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Simulating quantum dynamics is expected to be performed more easily on aquantum computer than on a classical computer. However, the currently availablequantum devices lack the capability to implement fault-tolerant quantumalgorithms for quantum simulation. Hybrid classical quantum algorithms such asthe variational quantum algorithms have been proposed to effectively usecurrent term quantum devices. One promising approach to quantum simulation inthe noisy intermediate-scale quantum (NISQ) era is the diagonalisation basedapproach, with some of the promising examples being the subspace VariationalQuantum Simulator (SVQS), Variational Fast Forwarding (VFF), fixed-stateVariational Fast Forwarding (fs-VFF), and the Variational HamiltonianDiagonalisation (VHD) algorithms. However, these algorithms require a feedbackloop between the classical and quantum computers, which can be a crucialbottleneck in practical application. Here, we present the Classical QuantumFast Forwarding (CQFF) as an alternative diagonalisation based algorithm forquantum simulation. CQFF shares some similarities with SVQS, VFF, fs-VFF andVHD but removes the need for a classical-quantum feedback loop and controlledmulti-qubit unitaries. The CQFF algorithm does not suffer from the barrenplateau problem and the accuracy can be systematically increased. Furthermore,if the Hamiltonian to be simulated is expressed as a linear combination oftensored-Pauli matrices, the CQFF algorithm reduces to the task of samplingsome many-body quantum state in a set of Pauli-rotated bases, which is easy todo in the NISQ era. We run the CQFF algorithm on existing quantum processorsand demonstrate the promise of the CQFF algorithm for current-term quantumhardware. Our work provides a $10^4$ improvement over the previous record.

Fast-Forwarding with NISQ Processors without Feedback Loop