arXiv subjects

Nicholas Chancellor

Publications and source records attributed to Nicholas Chancellor.

At least 55 records · Page 3Linked to original sources

arXiv2020

The challenge and opportunities of quantum literacy for future education and transdisciplinary problem-solving

Resulting from cross-disciplinary dialogue between physicists, computer scientists, educationalists, and industrial end users, we propose the concept of quantum literacy as one means of addressing the transdisciplinary nature of the complex problems that we see at the heart of issues around global sustainability. In this way, quantum literacy can contribute to UN Sustainable Development Goal 4, Quality Education. We argue that quantum literacy, as defined here, addresses the challenges of learning and skills acquisition within a highly bounded discipline and of access to the kind of powerful knowledge that should be more accessible to a wide group of learners throughout the life course, both students and professionals. It is increasingly important that the knowledge of quantum technologies is accessible to those who work with real world applications in a more inclusive way. We therefore argue for the importance of addressing pedagogic issues when powerful knowledge consists of dense concepts, as well as complex and hierarchical relations between concepts, in addition to presenting a strong barrier to entry in the form of mathematics. We introduce a specific puzzle visualization learning tool through which to achieve these pedagogic ends with respect to quantum computation. Visualization through puzzles can enable non-specialists to develop an intuitive, but still rigorous, understanding of universal quantum computation and provide a facility for non-specialists to discover increasingly complex and new quantum algorithms. Using the Hong-Ou-Mandel optical effect from quantum mechanics, we demonstrate how visual methods such as those made possible through the puzzle visualization tool, can be very useful for understanding underlying complex processes in quantum physics and beyond and therefore support the aims of quantum literacy.

physics.ed-ph↗

arXiv2020

Quantum Computing for Quantum Tunnelling

We demonstrate how quantum field theory problems can be embedded on quantum annealers. The general method we use is a discretisation of the field theory problem into a general Ising model, with the continuous field values being encoded into Ising spin chains. To illustrate the method, and as a simple proof of principle, we use a (hybrid) quantum annealer to recover the correct profile of the thin-wall tunnelling solution. This method is applicable to many nonperturbative problems.

hep-ph↗

arXiv2019

Finding spin-glass ground states using quantum walks

Quantum computation using continuous-time evolution under a natural hardware Hamiltonian is a promising near- and mid-term direction toward powerful quantum computing hardware. We investigate the performance of continuous-time quantum walks as a tool for finding spin glass ground states, a problem that serves as a useful model for realistic optimization problems. By performing detailed numerics, we uncover significant ways in which solving spin glass problems differs from applying quantum walks to the search problem. Importantly, unlike for the search problem, parameters such as the hopping rate of the quantum walk do not need to be set precisely for the spin glass ground state problem. Heuristic values of the hopping rate determined from the energy scales in the problem Hamiltonian are sufficient for obtaining a better than square-root scaling. This makes it practical to use quantum walks for solving such problems, and opens the door for a range of applications on suitable quantum hardware.

quant-ph↗

arXiv2019

Quantum codes from classical graphical models

We introduce a new graphical framework for designing quantum error correction codes based on classical principles. A key feature of this graphical language, over previous approaches, is that it is closely related to that of factor graphs or graphical models in classical information theory and machine learning. It enables us to formulate the description of the recently-introduced `coherent parity check' quantum error correction codes entirely within the language of classical information theory. This makes our construction accessible without requiring background in quantum error correction or even quantum mechanics in general. More importantly, this allows for a collaborative interplay where one can design new quantum error correction codes derived from classical codes.

