Kavli Affiliate: K. Birgitta Whaley
| First 5 Authors: Yulong Dong, K. Birgitta Whaley, Lin Lin, ,
| Summary:
Hamiltonian simulation is one of the most important problems in quantum
computation, and quantum singular value transformation (QSVT) is an efficient
way to simulate a general class of Hamiltonians. However, the QSVT circuit
typically involves multiple ancilla qubits and multi-qubit control gates. We
propose a drastically simplified quantum circuit called the minimal QSVT
circuit, which uses only one ancilla qubit to simulate a class of $n$-qubit
random Hamiltonians. We formulate a simple metric called the quantum unitary
evolution score (QUES), which is a scalable quantum benchmark and can be
verified without any need for classical computation. We demonstrate that QUES
is directly related to the circuit fidelity, and the classical hardness of an
associated quantum circuit sampling problem. Theoretical analysis suggests
under suitable assumptions, there exists an "optimal" simulation time
$t^{text{opt}}approx 4.81$, at which even a noisy quantum device may be
sufficient to demonstrate the classical hardness.
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