Efficient Graph State Construction Under the Barrett and Kok Scheme

Recently Barrett and Kok (BK) proposed an elegant method for entangling separated matter qubits. They outlined a strategy for using their entangling operation (EO) to build graph states, the resource for one-way quantum computing. However by viewing their EO as a graph fusion event, one perceives that each successful event introduces an ideal redundant graph edge, which growth strategies should exploit. For example, if each EO succeeds with probability p=0.4 then a highly connected graph can be formed with an overhead of only about ten EO attempts per graph edge. The BK scheme then becomes competitive with the more elaborate entanglement procedures designed to permit p to approach unity.Comment: 3 pages, 3 figures. Small refinement

Quantum Computing with Globally Controlled Exchange-type Interactions

If the interaction between qubits in a quantum computer has a non-diagonal form (e.g. the Heisenberg interaction), then one must be able to "switch it off" in order to prevent uncontrolled propagation of states. Therefore, such QC schemes typically demand local control of the interaction strength between each pair of neighboring qubits. Here we demonstrate that this degree of control is not necessary: it suffices to switch the interaction collectively - something that can in principle be achieved by global fields rather than with local manipulations. This observation may offer a significant simplification for various solid state, optical lattice and NMR implementations.Comment: 3 pages inc. 3 figure

Hierarchical surface code for network quantum computing with modules of arbitrary size

The network paradigm for quantum computing involves interconnecting many modules to form a scalable machine. Typically it is assumed that the links between modules are prone to noise while operations within modules have significantly higher fidelity. To optimise fault tolerance in such architectures we introduce a hierarchical generalisation of the surface code: a small `patch' of the code exists within each module, and constitutes a single effective qubit of the logic-level surface code. Errors primarily occur in a two-dimensional subspace, i.e. patch perimeters extruded over time, and the resulting noise threshold for inter-module links can exceed ~ 10% even in the absence of purification. Increasing the number of qubits within each module decreases the number of qubits necessary for encoding a logical qubit. But this advantage is relatively modest, and broadly speaking a `fine grained' network of small modules containing only ~ 8 qubits is competitive in total qubit count versus a `course' network with modules containing many hundreds of qubits.Comment: 12 pages, 11 figure

Efficient variational quantum simulator incorporating active error minimisation

One of the key applications for quantum computers will be the simulation of other quantum systems that arise in chemistry, materials science, etc, in order to accelerate the process of discovery. It is important to ask: Can this be achieved using near future quantum processors, of modest size and under imperfect control, or must it await the more distant era of large-scale fault-tolerant quantum computing? Here we propose a variational method involving closely integrated classical and quantum coprocessors. We presume that all operations in the quantum coprocessor are prone to error. The impact of such errors is minimised by boosting them artificially and then extrapolating to the zero-error case. In comparison to a more conventional optimised Trotterisation technique, we find that our protocol is efficient and appears to be fundamentally more robust against error accumulation.Comment: 13 pages, 5 figures; typos fixed and small update

Probabilistic growth of large entangled states with low error accumulation

The creation of complex entangled states, resources that enable quantum computation, can be achieved via simple 'probabilistic' operations which are individually likely to fail. However, typical proposals exploiting this idea carry a severe overhead in terms of the accumulation of errors. Here we describe an method that can rapidly generate large entangled states with an error accumulation that depends only logarithmically on the failure probability. We find that the approach may be practical for success rates in the sub-10% range, while ultimately becoming unfeasible at lower rates. The assumptions that we make, including parallelism and high connectivity, are appropriate for real systems including measurement-induced entanglement. This result therefore shows the feasibility for real devices based on such an approach.Comment: 5 pages, 3 figure

Simple Pulses for Universal Quantum Computation with a Heisenberg ABAB Chain

Recently Levy has shown that quantum computation can be performed using an ABAB.. chain of spin-1/2 systems with nearest-neighbor Heisenberg interactions. Levy notes that all necessary elementary computational `gates' can be achieved by using spin-resonance techniques involving modulating the spin-spin interaction strength at high frequency. Here we note that, as an alternative to that approach, it is possible to perform the elementary gates with simple, non-oscillatory pulses.Comment: 3 pages including 2 fig

Stabilisers as a design tool for new forms of Lechner-Hauke-Zoller Annealer

In a recent paper Lechner, Hauke and Zoller (LHZ) described a means to translate a Hamiltonian of $N$ spin-$\frac{1}{2}$ particles with 'all-to-all' interactions into a larger physical lattice with only on-site energies and local parity constraints. LHZ used this mapping to propose a novel form of quantum annealing. Here we provide a stabiliser-based formulation within which we can describe both this prior approach and a wide variety of variants. Examples include a triangular array supporting all-to-all connectivity, and moreover arrangements requiring only $2N$ or $N\log N$ spins but providing interesting bespoke connectivities. Further examples show that arbitrarily high order logical terms can be efficiently realised, even in a strictly 2D layout. Our stabilisers can correspond to either even-parity constraints, as in the LHZ proposal, or as odd-parity constraints. Considering the latter option applied to the original LHZ layout, we note it may simplify the physical realisation since the required ancillas are only spin-$\frac{1}{2}$ systems (i.e. qubits, rather than qutrits) and moreover the interactions are very simple. We make a preliminary assessment of the impact of this design choices by simulating small (few-qubit) systems; we find some indications that the new variant may maintain a larger minimum energy gap during the annealing process.Comment: A dramatically expanded revision: we now show how to use our stabiliser formulation to construct a wide variety of new physical layouts, including ones with fewer than Order N^2 spins but custom connectivities, and a means to achieve higher order coupling even in 2

Distributed quantum computation with arbitrarily poor photon detection

In a distributed quantum computer scalability is accomplished by networking together many elementary nodes. Typically the network is optical and inter-node entanglement involves photon detection. In complex networks the entanglement fidelity may be degraded by the twin problems of photon loss and dark counts. Here we describe an entanglement protocol which can achieve high fidelity even when these issues are arbitrarily severe; indeed the method succeeds with finite probability even if the detectors are entirely removed from the network. An experimental demonstration should be possible with existing technologies.Comment: 5 pages, 4 fig