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Register a new userEfficient simulation of so-called non-stoquastic superconducting flux circuits
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Added by
Thomas Halverson Halverson
Publication date
2020
fields
Physics
and research's language is
English
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There is a tremendous interest in fabricating superconducting flux circuits that are nonstoquastic---i.e., have positive off-diagonal matrix elements---in their qubit representation, as these circuits are thought to be unsimulable by classical approaches and thus could play a key role in the demonstration of speedups in quantum annealing protocols. We show however that the efficient simulation of these systems is possible by the direct simulation of the flux circuits. Our approach not only obviates the reduction to a qubit representation but also produces results that are more in the spirit of the experimental setup. We discuss the implications of our work. Specifically we argue that our results cast doubt on the conception that superconducting flux circuits represent the correct avenue for universal adiabatic quantum computers.
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Stoquastic Hamiltonians are characterized by the property that their off-diagonal matrix elements in the standard product basis are real and non-positive. Many interesting quantum models fall into this class including the Transverse field Ising Model (TIM), the Heisenberg model on bipartite graphs, and the bosonic Hubbard model. Here we consider the problem of estimating the ground state energy of a local stoquastic Hamiltonian $H$ with a promise that the ground state of $H$ has a non-negligible correlation with some `guiding state that admits a concise classical description. A formalized version of this problem called Guided Stoquastic Hamiltonian is shown to be complete for the complexity class MA (a probabilistic analogue of NP). To prove this result we employ the Projection Monte Carlo algorithm with a variable number of walkers. Secondly, we show that the ground state and thermal equilibrium properties of the ferromagnetic TIM can be simulated in polynomial time on a classical probabilistic computer. This result is based on the approximation algorithm for the classical ferromagnetic Ising model due to Jerrrum and Sinclair (1993).
Magnetic flux tunability is an essential feature in most approaches to quantum computing based on superconducting qubits. Independent control of the fluxes in multiple loops is hampered by crosstalk. Calibrating flux crosstalk becomes a challenging task when the circuit elements interact strongly. We present a novel approach to flux crosstalk calibration, which is circuit model independent and relies on an iterative process to gradually improve calibration accuracy. This method allows us to reduce errors due to the inductive coupling between loops. The calibration procedure is automated and implemented on devices consisting of tunable flux qubits and couplers with up to 27 control loops. We devise a method to characterize the calibration error, which is used to show that the errors of the measured crosstalk coefficients are all below 0.17%.
The ground state of a pair of ultrastrongly coupled bosonic modes is predicted to be a two-mode squeezed vacuum. However, the corresponding quantum correlations are currently unobservable in condensed matter where such a coupling can be reached, since it cannot be extracted from these systems. Here, we show that superconducting circuits can be used to perform an analog simulation of a system of two bosonic modes in regimes ranging from strong to ultrastrong coupling. More importantly, our quantum simulation setup enables us to detect output excitations that are related to the ground-state properties of the bosonic modes. We compute the emission spectra of this physical system and show that the produced state presents single- and two-mode squeezing simultaneously.
The role of non-stoquasticity in the field of quantum annealing and adiabatic quantum computing is an actively debated topic. We study a strongly-frustrated quasi-one-dimensional quantum Ising model on a two-leg ladder to elucidate how a first-order phase transition with a topological origin is affected by interactions of the $pm XX$-type. Such interactions are sometimes known as stoquastic (negative sign) and non-stoquastic (positive sign) catalysts. Carrying out a symmetry-preserving real-space renormalization group analysis and extensive density-matrix renormalization group computations, we show that the phase diagrams obtained by these two methods are in qualitative agreement with each other and reveal that the first-order quantum phase transition of a topological nature remains stable against the introduction of both $XX$-type catalysts. This is the first study of the effects of non-stoquasticity on a first-order phase transition between topologically distinct phases. Our results indicate that non-stoquastic catalysts are generally insufficient for removing topological obstacles in quantum annealing and adiabatic quantum computing.
Quantum simulators are attractive as a means to study many-body quantum systems that are not amenable to classical numerical treatment. A versatile framework for quantum simulation is offered by superconducting circuits. In this perspective, we discuss how superconducting circuits allow the engineering of a wide variety of interactions, which in turn allows the simulation of a wide variety of model Hamiltonians. In particular we focus on strong photon-photon interactions mediated by nonlinear elements. This includes on-site, nearest-neighbour and four-body interactions in lattice models, allowing the implementation of extended Bose-Hubbard models and the toric code. We discuss not only the present state in analogue quantum simulation, but also future perspectives of superconducting quantum simulation that open up when concatenating quantum gates in emerging quantum computing platforms.
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