Better-than-classical Grover search via quantum error detection and suppression

Grover's search algorithm is one of the first quantum algorithms to exhibit a provable quantum advantage. It forms the backbone of numerous quantum applications and is widely used in benchmarking efforts. Here, we report better-than-classical success probabilities for a complete Grover search algorithm on the largest scale demonstrated to date, of up to five qubits, using two different IBM superconducting transmon qubit platforms. This is enabled, on the four and five-qubit scale, by error suppression via robust dynamical decoupling pulse sequences, without which we do not observe better-than-classical results. 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 success probability of 99.5% 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 introduce algorithmic error tomography, a method of independent interest 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 algorithmic error tomography provides a stringent test of an error model based on a combination of amplitude damping, dephasing, and depolarization.Comment: 21 pages, 10 main figures + 9 supplementary figures, 3 table

Demonstration of algorithmic quantum speedup

Quantum algorithms theoretically outperform classical algorithms in solving problems of increasing size, but computational errors must be kept to a minimum to realize this potential. Despite the development of increasingly capable quantum computers (QCs), an experimental demonstration of a provable algorithmic quantum speedup employing today's non-fault-tolerant, noisy intermediate-scale quantum (NISQ) devices has remained elusive. Here, we unequivocally demonstrate such a speedup, quantified in terms of the scaling with the problem size of the time-to-solution metric. We implement the single-shot Bernstein-Vazirani algorithm, which solves the problem of identifying a hidden bitstring that changes after every oracle query, utilizing two different 27-qubit IBM Quantum (IBMQ) superconducting processors. The speedup is observed on only one of the two QCs (ibmq_montreal) when the quantum computation is protected by dynamical decoupling (DD) -- a carefully designed sequence of pulses applied to the QC that suppresses its interaction with the environment, but not without DD. In contrast to recent quantum supremacy demonstrations, the quantum speedup reported here does not rely on any additional assumptions or complexity-theoretic conjectures and solves a bona fide computational problem, in the setting of a game with an oracle and a verifier.Comment: 12 pages, 6 main figures + 5 supplementary figures, 1 tabl

Investigating the Chinese Postman Problem on a Quantum Annealer

The recent availability of quantum annealers has fueled a new area of information technology where such devices are applied to address practically motivated and computationally difficult problems with hardware that exploits quantum mechanical phenomena. D-Wave annealers are promising platforms to solve these problems in the form of quadratic unconstrained binary optimization. Here we provide a formulation of the Chinese postman problem that can be used as a tool for probing the local connectivity of graphs and networks. We treat the problem classically with a tabu algorithm and using a D-Wave device. We systematically analyze computational parameters associated with the specific hardware. Our results clarify how the interplay between the embedding due to limited connectivity of the Chimera graph, the definition of logical qubits, and the role of spin-reversal controls the probability of reaching the expected solution

Pulse variational quantum eigensolver on cross-resonance based hardware

State-of-the-art noisy digital quantum computers can only execute short-depth quantum circuits. Variational algorithms are a promising route to unlock the potential of noisy quantum computers since the depth of the corresponding circuits can be kept well below hardware-imposed limits. Typically, the variational parameters correspond to virtual $R_Z$ gate angles, implemented by phase changes of calibrated pulses. By encoding the variational parameters directly as hardware pulse amplitudes and durations we succeed in further shortening the pulse schedule and overall circuit duration. This decreases the impact of qubit decoherence and gate noise. As a demonstration, we apply our pulse-based variational algorithm to the calculation of the ground state of different hydrogen-based molecules (H$_2$, H$_3$ and H$_4$) using IBM cross-resonance-based hardware. We observe a reduction in schedule duration of up to $5\times$ compared to CNOT-based Ans\"atze, while also reducing the measured energy. In particular, we observe a sizable improvement of the minimal energy configuration of H$_3$ compared to a CNOT-based variational form. Finally, we discuss possible future developments including error mitigation schemes and schedule optimizations, which will enable further improvements of our approach paving the way towards the simulation of larger systems on noisy quantum devices

Dynamical decoupling for superconducting qubits: a performance survey

Dynamical Decoupling (DD) is perhaps the simplest and least resource-intensive error suppression strategy for improving quantum computer performance. Here we report on a large-scale survey of the performance of 60 different DD sequences from 10 families, including basic as well as advanced sequences with high order error cancellation properties and built-in robustness. The survey is performed using three different superconducting-qubit IBMQ devices, with the goal of assessing the relative performance of the different sequences in the setting of arbitrary quantum state preservation. We find that the high-order universally robust (UR) and quadratic DD (QDD) sequences generally outperform all other sequences across devices and pulse interval settings. Surprisingly, we find that DD performance for basic sequences such as CPMG and XY4 can be made to nearly match that of UR and QDD by optimizing the pulse interval, with the optimal interval being substantially larger than the minimum interval possible on each device.Comment: 22 pages (2 are citations), 5 main figures + 4 supplementary figures, 2 table