. The fixed number of the required additional levels (the choice of qutrits is optimal) and the use of the iSWAP gate as a native operation make our approach directly applicable for ongoing experiments with superconducting quantum processors. Specifically, we present a blueprint of the realization of the proposed scheme for the Aspen-9 processor supporting quantum operations with qutrits.

6 pages, 3 figures, 1 table

References in corpus (19)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum computational advantage using photons
• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
• Programmable quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms
• Qudits and high-dimensional quantum computing
• Molecular Spin Qudits for Quantum Algorithms
• Operating Quantum States in Single Magnetic Molecules: Implementation of Grover's Quantum Algorithm
• Efficient Toffoli Gates Using Qudits
• Coherence and Decay of Higher Energy Levels of a Superconducting Transmon Qubit
• Single qudit realization of the Deutsch algorithm using superconducting many-level quantum circuits
• Asymptotic Improvements to Quantum Circuits via Qutrits
• Multilevel superconducting circuits as two-qubit systems: Operations, state preparation, and entropic inequalities
• Generalized Toffoli gates using qudit catalysis
• Parallelism for Quantum Computation with Qudits
• Low-cost Fredkin gate with auxiliary space
• Time-efficient implementation of quantum search with qudits
• Universal quantum multi-qubit entangling gates with auxiliary spaces
• Reduction of circuit depth by mapping qubit-based quantum gates to a qudit basis
• Efficient multi-qubit subspace rotations via topological quantum walks

Cited by in corpus (25)

• Multiclass classification using quantum convolutional neural networks with hybrid quantum-classical learning
• Universal qudit gate synthesis for transmons
• Realizing quantum gates with optically-addressable ${}^{171}$Yb${}^{+}$ ion qudits
• Efficient realization of quantum algorithms with qudits
• Qudits for decomposing multiqubit gates and realizing quantum algorithms
• Controlled-Controlled-Phase Gates for Superconducting Qubits Mediated by a Shared Tunable Coupler
• Demonstration of a parity-time symmetry breaking phase transition using superconducting and trapped-ion qutrits
• Continuous dynamical decoupling of optical ${}^{171}$Yb${}^{+}$ qudits with radiofrequency fields
• Universal quantum computing with qubits embedded in trapped-ion qudits
• Towards multiqudit quantum processor based on a ${}^{171}$Yb${}^{+}$ ion string: Realizing basic quantum algorithms
• Generalized Toffoli gate decomposition using ququints: Towards realizing Grover's algorithm with qudits
• Simulating neutrino oscillations on a superconducting qutrit
• Scalable improvement of the generalized Toffoli gate realization using trapped-ion-based qutrits
• The power of qutrits for non-adaptive measurement-based quantum computing
• Efficient characterization of qudit logical gates with gate set tomography using an error-free Virtual-Z-gate model
• The Qupit Stabiliser ZX-travaganza: Simplified Axioms, Normal Forms and Graph-Theoretic Simplification
• Noise-adapted qudit codes for amplitude-damping noise
• Building Qutrit Diagonal Gates from Phase Gadgets
• Scaling W state circuits in the qudit Clifford hierarchy
• Supervised binary classification of small-scale digit images and weighted graphs with a trapped-ion quantum processor
• Robust Quantum Circuit for Clique Problem with Intermediate Qudits
• Transpiling quantum assembly language circuits to a qudit form
• Applying Grover-mixer quantum alternating operator ansatz algorithm to higher-order unconstrained binary optimization problems
• Scalable platform for qudit-based quantum computing using polar molecules
• Encoder Circuit Optimization for Non-Binary Quantum Error Correction Codes in Prime Dimensions: An Algorithmic Framework