quant-ph↗

arXiv2019

Practical designs for permutation symmetric problem Hamiltonians on hypercubes

We present a method to experimentally realize large-scale permutation-symmetric Hamiltonians for continuous-time quantum protocols such as quantum walk and adiabatic quantum computation. In particular, the method can be used to perform an encoded continuous-time quantum search on a hypercube graph with 2^n vertices encoded into 2n qubits. We provide details for a realistically achievable implementation in Rydberg atomic systems. Although the method is perturbative, the realization is always achieved at second order in perturbation theory, regardless of the size of the mapped system. This highly efficient mapping provides a natural set of problems which are tractable both numerically and analytically, thereby providing a powerful tool for benchmarking quantum hardware and experimentally investigating the physics of continuous-time quantum protocols.

quant-ph↗

arXiv2019

Domain wall encoding of discrete variables for quantum annealing and QAOA

In this paper I propose a new method of encoding discrete variables into Ising model qubits for quantum optimization. The new method is based on the physics of domain walls in one dimensional Ising spin chains. I find that these encodings and the encoding of arbitrary two variable interactions is possible with only two body Ising terms. Following on from similar results for the `one hot' method of encoding discrete variables [Hadfield et. al. Algorithms 12.2 (2019): 34] I also demonstrate that it is possible to construct two body mixer terms which do not leave the logical subspace, an important consideration for optimising using the quantum alternating operator ansatz (QAOA). I additionally discuss how, since the couplings in the domain wall encoding only need to be ferromagnetic and therefore could in principle be much stronger than anti-ferromagnetic couplers, application specific quantum annealers for discrete problems based on this construction may be beneficial. Finally, I compare embedding for synthetic scheduling and colouring problems with the domain wall and one hot encodings on two graphs which are relevant for quantum annealing, the chimera graph and the Pegasus graph. For every case I examine I find a similar or better performance from the domain wall encoding as compared to one hot, but this advantage is highly dependent on the structure of the problem. For encoding some problems, I find an advantage similar to the one found by embedding in a Pegasus graph compared to embedding in a chimera graph.

quant-ph↗

arXiv2019

Decoding quantum error correction with Ising model hardware

Fault tolerant quantum computers will require efficient co-processors for real-time decoding of their adopted quantum error correction protocols. In this work we examine the possibility of using specialised Ising model hardware to perform this decoding task. Examples of Ising model hardware include quantum annealers such as those produced by D-Wave Systems Inc., as well as classical devices such as those produced by Hitatchi and Fujitsu and optical devices known as coherent Ising machines. We use the coherent parity check (CPC) framework to derive an Ising model mapping of the quantum error correction decoding problem for an uncorrelated quantum error model. A specific advantage of our Ising model mapping is that it is compatible with maximum entropy inference techniques which can outperform maximum likelihood decoding in some circumstances. We use numerical calculations within our framework to demonstrate that maximum entropy decoding can not only lead to improved error suppression, but can also shift threshold values for simple codes. As a high value problem for which a small advantage can lead to major gains, we argue that decoding quantum codes is an ideal use case for quantum annealers. In addition, the structure of quantum error correction codes allows application specific integrated circuit (ASIC) annealing hardware to reduce embedding costs, a major bottleneck in quantum annealing. Finally, we also propose a way in which a quantum annealer could be optimally used as part of a hybrid quantum-classical decoding scheme.

quant-ph↗

arXiv2019

Quantum search with hybrid adiabatic-quantum walk algorithms and realistic noise

Computing using a continuous-time evolution, based on the natural interaction Hamiltonian of the quantum computer hardware, is a promising route to building useful quantum computers in the near-term. Adiabatic quantum computing, quantum annealing, computation by continuous-time quantum walk, and special purpose quantum simulators all use this strategy. In this work, we carry out a detailed examination of adiabatic and quantum walk implementation of the quantum search algorithm, using the more physically realistic hypercube connectivity, rather than the complete graph, for our base Hamiltonian. We calculate the optimal adiabatic schedule for the hypercube, and then interpolate between adiabatic and quantum walk searching, obtaining a family of hybrid algorithms. We show that all of these hybrid algorithms provide the quadratic quantum speed up when run with optimal parameter settings, which we determine and discuss in detail. We incorporate the effects of multiple runs of the same algorithm, noise applied to the qubits, and two types of problem misspecification, determining the optimal hybrid algorithm for each case. Our results reveal a rich structure of how these different computational mechanisms operate and should be balanced in different scenarios. For large systems with low noise and good control, quantum walk is the best choice, while hybrid strategies can mitigate the effects of many shortcomings in hardware and problem misspecification.

