Random Quantum Circuits are Approximate 2-designs
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Summary
It is shown that random circuits of only polynomial length will approximate the first and second moments of the Haar distribution, thus forming approximate 1- and 2-designs.
- Type
- article
- Published
- 2008-02-13
- Cited by
- 396
- References
- 36
- Access
- Open access
- OpenAlex
- https://openalex.org/W2070375169
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:6996178
Keywords
Mathematics, Qubit, Electronic circuit, Corollary, Discrete mathematics
References
- Mathematical Aspects of Mixing Times in Markov Chains
- Representations and Invariants of the Classical Groups
- Information-disturbance tradeoff in quantum measurement on the uniform ensemble
- Completely bounded maps and dilations
- Quantum information and computation
- Exact and approximate unitary 2-designs and their application to fidelity estimation
- The emergence of typical entanglement in two-party random processes
- Convergence conditions for random quantum circuits
- A Decoupling Approach to the Quantum Capacity
- COMPARISON THEOREMS FOR REVERSIBLE MARKOV CHAINS
- Reexamination of optimal quantum state estimation of pure states (5 pages)
- Multiplicativity of Completely Bounded p-Norms Implies a New Additivity Result
- Random Measurement Bases, Quantum State Distinction and Applications to the Hidden Subgroup Problem
- Generic entanglement can be generated efficiently.
- Stabilization of Quantum Computations by Symmetrization
- LOGARITHMIC SOBOLEV INEQUALITIES FOR FINITE MARKOV CHAINS
- Private quantum channels
- Quantum t-designs: t-wise Independence in the Quantum World
- Black holes as mirrors: Quantum information in random subsystems
- Evenly distributed unitaries: On the structure of unitary designs
Cited by
- Error characterization and quantum control benchmarking in liquid state NMR using quantum information processing techniques
- The role of quantum information in thermodynamics—a topical review
- Implementing Unitary 2-Designs Using Random Diagonal-unitary Matrices
- Propagation of correlations in local random quantum circuits
- Stringy effects in scrambling
- Scrambling speed of random quantum circuits
- Diagonal quantum circuits: Their computational power and applications
- Neural networks with quantum architecture and quantum learning
- Decoupling with unitary approximate two-designs
- Efficient and feasible state tomography of quantum many-body systems
- Random unitary maps for quantum state reconstruction
- Local random quantum circuits are approximate polynomial-designs: numerical results
- Quantum circuit for three-qubit random states
- Subsystem dynamics under random Hamiltonian evolution
- Comment on “Random Quantum Circuits are Approximate 2-designs” by A.W. Harrow and R.A. Low (Commun. Math. Phys. 291, 257–302 (2009))
- Randomized benchmarking of single- and multi-qubit control in liquid-state NMR quantum information processing
- Pure state thermodynamics with matrix product states
- Random circuits by measurements on weighted graph states
- Convergence rates for arbitrary statistical moments of random quantum circuits.
- Quantum to Classical Randomness Extractors
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