Gavin Brennen | Macquarie University (original) (raw)
Papers by Gavin Brennen
arXiv (Cornell University), Dec 12, 2022
arXiv (Cornell University), Oct 20, 2022
International Cyber Policy Centre, May 13, 2021
We present a quantum control strategy for preparing Dicke states on spin ensembles for use in sup... more We present a quantum control strategy for preparing Dicke states on spin ensembles for use in superabsorption and precision metrology. The method uses a dispersive coupling of nnn spins to a common bosonic mode and does not require selective addressing, adiabatic state transfer constraints, or direct interactions between the spins. Using a control sequence inspired by the quantum algorithm for amplitude amplification, a target Dicke state can be prepared using O(n5/4)O(n^{5/4})O(n5/4) geometric phase gates. By nature of the of the geometrically closed path of the control operators on the joint mode-spin space, the sequence has dynamical decoupling built in which provides resilience to dephasing errors.
We study the single particle dynamics of a mobile non-Abelian anyon hopping around many pinned an... more We study the single particle dynamics of a mobile non-Abelian anyon hopping around many pinned anyons on a surface. The dynamics is modelled by a discrete time quantum walk and the spatial degree of freedom of the mobile anyon becomes entangled with the fusion degrees of freedom of the collective system. Each quantum trajectory makes a closed braid on the world lines of the particles establishing a direct connection between statistical dynamics and quantum link invariants. We find that asymptotically a mobile Ising anyon becomes so entangled with its environment that its statistical dynamics reduces to a classical random walk with linear dispersion in contrast to particles with Abelian statistics which have quadratic dispersion.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2008
In this article we present a pedagogical introduction of the main ideas and recent advances in th... more In this article we present a pedagogical introduction of the main ideas and recent advances in the area of topological quantum computation. We give an overview of the concept of anyons and their exotic statistics, present various models that exhibit topological behaviour and establish their relation to quantum computation. Possible directions for the physical realization of topological systems and the detection of anyonic behaviour are elaborated.
Physical Review Letters, 2011
Fortschritte der Physik, 2006
New Journal of Physics, 2009
Since the early work by Ashkin in 1970,1 optical trapping has become one of the most powerful too... more Since the early work by Ashkin in 1970,1 optical trapping has become one of the most powerful tools for manipulating small particles, such as micron sized beads2 or single atoms.3 Interestingly, both an atom and a lump of dielectric material can be manipulated through the same mechanism: the interaction energy of a dipole and the electric field of the laser light. In the case of atom trapping, the dominant contribution typically comes from the allowed optical transition closest to the laser wavelength while it is given by the bulk polarisability for mesoscopic particles. This difference lead to two very different contexts of applications: one being the trapping of small objects mainly in biological settings,4 the other one being dipole traps for individual neutral atoms5 in the field of quantum optics. In this context, solid state artificial atoms present the interesting opportunity to combine these two aspects of optical manipulation. We are particularly interested in nanodiamonds ...
arXiv: Optics, 2015
We motivate metrology schemes based on topological singularities as a way to build robustness aga... more We motivate metrology schemes based on topological singularities as a way to build robustness against deformations of the system. In particular, we relate reference settings of metrological systems to topological singularities in the measurement outputs. As examples we discuss optical nano-position sensing (i) using a balanced photodetector and a quadrant photodetector, and (ii) a more general image based scheme. In both cases the reference setting is a scatterer position that corresponds to a topological singularity in an output space constructed from the scattered field intensity distributions.
Ledger
The key cryptographic protocols used to secure the internet and financial transactions of today a... more The key cryptographic protocols used to secure the internet and financial transactions of today are all susceptible to attack by the development of a sufficiently large quantum computer. One particular area at risk is cryptocurrencies, a market currently worth over 100 billion USD. We investigate the risk posed to Bitcoin, and other cryptocurrencies, by attacks using quantum computers. We find that the proof-of-work used by Bitcoin is relatively resistant to substantial speedup by quantum computers in the next 10 years, mainly because specialized ASIC miners are extremely fast compared to the estimated clock speed of near-term quantum computers. On the other hand, the elliptic curve signature scheme used by Bitcoin is much more at risk, and could be completely broken by a quantum computer as early as 2027, by the most optimistic estimates. We analyze an alternative proof-of-work called Momentum, based on finding collisions in a hash function, that is even more resistant to speedup b...