quant-ph↗

arXiv2018

Protecting quantum memories using coherent parity check codes

Coherent parity check (CPC) codes are a new framework for the construction of quantum error correction codes that encode multiple qubits per logical block. CPC codes have a canonical structure involving successive rounds of bit and phase parity checks, supplemented by cross-checks to fix the code distance. In this paper, we provide a detailed introduction to CPC codes using conventional quantum circuit notation. We demonstrate the implementation of a CPC code on real hardware, by designing a [[4,2,2]] detection code for the IBM 5Q superconducting qubit device. Whilst the individual gate-error rates on the IBM device are too high to realise a fault tolerant quantum detection code, our results show that the syndrome information from a full encode-decode cycle of the [[4,2,2]] CPC code can be used to increase the output state fidelity by post-selection. Following this, we generalise CPC codes to other quantum technologies by showing that their structure allows them to be efficiently compiled using any experimentally realistic native two-qubit gate. We introduce a three-stage CPC design process for the construction of hardware-optimised quantum memories. As a proof-of-concept example, we apply our design process to an idealised linear seven-qubit ion trap. In the first stage of the process, we use exhaustive search methods to find a large set of [[7,3,3]] codes that saturate the quantum Hamming bound for seven qubits. We then optimise over the discovered set of codes to meet the hardware and layout demands of the ion trap device. We also discuss how the CPC design process will generalise to larger-scale codes and other qubit technologies.

quant-ph↗

arXiv2018

Quantum walk transport properties on graphene structures

We present numerical studies of quantum walks on \C60 and related graphene structures, to investigate their transport properties. Also known as a \emph{honeycomb lattice}, the lattice formed by carbon atoms in the graphene phase can be rolled up to form nanotubes of various dimensions. Graphene nanotubes have many important applications, some of which rely on their unusual electrical conductivity and related properties. Quantum walks on graphs provide an abstract setting in which to study such transport properties independent of the other chemical and physical properties of a physical substance. They can thus be used to further the understanding of mechanisms behind such properties. We find that nanotube structures are significantly more efficient in transporting a quantum walk than cycles of equivalent size, provided the symmetry of the structure is respected in how they are used. We find faster transport on zig-zag nanotubes compared to armchair nanotubes, which is unexpected given that for the actual materials the armchair nanotube is metallic, while the zig-zag is semiconducting.

quant-ph↗

arXiv2017

Modernizing Quantum Annealing II: Genetic algorithms with the Inference Primitive Formalism

Quantum annealing allows for quantum fluctuations to be used used to assist in finding the solution to some of the worlds most challenging computational problems. Recently, this field has attracted much interest because of the construction of large-scale flux-qubit based quantum annealing devices. There has been recent work on [Chancellor NJP 19(2):023024, 2017] how the control protocols of these devices can be modified so that individual annealer calls on real devices can take initial conditions. Development is being undertaken to implement such protocols in the quantum annealing devices designed by D-Wave Systems Inc. and these features will be available to customers soon. In this paper, I develop a formalism for algorithmic design in quantum annealers, which I call the `inference primitive' formalism. This formalism allows for a natural description of calls to quantum annealers with a general control structure. This more generalized control structure includes not only the ability to include initial conditions in an annealer run, but also to control the annealing schedules of qubits or clusters of qubits independently, thereby representing relative certainty values of different parts of a candidate solution. I discuss the compatability of such controls with a wide variety of other current efforts to improve the performance of annealers, such as non-stoquatic drivers, synchronizing freeze times for the qubits, and belief propagation techniques. To demonstrate the power of the formalism I present here, I discuss how this new formalism can be used to represent annealer implementations of genetic algorithms, and can represent the addition of genetic components to currently used algorithms. The new tools I develop will allow a more complete understanding of the algorithmic space available to quantum annealers, and thereby make the field more competitive.

