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Abstract We report better-than-classical success probabilities for a complete Grover quantum search algorithm on the largest scale demonstrated to date, of up to five qubits, using two different IBM platforms. This is enabled by error suppression via robust dynamical decoupling. Further improvements arise after the use of measurement error mitigation, but the latter is insufficient by itself for achieving better-than-classical performance. For two qubits, we demonstrate a 99.5% success probability via the use of the [[4, 2, 2]] quantum error-detection (QED) code. This constitutes a demonstration of quantum algorithmic breakeven via QED. Along the way, we introducealgorithmic error tomography(AET), a method that provides a holistic view of the errors accumulated throughout an entire quantum algorithm, filtered via the errors detected by the QED code used to encode the circuit. We demonstrate that AET provides a stringent test of an error model based on a combination of amplitude damping, dephasing, and depolarization. 

Transmon qubits experience open-system effects that manifest as noise at a broad range of frequencies. We present a model of these effects using the Redfield master equation with a hybrid bath consisting of low- and high-frequency components. We use two-level fluctuators to simulate 1/f-like noise behavior, which is a dominant source of decoherence for superconducting qubits. By measuring quantum state fidelity under free evolution with and without dynamical decoupling (DD), we can fit the low- and high-frequency noise parameters in our model. We train and test our model using experiments on quantum devices available through IBM quantum experience. Our model accurately predicts the fidelity decay of random initial states, including the effect of DD pulse sequences. We compare our model with two simpler models and confirm the importance of including both high frequency and 1/f noise in order to accurately predict transmon behavior. 

We present a new quantum adiabatic theorem that allows one to rigorously bound the adiabatic timescale for a variety of systems, including those described by originally unbounded Hamiltonians that are made finite-dimensional by a cutoff. Our bound is geared towards the qubit approximation of superconducting circuits and presents a sufficient condition for remaining within the $2^n$-dimensional qubit subspace of a circuit model of $n$qubits. The novelty of this adiabatic theorem is that, unlike previous rigorous results, it does not contain $2^n$as a factor in the adiabatic timescale, and it allows one to obtain an expression for the adiabatic timescale independent of the cutoff of the infinite-dimensional Hilbert space of the circuit Hamiltonian. As an application, we present an explicit dependence of this timescale on circuit parameters for a superconducting flux qubit and demonstrate that leakage out of the qubit subspace is inevitable as the tunnelling barrier is raised towards the end of a quantum anneal. We also discuss a method of obtaining a $2^n\times 2^n$effective Hamiltonian that best approximates the true dynamics induced by slowly changing circuit control parameters. This article is part of the theme issue ‘Quantum annealing and computation: challenges and perspectives’. 

Abstract We present an open-source software package called “Hamiltonian Open Quantum System Toolkit (HOQST), a collection of tools for the investigation of open quantum system dynamics in Hamiltonian quantum computing, including both quantum annealing and the gate-model of quantum computing. It features the key master equations (MEs) used in the field, suitable for describing the reduced system dynamics of an arbitrary time-dependent Hamiltonian with either weak or strong coupling to infinite-dimensional quantum baths. We present an overview of the theories behind the various MEs and provide examples to illustrate typical workflows in HOQST. We present an example that shows that HOQST can provide order of magnitude speedups compared to “Quantum Toolbox in Python (QuTiP), for problems with time-dependent Hamiltonians. The package is ready to be deployed on high performance computing (HPC) clusters and is aimed at providing reliable open-system analysis tools for noisy intermediate-scale quantum (NISQ) devices.