Controlled Quantum Dynamics Theory - Research snapshots

Topological Order, Quantum Error Correction and Fault Tolerant Quantum Computing

A topological fault tolerant quantum computing scheme that can tolerate significant loss errors.

The ability to store and process quantum states is key to the nascent field of quantum information technology. However, quantum information is delicate. It can be corrupted by imperfect control of the 'knobs' accessible to the experimentalist, or by unwanted coupling to other systems.

One of the most important discoveries in quantum information in the last 15 years was the discovery of methods to protect quantum information from noise, and also to process the resulting protected states. Two main approaches have been developed - one based on the use of quantum generalizations of error correcting codes, the other based on a newly discovered property of matter known as 'topological order': topologically ordered systems can protect quantum information without active error correction. Within the CQD program, Dr. Sean Barrett and coworkers are currently studying an approach to protecting and coherently processing quantum information which combines both of these approaches. Two recent breakthroughs in the group have concerned the effect of a

Horizontal axis: loss error probability per qubit. Vertical axis: computational error probability. The large "correctable" region indicates that the practical realisation of quantum computing may be much easier than hitherto expected.

particular type of error where the information carrying entity (which could be an atom, photon, or solid state device) is completely lost. We have shown that certain error correcting codes can tolerate loss of up to half of their quantum bits, while still retaining the ability to correct for other types of noise [Phys. Rev. Lett. 102, 200501 (2009)]. Secondly, we have shown that a quantum computing scheme using such topological codes is also robust to loss errors at rates of up to 25 percent. These schemes, exhibiting very high thresholds that are comparable with state of the art experiments, indicate that the practical realisation of quantum computing may be much easier than hitherto expected [Phys. Rev. Lett. 105, 200502 (2010)].

Quantum Reference Frames

A comparison of probability of success for obtaining the ideal measurement result in three different cases of a small quantum reference frame. The dashed line corresponds to the case of sequential measurements without any correction, the dashed-dotted line is for the case in which we correct the measurement result via applying unitary interactions after any two measurements and the solid line belongs to the case of correction via applying corrections after specific outcomes are obtained.

It is common in quantum mechanics to assume that clocks and rulers – “reference frames” - with respect to which we measure all systems are perfect, and classical – i.e. large. We have been researching how to treat them in the quantum mechanical formalism and see what type of limitations doing this does or does not impose. This has interesting foundational issues in understanding quantum space and time in extreme conditions such as near black holes. However it also is important for building quantum information processing devices! For quantum computers the reference frames take the form of lasers, and we want to use as small and weak lasers as possible, to miniaturize the devices. Currently we are focusing on a program of research initiated by Dr. Rudolph and colleagues [Rev. Mod. Phys. 79, 555–609 (2007)] concerning how long a quantum reference frame (QRF) lasts if it is used as a resource for performing quantum operations and also how we can make it to last longer. The special case that we are looking at is the effect that the measurement of the angle between a directional quantum reference frame and a spin-1/2 particle has on the ability of QRF to act as a reliable reference for future measurements. We show that each time one of these spin-1/2 particles is measured against the QRF, it causes the reference frame to suffer from a back-action which makes the probability of getting the correct measurement result decrease as the number of measurements increases. We recently have found two different ways of fighting this seemingly inevitable degradation – either through an active corrective mechanism, or by a careful monitoring of the dynamics involved. In the figure below, we can see how these two ways of fighting the degradation of the QRF makes it useful for a larger number of measurements [Phys. Rev. A 82, 032320 (2010)].

Classical Notions in a Quantum Universe

CLASSICAL NOTIONS IN A QUANTUM UNIVERSE Quantum Mechanics encompasses not only t he strange particle world of atoms, photons and quarks, but also the more familiar classical world of galaxies, stars, trees and humans. How our classical notions fit into the counter-intuitive world of Quantum Mechanics is far from being a trivial question and brings with it delicate technical chal l enges and a greater mastery of how quantum information behaves. We are currently conducting research on how classical correlation patterns fundamentally fit into the underlying quantum world and asking the surprisingly difficult question:

How much classical correlation can we create in the simplest setting of two fundamental particles?

