Maximally mixed state spectral sampling is an unbiased quantum algorithm that allows for extraction of a finite-resolution spectral distribution from a Hamiltonian over potentially the entire allowed range of energies. We show how it may be focused on any desired area of the spectrum in order to learn about the full \textit{fingerprint} of the model of interest: from its ground state phenomena such as quantum criticality, obtained from the lowest lying energies, to its thermalization behavior, obtained from the mid-spectrum. We demonstrate this technique specifically on a $(1+1)d$ non-Abelian $SO(3)$ gauge theory, providing a comprehensive analysis of the steps necessary for performing this algorithm, as well as what is possible in the near-term with superconducting quantum hardware, performing simulations with circuits that are $78$ two-qubit gates deep. We show how this algorithm is able to take advantage of emerging dynamical circuit capabilities in near-term hardware to roughly halve the number required qubits, as well as how quantum readout error mitigation is trivial for this method. Along the way, we propose a novel strategy for compiling the controlled-time evolutions needed for spectral sampling by means of Pauli-frame optimizations. We illustrate two physical applications of quantum spectral sampling -- disordered many-body transitions, and mid-spectrum densities of states -- and what postprocessing steps they require beyond the Fourier outputs of the algorithm.
Graham Van Goffrier, Debasish Banerjee, Bipasha Chakraborty et al.· 0 citations
Quantum error mitigation (QEM) is at the very heart of near-term quantum simulations and lattice gauge theories are no exceptions, rather their physical symmetries provide natural consistency checks on noise quantum states. In this work, we exploit the parity and fermion-number symmetries of a gauge theory, the (1+1)-dimensional Schwinger model, under depolarising noise and investigate symmetry verification under digital quantum simulation. We investigate two set-ups - symmetry- sector post-selection in adiabatic state preparation followed by real-time measurements of the chiral condensate and symmetry verification within a variational quantum eigensolver (VQE). In the first case, post-selection reduces the bias in the chiral condensate consistently removing up to 60% of the quantum noise induced error in our system. Motivated by the observed regularity of the residual bias (in the low-noise regime), we further introduce a global-noise calibration obtained from classically accessible smaller lattices and implemented on larger lattices recovering noiseless chiral condensate values within statistical uncertainty. However, in VQE, symmetry verification does not seem to generally improve the optimised parameters or the fidelity of the prepared states, although it reduces the bias in the estimated ground-state energy. This demonstates that improving a noisy cost-function estimator in variational algorithms does not necessarily improve the outcome of the algorithm. Our results show the strength of symmetry verification in different approaches while establishing that its usefulness critically depends on where it is applied in the computational workflow, and provide practical guidance for symmetry-assisted quantum error mitigation in quantum simulations of lattice gauge theories.
Alexander Tomlinson, Graham Van Goffrier, Bipasha Chakraborty et al.· 0 citations