quant-ph↗

arXiv2017

Circuit design for multi-body interactions in superconducting quantum annealing system with applications to a scalable architecture

Quantum annealing provides a way of solving optimization problems by encoding them as Ising spin models which are implemented using physical qubits. The solution of the optimization problem then corresponds to the ground state of the system. Quantum tunnelling is harnessed to enable the system to move to the ground state in a potentially highly non-convex energy landscape. A major difficulty in encoding optimization problems in physical quantum annealing devices is the fact that many real world optimization problems require interactions of higher connectivity as well as multi-body terms beyond the limitations of the physical hardware. In this work we address the question of how to implement multi-body interactions using hardware which natively only provides two-body interactions. The main result is an efficient circuit design of such multi-body terms using superconducting flux qubits in which effective N-body interactions are implemented using N ancilla qubits and only two inductive couplers. It is then shown how this circuit can be used as the unit cell of a scalable architecture by applying it to a recently proposed embedding technique for constructing an architecture of logical qubits with arbitrary connectivity using physical qubits which have nearest-neighbor four-body interactions. It is further shown that this design is robust to non-linear effects in the coupling loops as well as mismatches in some of the circuit parameters.

quant-ph↗

arXiv2017

Modernizing Quantum Annealing using Local Searches

I describe how real quantum annealers may be used to perform local (in state space) searches around specified states, rather than the global searches traditionally implemented in the quantum annealing algorithm. Such protocols will have numerous advantages over simple quantum annealing. By using such searches the effect of problem mis-specification can be reduced, as only energy differences between the searched states will be relevant. The quantum annealing algorithm is an analogue of simulated annealing, a classical numerical technique which has now been superseded. Hence, I explore two strategies to use an annealer in a way which takes advantage of modern classical optimization algorithms. Specifically, I show how sequential calls to quantum annealers can be used to construct analogues of population annealing and parallel tempering which use quantum searches as subroutines. The techniques given here can be applied not only to optimization, but also to sampling. I examine the feasibility of these protocols on real devices and note that implementing such protocols should require minimal if any change to the current design of the flux qubit-based annealers by D-Wave Systems Inc. I further provide proof-of-principle numerical experiments based on quantum Monte Carlo that demonstrate simple examples of the discussed techniques.

quant-ph↗

arXiv2016

A Direct Mapping of Max k-SAT and High Order Parity Checks to a Chimera Graph

We demonstrate a direct mapping of max k-SAT problems (and weighted max k-SAT) to a Chimera graph, which is the non-planar hardware graph of the devices built by D-Wave Systems Inc. We further show that this mapping can be used to map a similar class of maximum satisfiability problems where the clauses are replaced by parity checks over potentially large numbers of bits. The latter is of specific interest for applications in decoding for communication. We discuss an example in which the decoding of a turbo code, which has been demonstrated to perform near the Shannon limit, can be mapped to a Chimera graph. The weighted max k-SAT problem is the most general class of satisfiability problems, so our result effectively demonstrates how any satisfiability problem may be directly mapped to a Chimera graph. Our methods faithfully reproduce the low energy spectrum of the target problems, so therefore may also be used for maximum entropy inference.

quant-ph↗

arXiv2016

An Overview of Approaches to Modernize Quantum Annealing Using Local Searches

I describe how real quantum annealers may be used to perform local (in state space) searches around specified states, rather than the global searches traditionally implemented in the quantum annealing algorithm. The quantum annealing algorithm is an analogue of simulated annealing, a classical numerical technique which is now obsolete. Hence, I explore strategies to use an annealer in a way which takes advantage of modern classical optimization algorithms, and additionally should be less sensitive to problem mis-specification then the traditional quantum annealing algorithm.

