Quantum pseudo-randomness from cluster-state quantum computation

Abstract

We show how to efficiently generate pseudo-random states suitable for quantum information processing via cluster-state quantum computation. By reformulating pseudo-random algorithms in the cluster-state picture, we identify a strategy for optimizing pseudo-random circuits by properly choosing single-qubit rotations. A Markov chain analysis provides the tool for analyzing convergence rates to the Haar measure and finding the optimal single-qubit gate distribution. Our results may be viewed as an alternative construction of approximate unitary 2-designs.

4 pages, 4 figures, version appearing in Phys. Rev. A

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Cited by in corpus (20)

• Architectures for quantum simulation showing a quantum speedup
• Random Quantum Operations
• Convergence rates for arbitrary statistical moments of random quantum circuits
• Emergent irreversibility and entanglement spectrum statistics
• Efficient unitary designs with nearly time-independent Hamiltonian dynamics
• Exact convergence times for generation of random bipartite entanglement
• Anticoncentration theorems for schemes showing a quantum speedup
• Quantum circuits for exact unitary $t$-designs and applications to higher-order randomized benchmarking
• Unitary $2$-designs from random $X$- and $Z$-diagonal unitaries
• Efficiency of Producing Random Unitary Matrices with Quantum Circuits
• Closing gaps of a quantum advantage with short-time Hamiltonian dynamics
• Parameters of Pseudo-Random Quantum Circuits
• Derandomizing quantum circuits with measurement based unitary designs
• Random circuits by measurements on weighted graph states
• One-Shot Randomized and Nonrandomized Partial Decoupling
• Decoupling with random diagonal unitaries
• Purity of thermal mixed quantum states
• Measurement-induced entanglement and complexity in random constant-depth 2D quantum circuits
• Pseudo-Random Circuits from Clifford Plus T-Gates
• Sampling and the complexity of nature