Derandomizing quantum circuits with measurement based unitary designs

Abstract

Entangled multipartite states are resources for universal quantum computation, but they can also give rise to ensembles of unitary transformations, a topic usually studied in the context of random quantum circuits. Using several graph state techniques, we show that these resources can `derandomize' circuit results by sampling the same kinds of ensembles quantum mechanically, (analogously to a quantum random number generator). Furthermore, we find simple examples that give rise to new ensembles whose statistical moments exactly match those of the uniformly random distribution over all unitaries up to order $t$, while foregoing adaptive feed-forward entirely. Such ensembles -- known as $t$-designs -- often cannot be distinguished from the `truly' random ensemble, and so they find use in many applications that require this implied notion of pseudorandomness.

References in corpus (11)

• Black holes as mirrors: quantum information in random subsystems
• Multi-party entanglement in graph states
• Resource-efficient linear optical quantum computation
• Evenly distributed unitaries: on the structure of unitary designs
• Randomizing quantum states: Constructions and applications
• Generalized Flow and Determinism in Measurement-based Quantum Computation
• Experimental demonstration of a graph state quantum error-correction code
• Optimizing quantum process tomography with unitary 2-designs
• Unitary designs and codes
• Quantum pseudo-randomness from cluster-state quantum computation
• Random circuits by measurements on weighted graph states

Cited by in corpus (12)

• Emergent quantum state designs from individual many-body wavefunctions
• Driven quantum dynamics: will it blend?
• Multi-qubit Randomized Benchmarking Using Few Samples
• Efficient quantum pseudorandomness with simple graph states
• Randomized benchmarking in measurement-based quantum computing
• Experimental Implementation of Efficient Quantum Pseudorandomness on a 12-spin System
• Fault-tolerant quantum speedup from constant depth quantum circuits
• Unitary $t$-designs from $relaxed$ seeds
• 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