cs.ET↗

arXiv2016

Experimental Freezing of mid-Evolution Fluctuations with a Programmable Annealer

For randomly selected couplers and fields, the D-Wave device typically yields a highly Boltzmann like distribution [ indicating equilibration. These equilibrated data however do not contain much useful information about the dynamics which lead to equilibration. To illuminate the dynamics, special Hamiltonians can be chosen which contain large energy barriers. In this paper we generalize this approach by considering a class of Hamiltonians which map clusters of spin-like qubits into 'superspins', thereby creating an energy landscape where local minima are separated by large energy barriers. These large energy barriers allow us to observe signatures of the transverse field frozen. To study these systems, we assume that the these frozen spins are describes by the Kibble-Zurek mechanism which was originally developed to describe formation of topological defects in the early universe. It was soon realized that it also has applications in analogous superconductor systems and later realized to also be important for the transverse field Ising model . We demonstrate that these barriers block equilibration and yield a non-trivial distribution of qubit states in a regime where quantum effects are expected to be strong, suggesting that these data should contain signatures of whether the dynamics are fundamentally classical or quantum. We exhaustively study a class of 3x3 square lattice superspin Hamiltonians and compare the experimental results with those obtained by exact diagonalisation. We find that the best fit to the data occurs at finite transverse field. We further demonstrate that under the right conditions, the superspins can be relaxed to equilibrium, erasing the signature of the transverse field. These results are interesting for a number of reasons. They suggest a route to detect signatures of quantum mechanics on the device on a statistical level.

quant-ph↗

arXiv2016

Pfaffian-like ground states for bosonic atoms and molecules in one-dimensional optical lattices

We study ground states and elementary excitations of a system of bosonic atoms and diatomic Feshbach molecules trapped in a one-dimensional optical lattice using exact diagonalization and variational Monte Carlo methods. We primarily study the case of an average filling of one boson per site. In agreement with bosonization theory, we show that the ground state of the system in the thermodynamic limit corresponds to the Pfaffian-like state when the system is tuned towards the superfluid-to-Mott insulator quantum phase transition. Our study clarifies the possibility of the creation of exotic Pfaffian-like states in realistic one-dimensional systems. We also present preliminary evidence that such states support non-Abelian anyonic excitations that have potential application for fault-tolerant topological quantum computation.

cond-mat.str-el↗

arXiv2016

Maximum-Entropy Inference with a Programmable Annealer

Optimisation problems in science and engineering typically involve finding the ground state (i.e. the minimum energy configuration) of a cost function with respect to many variables. If the variables are corrupted by noise then this approach maximises the likelihood that the solution found is correct. An alternative approach is to make use of prior statistical information about the noise in conjunction with Bayes's theorem. The maximum entropy solution to the problem then takes the form of a Boltzmann distribution over the ground and excited states of the cost function. Here we use a programmable Josephson junction array for the information decoding problem which we simulate as a random Ising model in a field. We show experimentally that maximum entropy decoding at finite temperature can in certain cases give competitive and even slightly better bit-error-rates than the maximum likelihood approach at zero temperature, confirming that useful information can be extracted from the excited states of the annealing device. Furthermore we introduce a microscopic bit-by-bit analytical method which is agnostic to the specific application and use it to show that the annealing device samples from a highly Boltzmann-like distribution. Machines of this kind are therefore candidates for use in a wide variety of machine learning applications which exploit maximum entropy inference, including natural language processing and image recognition. We further show that the limiting factor for performance in our experiments is likely to be control errors rather than failure to reach equilibrium. Our work also provides a method for determining if a system is in equilibrium which can be easily generalized. We discuss possible applications of this method to spin glasses and probing the performance of the quantum annealing algorithm.

quant-ph↗