Realization of quantum signal processing on a noisy quantum computer

Abstract

Quantum signal processing (QSP) is a powerful toolbox for the design of quantum algorithms and can lead to asymptotically optimal computational costs. Its realization on noisy quantum computers without fault tolerance, however, is challenging because it requires a deep quantum circuit in general. We propose a strategy to run an entire QSP protocol on noisy quantum hardware by carefully reducing overhead costs at each step. To illustrate the approach, we consider the application of Hamiltonian simulation for which QSP implements a polynomial approximation of the time evolution operator. We test the protocol by running the algorithm on the Quantinuum H1-1 trapped-ion quantum computer powered by Honeywell. In particular, we compute the time dependence of bipartite entanglement entropies for Ising spin chains and find good agreements with exact numerical simulations. To make the best use of the device, we determine optimal experimental parameters by using a simplified error model for the hardware and numerically studying the trade-off between Hamiltonian simulation time, polynomial degree, and total accuracy. Our results are the first step in the experimental realization of QSP-based quantum algorithms.

arXiv comment16 pages, 9 figures, 1 table. As published in npj Quantum Information

References in corpus (52)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Barren plateaus in quantum neural network training landscapes
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Hamiltonian Simulation by Qubitization
• Optimal Hamiltonian Simulation by Quantum Signal Processing
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Simulation of Many-Body Fermi Systems on a Universal Quantum Computer
• Synthesis of Quantum Logic Circuits
• Efficient quantum algorithms for simulating sparse Hamiltonians
• Quantum computers can search rapidly by using almost any transformation
• Probing entanglement entropy via randomized measurements
• Demonstration of the trapped-ion quantum-CCD computer architecture
• Toward the first quantum simulation with quantum speedup
• Universal Quantum Estimator
• Direct estimations of linear and non-linear functionals of a quantum state
• t$|$ket$⟩$ : A Retargetable Compiler for NISQ Devices
• An initialization strategy for addressing barren plateaus in parametrized quantum circuits
• Strong and weak thermalization of infinite non-integrable quantum systems
• The randomized measurement toolbox
• A random compiler for fast Hamiltonian simulation
• Mixed-state entanglement from local randomized measurements
• Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space
• Rényi Entropies from Random Quenches in Atomic Hubbard and Spin Models
• Direct detection of quantum entanglement
• Faster quantum simulation by randomization
• Statistical correlations between locally randomized measurements: a toolbox for probing entanglement in many-body quantum states
• An observable entanglement measure for unknown mixed quantum states
• Mitigating depolarizing noise on quantum computers with noise-estimation circuits
• Quantum circuits with uniformly controlled one-qubit gates
• The power of random measurements: measuring Tr(ρ^n) on single copies of ρ
• Efficient phase-factor evaluation in quantum signal processing
• A device for feasible fidelity, purity, Hilbert-Schmidt distance and entanglement witness measurements
• Efficient classical simulation of noisy random quantum circuits in one dimension
• Multipartite entanglement detection in bosons
• Classically optimized Hamiltonian simulation
• Barren plateaus in quantum tensor network optimization
• Product Decomposition of Periodic Functions in Quantum Signal Processing
• Entanglement spectroscopy on a quantum computer
• Efficient Fully-Coherent Quantum Signal Processing Algorithms for Real-Time Dynamics Simulation
• Hamiltonian simulation with random inputs
• Solving condensed-matter ground-state problems by semidefinite relaxations
• Variational Hamiltonian simulation for translational invariant systems via classical pre-processing
• Lower Bounds for Ground States of Condensed Matter Systems
• Finding Angles for Quantum Signal Processing with Machine Precision
• FABLE: Fast Approximate Quantum Circuits for Block-Encodings
• A quantum hamiltonian simulation benchmark
• 3-Local Hamiltonian is QMA-complete
• Grover's search with local and total depolarizing channel errors
• Explicit Quantum Circuits for Block Encodings of Certain Sparse Matrices
• Fault-ignorant Quantum Search
• Lower bounds to variational problems with guarantees
• Error Correction of Quantum Algorithms: Arbitrarily Accurate Recovery Of Noisy Quantum Signal Processing

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