Classical simulatability, entanglement breaking, and quantum computation thresholds

Abstract

We investigate the amount of noise required to turn a universal quantum gate set into one that can be efficiently modelled classically. This question is useful for providing upper bounds on fault tolerant thresholds, and for understanding the nature of the quantum/classical computational transition. We refine some previously known upper bounds using two different strategies. The first one involves the introduction of bi-entangling operations, a class of classically simulatable machines that can generate at most bipartite entanglement. Using this class we show that it is possible to sharpen previously obtained upper bounds in certain cases. As an example, we show that under depolarizing noise on the controlled-not gate, the previously known upper bound of 74% can be sharpened to around 67%. Another interesting consequence is that measurement based schemes cannot work using only 2-qubit non-degenerate projections. In the second strand of the work we utilize the Gottesman-Knill theorem on the classically efficient simulation of Clifford group operations. The bounds attained for the pi/8 gate using this approach can be as low as 15% for general single gate noise, and 30% for dephasing noise.

12 pages, 3 figures. v2: small typos changed, no change to results

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• Improved magic states distillation for quantum universality
• Robustness of Magic and Symmetries of the Stabiliser Polytope
• Qudit versions of the qubit "pi-over-eight" gate
• Entanglement of multiparty stabilizer, symmetric, and antisymmetric states
• A reversible theory of entanglement and its relation to the second law
• Quantum simulation of interacting high-dimensional systems: the influence of noise
• Error-detection-based quantum fault tolerance against discrete Pauli noise
• Tight Noise Thresholds for Quantum Computation with Perfect Stabilizer Operations
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• Quantum simulation of partially distinguishable boson sampling
• A relational quantum computer using only two-qubit total spin measurement and an initial supply of highly mixed single qubit states
• Nonlocality as a Benchmark for Universal Quantum Computation in Ising Anyon Topological Quantum Computers
• Spectral Properties Versus Magic Generation in $T$-doped Random Clifford Circuits
• Generalised state spaces and non-locality in fault tolerant quantum computing schemes
• New Limits on Fault-Tolerant Quantum Computation
• Upper bounds on fault tolerance thresholds of noisy Clifford-based quantum computers
• Bounding Fault-Tolerant Thresholds for Purification and Quantum Computation
• A lower bound on the space overhead of fault-tolerant quantum computation
• Tight Limits on Nonlocality from Nontrivial Communication Complexity; a.k.a. Reliable Computation with Asymmetric Gate Noise
• Separability Lindblad equation for dynamical open-system entanglement
• Unbreakable and breakable quantum censorship
• Restricted Monte Carlo wave function method and Lindblad equation for identifying entangling open-quantum-system dynamics
• Wigner's Theorem for stabilizer states and quantum designs
• Detection methods to rule out completely co-positive and bi-entangling operations
• A Converse for Fault-tolerant Quantum Computation
• Classical simulation of noisy quantum circuits via locally entanglement-optimal unravelings
• Efficient classical simulation of cluster state quantum circuits with alternative inputs
• The entangling power of non-entangling channels