Our interface with the quantum world is ultimately classical, so beyond its foundational importance, understanding how traditional classical information relates to quantum information is significant for the manipulation of quantum systems and for information processing tasks. We have recently solved this problem for a variety of special cases, and are now focussed on obtaining a fully general solution.

Time and the Second Law of Thermodynamics

Time Time is one of our most ancient mysteries, while in stark contrast it is only in the past century that we have become aware of the quantum mechanical properties of Nature. Why do events seem to flow past us only in one direction? Why do we only know the past and not the future? Why do all parts of the universe experience the same Arrow of Time? While these questions may seem better suited to a philosophy department, central to all these deep and significant questions is the notion of “information”, and within the field of Quantum Information Theory we are applying recent discoveries in the theory of quantum entanglement to better understand how Time works, and how entanglement in an actual physical system can be used to bend or even reverse the Arrow of Time! Beyond being of foundational importance, the research also offers practical insights into the fundamental limits in the efficiency of thermodynamic engines, and into how heat flow and energy transfer in quantum systems can be modified and controlled via quantum correlations. We were recently by Scientific American to comment on a provocative proposal by Maccone - our understanding of this issue allowed us to identify the flaw in his proposal [Physical Review Letters,104,148901], and to subsequently undertake a thorough analysis of the time reversals possible due to quantum entanglement [Phys. Rev. E 81, 061130 (2010)].

Quantum state engineering

Photons are one of the most useful tools to test paradoxes in quantum mechanics. Once the quantum-mechanical state of a photonic field is determined, all the statistical properties are known. Recent successes in engineering of the quantum-mechanical state of a radiation field heavily depend on the quantum-mechanical understanding of measurements. First, the radiation field is let to interact with an ancila. Then the ancila is measured to collapse the state of the system into a designated state.

Schematic diagram for quantum-state engineering

A probe system is made correlated with ancillas by their interaction. By measuring the ancilla system after the interaction the probe system is collapsed into a final state. this scheme can be realised in various physical systems and interaction models. For instance, the correlator can be a beam splitter for the quantum systems prepared in photonic fields. The correlation can be induced by strong/weak interaction between photons and atoms, atoms and atoms and bosonic and bosonic systems. The measurment can be local or collective.

Quantum-state engineering has given a possibility to realise the most basic operations in quantum field theory, namely bosonic annihilation and creation operations. We can directly test their commutation relation. In quantum-state engineering, the quantum measurement, single-photon interference and basic quantum operations seem to come together to unravel some of the profound questions in quantum mechanics. However, when the detail is concerned, it is not very clear where exactly quantum mechanics is hiding. We work on how far we can understand the measurement based quantum operations and quantum arithmetic using classical theories and find their limitations. We also work on the extension of quantum-state engineering for various systems beyond photonic fields.

Robust Computers Made of Light

(a)Macroscopic view (b) Microscopic view

A quantum paradigm for information promises more reliable communications and enhanced algorithms for many important problems, such as quantum chemistry leading to better drug design, simulation of light harvesting complexes leading to better solar cells or design of new exotic materials capable of withstanding extremes such as heat, pressure or electr ical current.

One of our areas of research in the CQD group is trying to bring the quantum computer closer. Our focus is on optical and solid state (semiconductor) systems. Recently [Phys. Rev. Lett.103, 113602 (2009)] we proposed a device at the interface of these two technologies – a “quantum dot machine gun” for entangled photons. This idea captured some media attention and is currently being pursued by three different experimental groups. Even having such a device we

Schematic setting of our proposal: An array of quantum dots (purple) fire strings of photons which at a later stage are combined in the optical gates to create correlations between parallel beams (yellow vertical lines). This constitutes the substrate

still need a robust way of computing with it. To this end we have been investigating how it could be used in a so-called “fault tolerant one-way quantum computer”, a model in which one starts with a three-dimensional lattice of correlated quantum bits and then measures them out following an order dictated by the quantum algorithm, in such a way that the overall shape of the resulting lattice will enact a series of quantum logical gates. We have proposed a way of building of this lattice using arrays of quantum dots – tiny pyramidal structures that are able of firing correlated photons - linear optical gates and very efficient detectors. All these components offer very good controllability and scalability. Simulations have been carried out which suggest that our proposal would be quite robust against errors in the quantum dots, the optical gates and in the detectors.