arXiv (Cornell University), Dec 12, 2022
arXiv (Cornell University), Oct 20, 2022
International Cyber Policy Centre, May 13, 2021
We present a quantum control strategy for preparing Dicke states on spin ensembles for use in sup... more We present a quantum control strategy for preparing Dicke states on spin ensembles for use in superabsorption and precision metrology. The method uses a dispersive coupling of nnn spins to a common bosonic mode and does not require selective addressing, adiabatic state transfer constraints, or direct interactions between the spins. Using a control sequence inspired by the quantum algorithm for amplitude amplification, a target Dicke state can be prepared using O(n5/4)O(n^{5/4})O(n5/4) geometric phase gates. By nature of the of the geometrically closed path of the control operators on the joint mode-spin space, the sequence has dynamical decoupling built in which provides resilience to dephasing errors.
We study the single particle dynamics of a mobile non-Abelian anyon hopping around many pinned an... more We study the single particle dynamics of a mobile non-Abelian anyon hopping around many pinned anyons on a surface. The dynamics is modelled by a discrete time quantum walk and the spatial degree of freedom of the mobile anyon becomes entangled with the fusion degrees of freedom of the collective system. Each quantum trajectory makes a closed braid on the world lines of the particles establishing a direct connection between statistical dynamics and quantum link invariants. We find that asymptotically a mobile Ising anyon becomes so entangled with its environment that its statistical dynamics reduces to a classical random walk with linear dispersion in contrast to particles with Abelian statistics which have quadratic dispersion.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2008
In this article we present a pedagogical introduction of the main ideas and recent advances in th... more In this article we present a pedagogical introduction of the main ideas and recent advances in the area of topological quantum computation. We give an overview of the concept of anyons and their exotic statistics, present various models that exhibit topological behaviour and establish their relation to quantum computation. Possible directions for the physical realization of topological systems and the detection of anyonic behaviour are elaborated.
Physical Review Letters, 2011
Fortschritte der Physik, 2006
New Journal of Physics, 2009
Since the early work by Ashkin in 1970,1 optical trapping has become one of the most powerful too... more Since the early work by Ashkin in 1970,1 optical trapping has become one of the most powerful tools for manipulating small particles, such as micron sized beads2 or single atoms.3 Interestingly, both an atom and a lump of dielectric material can be manipulated through the same mechanism: the interaction energy of a dipole and the electric field of the laser light. In the case of atom trapping, the dominant contribution typically comes from the allowed optical transition closest to the laser wavelength while it is given by the bulk polarisability for mesoscopic particles. This difference lead to two very different contexts of applications: one being the trapping of small objects mainly in biological settings,4 the other one being dipole traps for individual neutral atoms5 in the field of quantum optics. In this context, solid state artificial atoms present the interesting opportunity to combine these two aspects of optical manipulation. We are particularly interested in nanodiamonds ...
arXiv: Optics, 2015
We motivate metrology schemes based on topological singularities as a way to build robustness aga... more We motivate metrology schemes based on topological singularities as a way to build robustness against deformations of the system. In particular, we relate reference settings of metrological systems to topological singularities in the measurement outputs. As examples we discuss optical nano-position sensing (i) using a balanced photodetector and a quadrant photodetector, and (ii) a more general image based scheme. In both cases the reference setting is a scatterer position that corresponds to a topological singularity in an output space constructed from the scattered field intensity distributions.
Ledger
The key cryptographic protocols used to secure the internet and financial transactions of today a... more The key cryptographic protocols used to secure the internet and financial transactions of today are all susceptible to attack by the development of a sufficiently large quantum computer. One particular area at risk is cryptocurrencies, a market currently worth over 100 billion USD. We investigate the risk posed to Bitcoin, and other cryptocurrencies, by attacks using quantum computers. We find that the proof-of-work used by Bitcoin is relatively resistant to substantial speedup by quantum computers in the next 10 years, mainly because specialized ASIC miners are extremely fast compared to the estimated clock speed of near-term quantum computers. On the other hand, the elliptic curve signature scheme used by Bitcoin is much more at risk, and could be completely broken by a quantum computer as early as 2027, by the most optimistic estimates. We analyze an alternative proof-of-work called Momentum, based on finding collisions in a hash function, that is even more resistant to speedup b...