The ability to prepare sizeable multi-qubit entangled states with full qubit control is a critical milestone for physical platforms upon which quantum computers are built. We investigate the extent to which entanglement is found within a prepared graph state on the 20-qubit superconducting quantum computer IBM Q Poughkeepsie. We prepared a graph state along a path consisting of all twenty qubits within the device and performed full quantum state tomography on all groups of four connected qubits along this path. We determined that each pair of connected qubits was inseparable and hence the prepared state was entangled. Additionally, a genuine multipartite entanglement witness was measured on all qubit subpaths of the graph state and we found genuine multipartite entanglement on chains of up to three qubits. These results represent a demonstration of entanglement in one of the largest solid-state qubit arrays to date and indicate the positive direction of progress towards the goal of implementing complex quantum algorithms relying on such effects.

Generating and detecting genuine multipartite entanglement (GME) of sizeable quantum states prepared on physical devices is an important benchmark for highlighting the progress of near-term quantum computers. A common approach to certify GME is to prepare a Greenberger-Horne-Zeilinger (GHZ) state and measure a GHZ fidelity of at least 0.5. We measure the fidelities using multiple quantum coherences of GHZ states on 11 to 27 qubits prepared on the IBM Quantum ibmq_montreal device. Combinations of quantum readout error mitigation (QREM) and parity verification error detection are applied to the states. A fidelity of 0.546 ± 0.017 was recorded for a 27-qubit GHZ state when QREM was used, demonstrating GME across the full device with a confidence level of 98.6%. We benchmarked the effect of parity verification on GHZ fidelity for two GHZ state preparation embeddings on the heavy-hexagon architecture. The results show that the effect of parity verification, while relatively modest, led to a detectable improvement of GHZ fidelity.

The ability to generate large-scale entanglement is an important progenitor of quantum information processing capability in noisy intermediate-scale quantum (NISQ) devices. In this paper, the extent to which entangled quantum states over large numbers of qubits can be prepared on current superconducting quantum devices is investigated. Native-graph states on the IBM Quantum 65-qubit ibmq_manhattan device and the 53-qubit ibmq_rochester device are prepared and quantum readout-error mitigation (QREM) is applied. Connected entanglement graphs spanning each of the full devices are detected, indicating bipartite entanglement over the whole of each device. The application of QREM is shown to increase the observed entanglement within all measurements, in particular, the detected number of entangled pairs of qubits found within ibmq_rochester increases from 31 to 56 of the total 58 connected pairs. The results of this work indicate full bipartite entanglement in two of the largest superconducting devices to date.

We introduce a framework for mapping NP-Hard problems to adiabatic quantum computing (AQC) architectures that are heavily restricted in both connectivity and dynamic range of couplings, for which minor-embedding -the standard problem mapping method -cannot be directly applied. Separating the mapping into two distinct stages, we introduce problem-specific reductions for both quadratic unconstrained binary optimisation (QUBO) and satisfiability (SAT) and develop the subdivision-embedding method that is suitable for directly embedding onto these heavily restricted architectures. The theory underpinning this framework provides tools to aid in the manipulation of Ising Hamiltonians for the purposes of Ising energy minimisation, and could be used to assist in developing and optimising further problem mapping techniques. For each of the problem mapping methods presented, we examine how the physical qubit count scales with problem size on architectures of varying connectivity.

For universal quantum computation, a major challenge to overcome for practical implementation is the large amount of resources required for fault-tolerant quantum information processing. An important aspect is implementing arbitrary unitary operators built from logical gates within the quantum error correction code. A synthesis algorithm can be used to approximate any unitary gate up to arbitrary precision by assembling sequences of logical gates chosen from a small set of universal gates that are fault-tolerantly performable while encoded in a quantum error-correction code. However, current procedures do not yet support individual assignment of base gate costs and many do not support extended sets of universal base gates. We analysed cost-optimal sequences using an exhaustive search based on Dijkstra’s pathfinding algorithm for the canonical Clifford+T set of base gates and compared them to when additionally including Z-rotations from higher orders of the Clifford hierarchy. Two approaches of assigning base gate costs were used. First, costs were reduced to T-counts by recursively applying a Z-rotation catalyst circuit. Second, costs were assigned as the average numbers of raw (i.e. physical level) magic states required to directly distil and implement the gates fault-tolerantly. We found that the average sequence cost decreases by up to 54±3% when using the Z-rotation catalyst circuit approach and by up to 33±2% when using the magic state distillation approach. In addition, we investigated observed limitations of certain assignments of base gate costs by developing an analytic model to estimate the proportion of sets of Z-rotation gates from higher orders of the Clifford hierarchy that are found within sequences approximating random target gates.