Practical verification protocols for analog quantum simulators

Abstract

Analog quantum simulation is expected to be a significant application of near-term quantum devices. Verification of these devices without comparison to known simulation results will be an important task as the system size grows beyond the regime that can be simulated classically. We introduce a set of experimentally-motivated verification protocols for analog quantum simulators, discussing their sensitivity to a variety of error sources and their scalability to larger system sizes. We demonstrate these protocols experimentally using a two-qubit trapped-ion analog quantum simulator and numerically using models of up to five qubits.

Experimental proposal to probe the extended Pauli principle

“…The simulated states are all subject to the weakened relation (Figure 3(b,d)). In Appendix B, a procedure to prepare the state then rewind the preparation expecting the system to return to the initial state (Loschmidt echo [31]) is simulated to enforce the credibility of the numerical methods.…”

“…The purity of a quantum state with density operator ρ is defined as trρ 2 . The purity of an experimentally prepared multi-particle entangled state can be estimated with the "entangle-disentangle" procedure as described in [18], which is formally known as Loschmidt echo [31] in the quantum simulation community. The key idea is that if the system is initially prepared in an eigenstate, by implementing a forward time evolution followed by a backward time evolution that is the conjugate of the former, the system is expected to return to the initial state.…”

How to engineer a quantum wavefunction

“…3 With the advent of versatile and universal quantum simulators and computers, ways have been developed of both characterising directly and verifying the features of the object of interest in an experimental scenario -the quantum state, Hamiltonian, or process (Eisert et al, 2020). But also for analogue systems, methods for direct validation of the experimentally implemented object of interest have been developed, including in particular the identification of the Hamiltonian or Liouvillian parameters (Hangleiter et al, 2021;Samach et al, 2021), benchmarking of Hamiltonian time-evolution across the parameter range accessible in the experiment (Helsen et al, 2020;Derbyshire et al, 2020;Shaffer et al, 2021), and fidelity estimation of a quantum state (Elben et al, 2020). In another vein, it has also been argued that analogue simulations might often be insensitive to certain details of the experiment, for example due to slack in the model space (Sarovar et al, 2017), or because certain noise processes affect both the simulator and the target in the same way (Cubitt et al, 2018).…”

Stochastic search for approximate compilation of unitaries

“…Compilation with STOQ, on the other hand, can in principle be performed for any target unitary operation and with any gate alphabet. The use of a stochastic compilation protocol similar to STOQ has been demonstrated to have potential advantages for characterization of analog quantum simulators [19], in which many approximately-equivalent sequences are compiled and executed in order to assess the accuracy with which an analog quantum simulator has implemented the dynamics of the target Hamiltonian. We suggest that STOQ may also be useful for similar applications which do not require exact compilation, given that its requirements are less stringent than traditional protocols.…”