Asymptotic Improvements to Quantum Circuits via Qutrits

Abstract

Quantum computation is traditionally expressed in terms of quantum bits, or qubits. In this work, we instead consider three-level qu$trits$. 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 equivalent. Our circuit construction also features a 70x improvement in two-qudit gate count over the qubit-only equivalent decomposition. This results in circuit cost reductions for important algorithms like quantum neurons and Grover search. We develop an open-source circuit simulator for qutrits, along with realistic near-term noise models which account for the cost of operating qutrits. Simulation results for these noise models indicate over 90% mean reliability (fidelity) for our circuit construction, versus under 30% for the qubit-only baseline. These results suggest that qutrits offer a promising path towards scaling quantum computation.

arXiv commentIn ISCA '19: 46th International Symposium on Computer Architecture, 13 pages, 11 figures

References in corpus (36)

• Quantum Computing in the NISQ era and beyond
• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• Elementary gates for quantum computation
• QuTiP 2: A Python framework for the dynamics of open quantum systems
• QuTiP: An open-source Python framework for the dynamics of open quantum systems
• Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
• Experimental Quantum Error Correction
• Experimental Comparison of Two Quantum Computing Architectures
• Multi-valued Logic Gates for Quantum Computation
• Implementation of a Toffoli Gate with Superconducting Circuits
• A quantum memory with near-millisecond coherence in circuit QED
• Efficient Toffoli Gates Using Qudits
• A simple model of quantum trajectories
• An Artificial Neuron Implemented on an Actual Quantum Processor
• Compiling quantum circuits to realistic hardware architectures using temporal planners
• Random access quantum information processors
• Realization of a $\Lambda$ system with metastable states of a capacitively-shunted fluxonium
• Factoring with Qutrits: Shor's Algorithm on Ternary and Metaplectic Quantum Architectures
• Maximizing the Hilbert space for a finite number of distinguishable quantum states
• A C++ library using quantum trajectories to solve quantum master equations
• Toward fault-tolerant quantum computation without concatenation
• Understanding the effects of leakage in superconducting quantum error detection circuits
• Efficient preparation and detection of microwave dressed-state qubits and qutrits with trapped ions
• Quantum Error-Correcting Codes for Qudit Amplitude Damping
• Two-step approach to scheduling quantum circuits
• Optimized Surface Code Communication in Superconducting Quantum Computers
• Time-efficient implementation of quantum search with qudits
• Generation of high-fidelity quantum control methods for multi-level systems
• Comparing Zeeman qubits to hyperfine qubits in the context of the surface code: ${}^{174}$Yb${}^{+}$ and ${}^{171}$Yb${}^{+}$
• Fast microwave-driven three-qubit gates for cavity-coupled superconducting qubits
• Elementary gates for ternary quantum logic circuit
• Magic-State Functional Units: Mapping and Scheduling Multi-Level Distillation Circuits for Fault-Tolerant Quantum Architectures
• Propagation of generalized Pauli errors in qudit Clifford circuits
• Co-Designing a Scalable Quantum Computer with Trapped Atomic Ions
• Factoring with n+2 clean qubits and n-1 dirty qubits
• Characterization of qutrit channels in terms of their covariance and symmetry properties

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• Shallow unitary decompositions of quantum Fredkin and Toffoli gates for connectivity-aware equivalent circuit averaging
• Towards multiqudit quantum processor based on a ${}^{171}$Yb${}^{+}$ ion string: Realizing basic quantum algorithms
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• Qudit States in Noisy Quantum Channels
• QuDiet: A Classical Simulation Platform for Qubit-Qudit Hybrid Quantum Systems
• Time-Efficient Qudit Gates through Incremental Pulse Re-seeding
• Circuit Design for $k$-coloring Problem and Its Implementation in Any Dimensional Quantum System
• The Qupit Stabiliser ZX-travaganza: Simplified Axioms, Normal Forms and Graph-Theoretic Simplification
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• Building Qutrit Diagonal Gates from Phase Gadgets
• Quantum-classical tradeoffs and multi-controlled quantum gate decompositions in variational algorithms
• Robust Quantum Arithmetic Operations with Intermediate Qutrits in the NISQ-era
• Scaling W state circuits in the qudit Clifford hierarchy
• Outcome determinism in measurement-based quantum computation with qudits
• Qudit vs. Qubit: Simulated performance of error correction codes in higher dimensions
• Qudit low-density parity-check codes
• Robust Control and Entanglement of Qudits in Neutral Atom Arrays
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• Transpiling quantum assembly language circuits to a qudit form
• Single photonic qutrit in a collective Rydberg polariton
• Measurement-based quantum computing with qudit stabilizer states
• 'Complementarity' in paraxial and non-paraxial optical beams
• Encoder Circuit Optimization for Non-Binary Quantum Error Correction Codes in Prime Dimensions: An Algorithmic Framework
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• Constructing all qutrit controlled Clifford+T gates in Clifford+T