Fast-Forwarding with NISQ Processors without Feedback Loop

Abstract

Simulating quantum dynamics is expected to be performed more easily on a quantum computer than on a classical computer. However, the currently available quantum devices lack the capability to implement fault-tolerant quantum algorithms for quantum simulation. Hybrid classical quantum algorithms such as the variational quantum algorithms have been proposed to effectively use current term quantum devices. One promising approach to quantum simulation in the noisy intermediate-scale quantum (NISQ) era is the diagonalisation based approach, with some of the promising examples being the subspace Variational Quantum Simulator (SVQS), Variational Fast Forwarding (VFF), fixed-state Variational Fast Forwarding (fs-VFF), and the Variational Hamiltonian Diagonalisation (VHD) algorithms. However, these algorithms require a feedback loop between the classical and quantum computers, which can be a crucial bottleneck in practical application. Here, we present the Classical Quantum Fast Forwarding (CQFF) as an alternative diagonalisation based algorithm for quantum simulation. CQFF shares some similarities with SVQS, VFF, fs-VFF and VHD but removes the need for a classical-quantum feedback loop and controlled multi-qubit unitaries. The CQFF algorithm does not suffer from the barren plateau problem and the accuracy can be systematically increased. Furthermore, if the Hamiltonian to be simulated is expressed as a linear combination of tensored-Pauli matrices, the CQFF algorithm reduces to the task of sampling some many-body quantum state in a set of Pauli-rotated bases, which is easy to do in the NISQ era. We run the CQFF algorithm on existing quantum processors and demonstrate the promise of the CQFF algorithm for current-term quantum hardware. Our work provides a $10^4$ improvement over the previous record.

arXiv comment12 pages, 7 figures

References in corpus (16)

• Quantum Computing in the NISQ era and beyond
• A variational eigenvalue solver on a quantum processor
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Barren plateaus in quantum neural network training landscapes
• Noise-Induced Barren Plateaus in Variational Quantum Algorithms
• Efficient quantum algorithms for simulating sparse Hamiltonians
• Efficient variational quantum simulator incorporating active error minimisation
• Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States
• Theory of variational quantum simulation
• Variational Fast Forwarding for Quantum Simulation Beyond the Coherence Time
• Methodology for replacing indirect measurements with direct measurements
• An efficient quantum algorithm for the time evolution of parameterized circuits
• Fast-forwarding of Hamiltonians and Exponentially Precise Measurements
• Quantum Assisted Simulator
• Iterative Quantum Assisted Eigensolver
• Quantum Assisted Eigensolver