Optimal probabilistic storage and retrieval of unitary channels

Abstract

We address the question of a quantum memory storage of quantum dynamics. In particular, we design an optimal protocol for $N\to 1$ probabilistic storage-and-retrieval of unitary channels on $d$-dimensional quantum systems. If we may access the unknown unitary gate only $N$-times, the optimal success probability of perfect retrieval of its single use is $N/(N-1+d^2)$. The derived size of the memory system exponentially improves the known upper bound on the size of the program register needed for probabilistic programmable quantum processors. Our results are closely related to probabilistic perfect alignment of reference frames and probabilistic port-based teleportation.

5+8 pages, 4 figures

References in corpus (12)

• Quantum Circuits Architecture
• Transforming quantum operations: quantum supermaps
• Asymptotic teleportation scheme as a universal programmable quantum processor
• Quantum teleportation scheme by selecting one of multiple output ports
• Quantum communication using a bounded-size quantum reference frame
• Optimal cloning of unitary transformations
• Universal super-replication of unitary gates
• Resource Quantification for the No-Programming Theorem
• Deterministic superreplication of one-parameter unitary transformations
• Optimality of programmable quantum measurements
• Quantum Information Processing and Composite Quantum Fields
• On some new hook-content identities

Cited by in corpus (45)

• Efficient Learning for Deep Quantum Neural Networks
• Reversing Unknown Quantum Transformations: Universal Quantum Circuit for Inverting General Unitary Operations
• Probabilistic exact universal quantum circuits for transforming unitary operations
• Optimal universal programming of unitary gates
• Unitary channel discrimination beyond group structures: Advantages of sequential and indefinite-causal-order strategies
• Quantification of quantum dynamics with input-output games
• Deterministic transformations between unitary operations: Exponential advantage with adaptive quantum circuits and the power of indefinite causality
• Reversing Unknown Qubit-Unitary Operation, Deterministically and Exactly
• Query-optimal estimation of unitary channels in diamond distance
• Efficient multi port-based teleportation schemes
• Success-or-Draw: A Strategy Allowing Repeat-Until-Success in Quantum Computation
• Higher-order Process Matrix Tomography of a passively-stable Quantum SWITCH
• Multiport based teleportation -- transmission of a large amount of quantum information
• Communication Cost of Quantum Processes
• Choi states, symmetry-based quantum gate teleportation, and stored-program quantum computing
• Probabilistic storage and retrieval of qubit phase gates
• Optimal universal quantum circuits for unitary complex conjugation
• Reversing Unknown Quantum Processes via Virtual Combs for Channels with Limited Information
• Quantum-enhanced learning of rotations about an unknown direction
• Universal construction of decoders from encoding black boxes
• On the probabilistic quantum error correction
• Quantum Information Processing and Composite Quantum Fields
• Minimal Port-based Teleportation
• No-signalling constrains quantum computation with indefinite causal structure
• Quantum Tensor Product Decomposition from Choi State Tomography
• Storage and retrieval of von Neumann measurements
• Port-based entanglement teleportation via noisy resource states
• Achieving the Multi-parameter Quantum Cramér-Rao Bound with Antiunitary Symmetry
• Topological obstructions to quantum computation with unitary oracles
• Universal adjointation of isometry operations using conversion of quantum supermaps
• Teleportation of Post-Selected Quantum States
• Port-Based State Preparation and Applications
• Representation matching for delegated quantum computing
• Parameterized quantum comb and simpler circuits for reversing unknown qubit-unitary operations
• Experimentally undoing an unknown single-qubit unitary
• From port-based teleportation to Frobenius reciprocity theorem: partially reduced irreducible representations and their applications
• Quantum Advantage in Storage and Retrieval of Isometry Channels
• A hybrid quantum-classical neural network with deep residual learning
• Robustness of optimal probabilistic storage and retrieval of unitary channels to noise
• Asymptotic teleportation schemes bridging between standard and port-based teleportation
• Square-root measurements and degradation of the resource state in port-based teleportation scheme
• Compression of quantum shallow-circuit states
• Analytical Lower Bound on Query Complexity for Transformations of Unknown Unitary Operations
• On the distinguishability of geometrically uniform quantum states
• A resource theory of asynchronous quantum information processing