On-Chip Photonics Networks

On-chip network of photonic waveguides generating entangled resource states for measurement-based quantum control.

Quantum Mechanics encompasses not only the strange particle world of atoms, photons and quarks, but also the mo re familiar classical world of galaxies, stars, trees and humans. How our classical notions f it into the c ounter-intuitive world of Quantum Mechanics is far from being a trivial quest ion and brings with it delicate technical challenges and a greater mastery of how quantum information behaves. We are currently conducting research on how classical correla tion patterns fundamentally fit into the under lying quantum world and asking the surprisingly difficult question: How much classical correlation can we create in the simplest setting of two fundamental particles?

Relativistic Quantum Information Theory

Relativistic QIT When we combine Relativity with Quantum Mechanics we are inexorably lead to the notion of a quantum field. Currently quantum field theories in the setting of curved spacetimes are pushing the frontier of our understanding of the laws of Nature. In recent times we have come to realise the important role that certain information theoretic notions play at this frontier. The most famous being the so-called Black Hole Information Paradox, which asks whether information is truly destroyed in the most extreme conditions of a black hole. Relativistic Quantum Information Theory seeks to investigate at a fundamental level, how does information behave in the presence of gravity and at velocities close to the speed of light. Two such questions of interest for us are: How does vacuum entanglement relate to the causal structure of a spacetime? How are global spacetime properties encoded in the local state of a quantum field that we access with a particle detector? For many years the question has been open of whether the relativistic version of quantum information theory is different with respect to fundamental information processing power from non-relativistic quantum information theory. By considering these foundational questions we have rece ntly managed to show that certain important cryptographic protoc ols – such as “secure gambling on the quantum internet” are possible only in relativis tic quantum information theory, a result which may lea d to many n ew practic al uses for quantum communication theory.

Nonlinear Quantum Optics with Nanostructured Media

Efficient single-photon excitation of on-chip surface plasmon polaritons using attenuated-reflection geometries.

An active area of our research is the generation of large nonlinear effects at the quantum level – a field in which Imperial researchers have been leading the world for many years. A major problem for quantum information processing is that photons interact very weakly with each other. If large nonlinear effects become possible in the single-photon regime, it will allow the efficient production of entangled states, the generation of nonclassical states such as Schrödinger cat states, and the processing of quantum information encoded into continuous and discrete variables. To tackle this problem we consider surface plasmon polaritons (see figure), an exotic form of light (photons) coupled to matter (electrons), where it has recently been recognised that they provide the potential for achieving large nonlinear effects with deep sub-wavelength field confinement in nanostructured media. We are working on developing efficient nonlinear plasmonic waveguides and investigating coupled nonlinear plasmonic systems. The proposal of experimentally realisable schemes for plasmonic quantum control and information processing is one of our major goals. Mathematical modelling and careful application of quantum optics theory is essential in our research on this topic.

Peeking Inside The Quantum Box: Indirect System Theory For Many-Body Hamiltonians

Estimating the nature and strength of interactions has been one of the main goals in quantum theory for almost a century. But it is only now that we are capable, in principle, of experimentally identifying the s pecific individual interactions – so cal led “Hamiltonians” of large systems of particles. However ; in general the complexity of such Hamiltonian estimation is vast, as each particle needs to be initialised and its dynamics monitored. In collaboration with RIKEN, Japan, we have discovered efficient methods for estimating certain types of interactions often encountered in experiments. These can be identified indirectly- by only monitoring the quantum dynamics of the surface of the system, the inner dynamics is revealed. This is analogous to tomography as used in, e.g., seismology and ultrasonography. Our results provide further evidence for a “holographic principle” of many-body Hamiltonians, which was previously conjectured by our group based on the scaling of entanglement in these systems.