Outcome determinism in measurement-based quantum computation with qudits
arXiv:2109.13810 · doi:10.1088/1751-8121/acbace
Abstract
In measurement-based quantum computing (MBQC), computation is carried out by a sequence of measurements and corrections on an entangled state. Flow, and related concepts, are powerful techniques for characterising the dependence of the corrections on previous measurement outcomes. We introduce flow-based methods for MBQC with qudit graph states, which we call Zd-flow, when the local dimension is an odd prime. Our main results are proofs that Zd-flow is a necessary and sufficient condition for a strong form of outcome determinism. Along the way, we find a suitable generalisation of the concept of measurement planes to this setting and characterise the allowed measurements in a qudit MBQC. We also provide a polynomial-time algorithm for finding an optimal Zd-flow whenever one exists.
arXiv comment16 pages + 10 pages of appendices, 1 figure
References in corpus (38)
- Persistent entanglement in arrays of interacting particles
- How to share a quantum secret
- Security of quantum key distribution using d-level systems
- Twisted Photons: New Quantum Perspectives in High Dimensions
- Qudits and high-dimensional quantum computing
- Quantum Cryptography using larger alphabets
- Cluster-state quantum computation
- Methodology for quantum logic gate constructions
- Unconditionally verifiable blind computation
- Quantum key distribution with higher-order alphabets using spatially-encoded qudits
- Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus
- Quantum computation based on d-level cluster states
- Fault-tolerant detection of a quantum error
- Reducing T-count with the ZX-calculus
- Fault-Tolerant Quantum Computation with Higher-Dimensional Systems
- Determinism in the one-way model
- Generalized Flow and Determinism in Measurement-based Quantum Computation
- Parallelizing Quantum Circuits
- Asymptotic Improvements to Quantum Circuits via Qutrits
- There and back again: A circuit extraction tale
- Scalable quantum computing with qudits on a graph
- Quantum key distribution overcoming extreme noise: simultaneous subspace coding using high-dimensional entanglement
- Quantum Control in the Cs 6S_{1/2} Ground Manifold Using rf and μw Magnetic Fields
- Quantum Phase Estimation with Time-Frequency Qudits in a Single Photon
- Arbitrary d-dimensional Pauli X-Gates of a flying Qudit
- Properties of the extended Clifford group with applications to SIC-POVMs and MUBs
- Finding Optimal Flows Efficiently
- Flow Ambiguity: A Path Towards Classically Driven Blind Quantum Computation
- Closed timelike curves in measurement-based quantum computation
- An analysis of the trade-off between spatial and temporal resources for measurement-based quantum computation
- Pauli Fusion: a Computational Model to Realise Quantum Transformations from ZX Terms
- Logical measurement-based quantum computation in circuit-QED
- Ancilla-driven quantum computation for qudits and continuous variables
- Adiabatic graph-state quantum computation
- Geometry-Based Optimization of One-Way Quantum Computation Measurement Patterns
- Flow conditions for continuous variable measurement-based quantum computing
- Measurement-based quantum computation--a quantum-mechanical toy model for spacetime?
- Proceedings 16th International Conference on Quantum Physics and Logic
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