Fault-tolerance in qudit circuit design

Abstract

The efficient decomposition of multi-controlled gates is a significant factor in quantum compiling, both in circuit depth and T-gate count. Recent work has demonstrated that qudits have the potential to reduce resource requirements from linear to logarithmic depth and to avoid fractional phase rotations. Here we argue, based on the scaling of decoherence in high-index states, that circuit depth is not the primary factor, and that both the choice of entangling gate and interaction network topology act together to determine the spread of errors and ultimate failure rate in a circuit. We further show that for certain linear-depth circuits, additional error mitigation is possible via selective application of resources.

References in corpus (23)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Elementary gates for quantum computation
• Encoding a qubit in an oscillator
• Strong quantum computational advantage using a superconducting quantum processor
• Implementation of a Toffoli Gate with Superconducting Circuits
• Efficient Toffoli Gates Using Qudits
• Halving the cost of quantum addition
• Quantum computing with rotation-symmetric bosonic codes
• Improved Quantum Cost for n-bit Toffoli Gates
• Random access quantum information processors
• High-fidelity three-qubit iToffoli gate for fixed-frequency superconducting qubits
• Extracting Success from IBM's 20-Qubit Machines Using Error-Aware Compilation
• Compiling quantum algorithms for architectures with multi-qubit gates
• Three-dimensional surface codes: Transversal gates and fault-tolerant architectures
• Single-step implementation of high fidelity $n$-bit Toffoli gate
• Linear-Depth Quantum Circuits for n-qubit Toffoli gates with no Ancilla
• Resilience of quantum random access memory to generic noise
• Generalized Toffoli gates using qudit catalysis
• Scalable algorithm simplification using quantum AND logic
• A programmable three-qubit superconducting processor with all-to-all connectivity
• Quantifying nonlocality: how outperforming local quantum codes is expensive
• A four-dimensional toric code with non-Clifford transversal gates
• Native three-body interaction in superconducting circuits

Cited by in corpus (2)

• Qudits for decomposing multiqubit gates and realizing quantum algorithms
• Generalising multipartite concentratable entanglement for practical applications: mixed, qudit, and optical states