Optimal universal programming of unitary gates

Abstract

A universal quantum processor is a device that takes as input a (quantum) program, containing an encoding of an arbitrary unitary gate, and a (quantum) data register, on which the encoded gate is applied. While no perfect universal quantum processor can exist, approximate processors have been proposed in the past two decades. A fundamental open question is how the size of the smallest quantum program scales with the approximation error. Here we answer the question, by proving a bound on the size of the program and designing a concrete protocol that attains the bound in the asymptotic limit. Our result is based on a connection between optimal programming and the Heisenberg limit of quantum metrology, and establishes an asymptotic equivalence between the tasks of programming, learning, and estimating unitary gates.

arXiv comment4 pages, 2 figures + Appendix; the upper bound's scaling with respect to d is improved compared to the published version (the main result remains unchanged)

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Cited by in corpus (28)

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• Fisher Information in Noisy Intermediate-Scale Quantum Applications
• Fundamental limitations on distillation of quantum channel resources
• Fundamental energy requirement of reversible quantum operations
• Optimal Universal Quantum Error Correction via Bounded Reference Frames
• Query-optimal estimation of unitary channels in diamond distance
• A comparative study of universal quantum computing models: towards a physical unification
• Programmability of covariant quantum channels
• A prototype of quantum von Neumann architecture
• Covariant catalysis requires correlations and good quantum reference frames degrade little
• Universal construction of decoders from encoding black boxes
• Energy requirement for implementing unitary gates on energy-unbounded systems
• Encrypted Qubits can be Cloned
• A survey of universal quantum von Neumann architecture
• Storage and retrieval of von Neumann measurements
• Universal adjointation of isometry operations using conversion of quantum supermaps
• Topological obstructions to quantum computation with unitary oracles
• A family of quantum von Neumann architecture
• Port-Based State Preparation and Applications
• Heisenberg scaling based on population coding
• Agnostic Process Tomography
• Nearly query-optimal classical shadow estimation of unitary channels
• Representation matching for delegated quantum computing
• Programming of channels in generalized probabilistic theories
• Quantum Advantage in Storage and Retrieval of Isometry Channels
• Compression of quantum shallow-circuit states
• Analytical Lower Bound on Query Complexity for Transformations of Unknown Unitary Operations
• On the query complexity of unitary channel certification