Quantum Computing: Unique Mathematical Perspectives
Thursday 8 November 2018, 10:30am - 4:30pm
London Mathematical Society, De Morgan House, London WC1B 4HS
The LMS Computer Science Colloquium is an annual day of themed talks on a topical issue at the interface of mathematics and computer science. The topic of the next colloquium will be Quantum Computing: Unique Mathematical Perspectives. The speakers will be:
Richard Jozsa (Cambridge), Foundations of Quantum Computation and Complexity
Quantum computing is based on the use of intrinsically quantum effects for information processing tasks. In some cases considerable benefits, even exponential benefits, can be obtained, compared to any known classical method for the task. The subject is currently attracting an astounding amount of attention, fuelled by an expectation of the imminent availability of a practical quantum computing device, seen by some as heralding a quantum revolution in technology. As a kind of converse to its technological exploitation, and even more importantly, the theory of quantum computing and complexity also provides a novel perspective on the foundations of physics itself and the enigma that is quantum theory.
In this talk we will begin by briefly mentioning highlights and areas of applicability where quantum computing is currently expected to be able to make a transformative impact. Then for the main part, we will introduce the basic ingredients of the mathematical formalism of quantum theory and discuss their significance for issues of computational complexity and use in quantum algorithms. We will introduce Pauli and Clifford operations, based on constructions from group theory, which play a fundamental role in many aspects of quantum computing, and we will use them to provide transparent illustrations of some key complexity issues. All of this discussion could also serve as background for more indepth or specific applications that may be featured in other talks.
Vivien Kendon (Durham), Solving Problems By Finding Low Energy Quantum States
There are many ways to solve problems using a quantum computer. One natural way is to use a Hamiltonian (natural or engineered) that drives the quantum system continuously in time, until the final state is measured to provide the answer. I will explain why this is a natural way to compute using quantum systems. Through examples of continuous-time quantum algorithms, based on quantum versions of random walks and on adiabatic quantum state transfer, I will illustrate how matching the problem to the Hamiltonian driver can play an important role in making the algorithms practical to implement.
Ashley Montanaro (Bristol), Quantum Algorithms: From Foundations To Applications
Quantum computers are designed to outperform their classical counterparts by running quantum algorithms, which use uniquely quantum-mechanical features such as superposition and entanglement to do things that cannot be done by classical algorithms. In this talk I will introduce the key mathematical ideas behind fundamental quantum algorithms for tasks such as integer factorisation and combinatorial search, and then describe recent work on using quantum algorithms for practical applications.
Earl Campbell (Sheffield), Homological and hypergraph product codes for quantum error correction
Quantum error correction can be built from pairs of classical error correction properties. Generally, the more efficient the classical error correcting code, the better the quantum code. However, the standard CCS construction requires the classical codes to have a special duality property and this prevents us from using the best known classical code (e.g. LDPC codes based on expander graphs). Recently, the hypergraph and homological product have emerged as new techniques for constructing quantum codes without the demanding duality property. This leads to quantum LDPC codes with more efficient rates than any previously known construction. I will review the prior art on homological and hypergraph product codes before presenting some of my recent work on double homological product codes that have an intriguing resilience to measurement noise, a property known as single-shot error correction.
Mark Howard (Sheffield), Topics in Stabilizer Quantum Computation
The central question in quantum information theory is to delineate the operational capabilities achievable under the rules of quantum mechanics but not achievable with classical physics. As such, it can be useful to tinker with hypothetical theories having different sets of allowed state preparations, transformations and measurements; different combinations can give us theories that are less powerful than, equal to, or more powerful than quantum mechanics. When we attempt to understand the computational power of circuits, so-called stabilizer circuits comprise a restricted class that are provably weaker than a general ("universal") quantum computer. For stabilizer circuits, the description of the achievable states and their updates is efficient leading to a classical simulation algorithm that is polynomial in the number of qubits. Remarkably, it is easy to boost the power of stabilizer circuits to that of a universal quantum computer by adding access to non-stabilizer states or operations. When error-correction is used these additional states or operations are typically very costly. All of the above naturally suggests a few questions that I will address:
1) What quantum mechanical property is missing from stabilizer circuits but present in universal quantum computers?
2) How can we minimize the use of costly non-stabilizer operations?
3) How should we classically simulate stabilizer circuits interspersed with a few non-stabilizer gates, and how does the runtime scale?
The event is aimed at PhD students and post-docs, although others are welcome to attend. The event is free for students and £5 for others, which is payable on the day. Lunch will be provided.
Limited funds (maximum £50 per person) are available to help with students' travel costs. Click the link below to access the application form. Please complete and return it to firstname.lastname@example.org. The deadline for applications is 7 November 2018.
Click 'register now' to register your attendance at this event.
57-58 Russell Square
De Morgan House, 57-58 Russell Square
London, WC1B 4HS-WC1B 4HS