QuEST and High Performance Simulation of Quantum Computers

We introduce QuEST, the Quantum Exact Simulation Toolkit, and compare it to ProjectQ, qHipster and a recent distributed implementation of Quantum++. QuEST is the first open source, OpenMP and MPI hybridised, GPU accelerated simulator of universal quantum circuits. Embodied as a C library, it is designed so that a user's code can be deployed seamlessly to any platform from a laptop to a supercomputer. QuEST is capable of simulating generic quantum circuits of general single-qubit gates and multi-qubit controlled gates, on pure and mixed states, represented as state-vectors and density matrices, and under the presence of decoherence. Using the ARCUS Phase-B and ARCHER supercomputers, we benchmark QuEST's simulation of random circuits of up to 38 qubits, distributed over up to 2048 compute nodes, each with up to 24 cores. We directly compare QuEST's performance to ProjectQ's on single machines, and discuss the differences in distribution strategies of QuEST, qHipster and Quantum++. QuEST shows excellent scaling, both strong and weak, on multicore and distributed architectures.Comment: 8 pages, 8 figures; fixed typos; updated QuEST URL and fixed typo in Fig. 4 caption where ProjectQ and QuEST were swapped in speedup subplot explanation; added explanation of simulation algorithm, updated bibliography; stressed technical novelty of QuEST; mentioned new density matrix suppor

Variational ansatz-based quantum simulation of imaginary time evolution

Imaginary time evolution is a powerful tool for studying quantum systems. While it is possible to simulate with a classical computer, the time and memory requirements generally scale exponentially with the system size. Conversely, quantum computers can efficiently simulate quantum systems, but not non-unitary imaginary time evolution. We propose a variational algorithm for simulating imaginary time evolution on a hybrid quantum computer. We use this algorithm to find the ground-state energy of many-particle systems; specifically molecular hydrogen and lithium hydride, finding the ground state with high probability. Our method can also be applied to general optimisation problems and quantum machine learning. As our algorithm is hybrid, suitable for error mitigation and can exploit shallow quantum circuits, it can be implemented with current quantum computers.Comment: 14 page

QuESTlink -- Mathematica embiggened by a hardware-optimised quantum emulator

We introduce QuESTlink, pronounced "quest link", an open-source Mathematica package which efficiently emulates quantum computers. By integrating with the Quantum Exact Simulation Toolkit (QuEST), QuESTlink offers a high-level, expressive and usable interface to a high-performance, hardware-accelerated emulator. Requiring no installation, QuESTlink streamlines the powerful analysis capabilities of Mathematica into the study of quantum systems, even utilising remote multicore and GPU hardware. We demonstrate the use of QuESTlink to concisely and efficiently simulate several quantum algorithms, and present some comparative benchmarking against core QuEST.Comment: 11 pages, 5 figures; added new facilities and remote benchmarkin

Quantum compilation and circuit optimisation via energy dissipation

We describe a method for automatically recompiling a quantum circuit A into a target circuit B, with the goal that both circuits have the same action on a specific input i.e. A|in> = B|in>. This is of particular relevance to hybrid, NISQ-era algorithms for dynamical simulation or eigensolving. The user initially specifies B as a blank template: a layout of parameterised unitary gates configured to the identity. The compilation then proceeds using quantum hardware to perform an isomorphic energy-minimisation task, and optionally a gate elimination phase to compress the circuit. We use a recently introduced imaginary-time technique derived from McLachlan's variational principle. If the template for B is too shallow for perfect recompilation then the method will result in an approximate solution. As a demonstration we successfully recompile a 7-qubit circuit involving 186 gates of multiple types into an alternative form with a different topology, a far lower two-qubit gate count, and a smaller family of gate types. We test the scaling of our algorithm on up to 20 qubits, recompiling into circuits with up to 400 parameterized gates, and incorporate a novel adaptive timestep technique. We note that a classical simulation of the process can be useful to optimise circuits for today's prototypes, and more generally the method may enable `blind' compilation i.e. harnessing a device whose response to control parameters is deterministic but unknown.Comment: 13 pages, 10 figures; fixed table formats, elaborated on applications and Trotter method in supplementary; added scaling tests and adaptive timeste

The LSST Data Mining Research Agenda

We describe features of the LSST science database that are amenable to scientific data mining, object classification, outlier identification, anomaly detection, image quality assurance, and survey science validation. The data mining research agenda includes: scalability (at petabytes scales) of existing machine learning and data mining algorithms; development of grid-enabled parallel data mining algorithms; designing a robust system for brokering classifications from the LSST event pipeline (which may produce 10,000 or more event alerts per night); multi-resolution methods for exploration of petascale databases; indexing of multi-attribute multi-dimensional astronomical databases (beyond spatial indexing) for rapid querying of petabyte databases; and more.Comment: 5 pages, Presented at the "Classification and Discovery in Large Astronomical Surveys" meeting, Ringberg Castle, 14-17 October, 200

Distributed Simulation of Statevectors and Density Matrices

Classical simulation of quantum computers is an irreplaceable step in the design of quantum algorithms. Exponential simulation costs demand the use of high-performance computing techniques, and in particular distribution, whereby the quantum state description is partitioned between a network of cooperating computers - necessary for the exact simulation of more than approximately 30 qubits. Distributed computing is notoriously difficult, requiring bespoke algorithms dissimilar to their serial counterparts with different resource considerations, and which appear to restrict the utilities of a quantum simulator. This manuscript presents a plethora of novel algorithms for distributed full-state simulation of gates, operators, noise channels and other calculations in digital quantum computers. We show how a simple, common but seemingly restrictive distribution model actually permits a rich set of advanced facilities including Pauli gadgets, many-controlled many-target general unitaries, density matrices, general decoherence channels, and partial traces. These algorithms include asymptotically, polynomially improved simulations of exotic gates, and thorough motivations for high-performance computing techniques which will be useful for even non-distributed simulators. Our results are derived in language familiar to a quantum information theory audience, and our algorithms formalised for the scientific simulation community. We have implemented all algorithms herein presented into an isolated, minimalist C++ project, hosted open-source on Github with a permissive MIT license, and extensive testing. This manuscript aims both to significantly improve the high-performance quantum simulation tools available, and offer a thorough introduction to, and derivation of, full-state simulation techniques.Comment: 56 pages, 18 figures, 28 algorithms, 1 tabl

The Virtual Quantum Device (VQD): A tool for detailed emulation of quantum computers

We present the Virtual Quantum Device (VQD) platform, a system based on the QuEST quantum emulator. Through the use of VQDs, non-expert users can emulate specific quantum computers with detailed error models, bespoke gate sets and connectivities. The platform boasts an intuitive interface, powerful visualisation, and compatibility with high-performance computation for effective testing and optimisation of complex quantum algorithms or ideas across a range of quantum computing hardware. We create and explore five families of VQDs corresponding to trapped ions, nitrogen-vacancy-centres, neutral atom arrays, silicon quantum dot spins, and superconducting devices. Each is highly configurable through a set of tailored parameters. We showcase the key characteristics of each virtual device, providing practical examples of the tool's usefulness and highlighting each device's specific attributes. By offering user-friendly encapsulated descriptions of diverse quantum hardware, the VQD platform offers researchers the ability to rapidly explore algorithms and protocols in a realisitic setting; meanwhile hardware experts can create their own VQDs to compare with their experiments.Comment: 21 pages, 17 figures, comments are welcom