Decoherence in Discrete Quantum Walks

We present an introduction to coined quantum walks on regular graphs, which have been developed in the past few years as an alternative to quantum Fourier transforms for underpinning algorithms for quantum computation. We then describe our results on the effects of decoherence on these quantum walks on a line, cycle and hypercube. We find high sensitivity to decoherence, increasing with the number of steps in the walk, as the particle is becoming more delocalised with each step. However, the effect of a small amount of decoherence can be to enhance the properties of the quantum walk that are desirable for the development of quantum algorithms, such as fast mixing times to uniform distributions.Comment: 15 pages, Springer LNP latex style, submitted to Proceedings of DICE 200

The expressive power of quantum walks in terms of language acceptance

Discrete time quantum walks are known to be universal for quantum computation. This has been proven by showing that they can simulate a universal quantum gate set. In this paper, we examine computation by quantum walks in terms of language acceptance, and present two ways in which discrete time quantum walks can accept some languages with certainty. These walks can take quantum as well as classical inputs, and we show that when the input is quantum, the walks can also be interpreted as performing the task of quantum state discrimination.Comment: In Proceedings QPL 2012, arXiv:1407.842

Universal quantum computation by the unitary control of ancilla qubits and using a fixed ancilla-register interaction

We characterise a model of universal quantum computation where the register (computational) qubits are controlled by ancillary qubits, using only a single fixed interaction between register and ancillary qubits. No additional access is required to the computational register and the dynamics of both the register and ancilla are unitary. This scheme is inspired by the measurement-based ancilla-driven quantum computation of Anders et al. [PRA 82, 020301(R), 2010], but does not require measurements of the ancillas, and in this respect is similar to the original gate based model of quantum computation. We consider what possible forms this ancilla-register interaction can take, with a proof that the interaction is necessarily locally equivalent to SWAP combined with an entangling controlled gate. We further show which Hamiltonians can create such interactions and discuss two examples; the two-qubit XY Hamiltonian and a particular case of the XXZ Hamiltonian. We then give an example of a simple, finite and fault tolerant gate set for universal quantum computation in this model.Comment: 10 pages, Published versio

Quantum walks on general graphs

Quantum walks, both discrete (coined) and continuous time, on a general graph of N vertices with undirected edges are reviewed in some detail. The resource requirements for implementing a quantum walk as a program on a quantum computer are compared and found to be very similar for both discrete and continuous time walks. The role of the oracle, and how it changes if more prior information about the graph is available, is also discussed.Comment: 8 pages, v2: substantial rewrite improves clarity, corrects errors and omissions; v3: removes major error in final section and integrates remainder into other sections, figures remove

Quantum computing using continuous-time evolution : continuous-time quantum computing

Computational methods are the most effective tools we have besides scientific experiments to explore the properties of complex biological systems. Progress is slowing because digital silicon computers have reached their limits in terms of speed. Other types of computation using radically different architectures, including neuromorphic and quantum, promise breakthroughs in both speed and efficiency. Quantum computing exploits the coherence and superposition properties of quantum systems to explore many possible computational paths in parallel. This provides a fundamentally more efficient route to solving some types of computational problems, including several of relevance to biological simulations. In particular, optimization problems, both convex and non-convex, feature in many biological models, including protein folding and molecular dynamics. Early quantum computers will be small, reminiscent of the early days of digital silicon computing. Understanding how to exploit the first generation of quantum hardware is crucial for making progress in both biological simulation and the development of the next generations of quantum computers. This review outlines the current state-of-the-art and future prospects for quantum computing, and provides some indications of how and where to apply it to speed up bottlenecks in biological simulation

The Natural Science of Computing

As unconventional computing comes of age, we believe a revolution is needed in our view of computer science