Efficient quantum pseudorandomness with simple graph states

Abstract

Measurement based (MB) quantum computation allows for universal quantum computing by measuring individual qubits prepared in entangled multipartite states, known as graph states. Unless corrected for, the randomness of the measurements leads to the generation of ensembles of random unitaries, where each random unitary is identified with a string of possible measurement results. We show that repeating an MB scheme an efficient number of times, on a simple graph state, with measurements at fixed angles and no feed-forward corrections, produces a random unitary ensemble that is an ε-approximate t-design on n-qubits. Unlike previous constructions, the graph is regular and is also a universal resource for measurement based quantum computing, closely related to the brickwork state

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• Nonadaptive fault-tolerant verification of quantum supremacy with noise
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• Measurement-induced entanglement and complexity in random constant-depth 2D quantum circuits
• Efficient Construction of Quantum Physical Unclonable Functions with Unitary t-designs
• Unitary $t$-designs from $relaxed$ seeds
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• Matchgate circuits deeply thermalize
• Measurement-based interleaved randomised benchmarking using IBM processors
• Implementation of single-qubit measurement-based t-designs using IBM processors
• Investigating the effect of noise channels on the quality of unitary t-designs
• Studies of properties of bipartite graphs with quantum programming