Neil J. Ross

Quipper: a scalable quantum programming language

The field of quantum algorithms is vibrant. Still, there is currently a lack of programming languages for describing quantum computation on a practical scale, i.e., not just at the level of toy problems. We address this issue by introducing Quipper, a scalable, expressive, functional, higher-order quantum programming language. Quipper has been used to program a diverse set of non-trivial quantum algorithms, and can generate quantum gate representations using trillions of gates. It is geared towards a model of computation that uses a classical computer to control a quantum device, but is not dependent on any particular model of quantum hardware. Quipper has proven effective and easy to use, and opens the door towards using formal methods to analyze quantum algorithms.

An introduction to quantum programming in quipper

Quipper is a recently developed programming language for expressing quantum computations. This paper gives a brief tutorial introduction to the language, through a demonstration of how to make use of some of its key features. We illustrate many of Quippers language features by developing a few well known examples of Quantum computation, including quantum teleportation, the quantum Fourier transform, and a quantum circuit for addition.

Programming the quantum future

The Quipper language offers a unified general-purpose programming framework for quantum computation.

Toward the first quantum simulation with quantum speedup

Significance Near-term quantum computers will have limited numbers of qubits and will only be able to reliably perform limited numbers of gates. Therefore, it is crucial to identify applications of quantum processors that use the fewest possible resources. We argue that simulating the time evolution of spin systems is a classically hard problem of practical interest that is among the easiest to address with early quantum devices. We develop optimized implementations and perform detailed resource analyses for several leading quantum algorithms for this problem. By evaluating the best approaches to small-scale quantum simulation, we provide a detailed blueprint for what could be an early practical application of quantum computers. With quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical computers, but that requires the fewest resources for a quantum computer. We consider quantum simulation of spin systems, which could be applied to understand condensed matter phenomena. We synthesize explicit circuits for three leading quantum simulation algorithms, using diverse techniques to tighten error bounds and optimize circuit implementations. Quantum signal processing appears to be preferred among algorithms with rigorous performance guarantees, whereas higher-order product formulas prevail if empirical error estimates suffice. Our circuits are orders of magnitude smaller than those for the simplest classically infeasible instances of factoring and quantum chemistry, bringing practical quantum computation closer to reality.

Automated optimization of large quantum circuits with continuous parameters

We develop and implement automated methods for optimizing quantum circuits of the size and type expected in quantum computations that outperform classical computers. We show how to handle continuous gate parameters and report a collection of fast algorithms capable of optimizing large-scale quantum circuits. For the suite of benchmarks considered, we obtain substantial reductions in gate counts. In particular, we provide better optimization in significantly less time than previous approaches, while making minimal structural changes so as to preserve the basic layout of the underlying quantum algorithms. Our results help bridge the gap between the computations that can be run on existing hardware and those that are expected to outperform classical computers.Quantum computation: optimizing quantum circuitsA new software tool significantly reduces the size of arbitrary quantum circuits, automatically optimizing the number of gates required for running algorithms. Yunseong Nam and colleagues from the University of Maryland developed a set of subroutines which, given a certain quantum circuit, would remove redundant gates by changing the order of individual or multiple operations and combining them. After a pre-processing phase, the execution of these routines in careful order constitutes a powerful automatized approach for reducing the resources required to implement a given algorithm. The heuristic nature of this optimization makes its computational cost scale well with the size of the circuit, as shown by comparisons for the computation of discrete logarithms and Hamiltonian simulations. This makes it applicable to computations that can be run on existing hardware and might outperform classical computers.

Full abstraction for set-based models of the symmetric interaction combinators

The symmetric interaction combinators are a model of distributed and deterministic computation based on Lafonts interaction nets, a special form of graph rewriting. The interest of the symmetric interaction combinators lies in their universality, that is, the fact that they may encode all other interaction net systems; for instance, several implementations of the lambda-calculus in the symmetric interaction combinators exist, related to Lampings sharing graphs for optimal reduction. A certain number of observational equivalences were introduced for this system, by Lafont, Fernandez and Mackie, and the first author. In this paper, we study the problem of full abstraction with respect to one of these equivalences, using a class of very simple denotational models based on pointed sets.