Higher-order quantum transformations of Hamiltonian dynamics

Abstract

We present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. Namely, the algorithm takes as input a finite number of queries to a black-box seed Hamiltonian dynamics to simulate a desired Hamiltonian. Our algorithm efficiently simulates linear transformations of any seed Hamiltonian with a bounded energy range consisting of a polynomial number of terms in system size, making use of only controlled-Pauli gates and time-correlated randomness. This algorithm is an instance of quantum functional programming, where the desired function is specified as a concatenation of higher-order quantum transformations. By way of example, we demonstrate the simulation of negative time-evolution and time-reversal, and perform a Hamiltonian learning task.

References in corpus (28)

• Quantum Resource Theories
• Hamiltonian Simulation by Qubitization
• Optimal Hamiltonian Simulation by Quantum Signal Processing
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Quantum correlations with no causal order
• Toward the first quantum simulation with quantum speedup
• Quantum computations without definite causal structure
• Theoretical framework for quantum networks
• Quantum Circuits Architecture
• Complete universal quantum gate set approaching fault-tolerant thresholds with superconducting qubits
• A random compiler for fast Hamiltonian simulation
• Transforming quantum operations: quantum supermaps
• Non-Markovian quantum processes: complete framework and efficient characterisation
• Robust Online Hamiltonian Learning
• Quantum circuits cannot control unknown operations
• Quantum methods for clock synchronization: Beating the standard quantum limit without entanglement
• Quantum Shannon theory with superpositions of trajectories
• Implementing quantum control for unknown subroutines
• A Robust Method for Estimating the Lindblad Operators of a Dissipative Quantum Process from Measurements of the Density Operator at Multiple Time Points
• Quantum Hamiltonian Learning Using Imperfect Quantum Resources
• Reversing Unknown Quantum Transformations: Universal Quantum Circuit for Inverting General Unitary Operations
• Learning many-body Hamiltonians with Heisenberg-limited scaling
• Theoretical framework for Higher-Order Quantum Theory
• Probabilistic exact universal quantum circuits for transforming unitary operations
• Reversing Unknown Qubit-Unitary Operation, Deterministically and Exactly
• Complex conjugation supermap of unitary quantum maps and its universal implementation protocol
• Quantum algorithm for universal implementation of projective measurement of energy
• Probabilistic state synthesis based on optimal convex approximation

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• Reversing Unknown Quantum Processes via Virtual Combs for Channels with Limited Information
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• Quantum Dynamic Programming
• Modular quantum signal processing in many variables
• Parameterized quantum comb and simpler circuits for reversing unknown qubit-unitary operations
• Learning the structure of any Hamiltonian from minimal assumptions
• Optimal Hamiltonian recognition of unknown quantum dynamics