Conference

Constructing good quantum LDPC codes remains an important problem in quantum coding theory. We contribute to the ongoing discussion on this topic by proposing two approaches to constructing quantum LDPC codes. In the first, we rely on an algebraic method that uses a redundant description of the parity check matrix to overcome the problem of 4-cycles in the Tanner graph that degrade the performance of iterative decoding. In the second we use the fact that subsystem coding can simplify the decoding process. We show that if there exist classical LDPC codes with large error exponents, then we can construct degenerate subsystem LDPC codes with the stabilizer generators having low weight.

We investigate which families of quantum states can be used as resources for approximate and/or stochastic universal measurement-based quantum computation, in the sense that single-qubit operations and classical communication are sufficient to prepare (with some fixed precision and/or probability) any quantum state from the initial resource. We find entanglement-based criteria for non-universality in the approximate and/or stochastic case. By applying them, we are able to discard some families of states as not universal also in this weaker sense. Finally, we show that any family $Sigma$ of states that is \'close\' to an (approximate and/or stochastic) universal family $Gamma$ is approximate and stochastic universal, and we prove that if $Gamma$ was efficiently universal then also $Sigma$ is.

Quantum computers provide new resources to solve combinatorial optimization problems (COPs). Using techniques borrowed from quantum information theory, I will present a quantum algorithm that simulates classical annealing processes, where the (quantum) annealing rate greatly outperforms other classical methods like Markov chain Monte-Carlo based algorithms. Our quantum algorithm provides quadratic speedups to find both, the solution to particular instances of COPs, and the preparation of (quantum) Gibbs\' states.

I will present a new protocol that was developed entirely in the measurement-based model for quantum computation. Our protocol allows Alice to have Bob carry out a quantum computation for her such that Alice\'s inputs, outputs and computation remain perfectly private, and where Alice does not require any quantum computational power or memory. Alice only needs to be able to prepare single qubits from a finite set and send them to Bob, who has the balance of the required quantum computational resources. Our protocol is interactive: after the initial preparation of quantum states, Alice and Bob use two-way classical communication which enables Alice to drive the computation, giving single-qubit measurement instructions to Bob, depending on previous measurement outcomes. Our protocol is efficient and is presented for the special case of a classical-input, and classical-output; modifications allow the general case of quantum inputs and outputs. We also discuss the use of authentication in order for Alice to detect an uncooperative Bob. Based on joint work with Joseph Fitzsimons and Elham Kashefi

We consider the question of forward and backward translation between measurement-based quantum computing, called patterns, and quantum circuit computation. It is known that the class of patterns with a particular properties, having flow, is in one-to-one correspondence with quantum circuits. However we show that a more general class of patterns, those having generalised flow, will sometime translate to imaginary circuits, quantum circuits with time-like curves. Extending this approach, we first present the semantics of quantum circuits with time-like curves in terms of post-selection quantum computing and then characterise the class of curves with unitary or completely-positive semantic. Finally we present the re-write rules for opening the loops to transform an imaginary circuit to a normal circuit and discuss the connection between time-like curves and depth complexity.

I will talk about a scheme of the ground-code measurement-based quantum computer, which enjoys two major advantages. (i) Every logical qubit is encoded in the gapped degenerate ground subspace of a spin-1 chain with nearest-neighbor two-body interactions, so that it equips built-in robustness against noise. (ii) Computation is processed by single-spin measurements along multiple chains dynamically coupled on demand, so as to keep teleporting only logical information into a gap-protected ground state of the rest chains after the interactions with spins to be measured are adiabatically turned off. Our scheme is a conceptual advance, since measurements generally create excitations in the system so that two desired properties, keeping the information in the ground state and processing the information by measurements, are not seemingly compatible. I may shortly describe implementations using trapped atoms or polar molecules in an optical lattice, where the gap is expected to be as large as 0.2 KHz or 4.8 KHz respectively. This is a joint work with G.K. Brennen.

One-way quantum computing allows any quantum algorithm to be implemented by the sole use of single-qubit measurements. The difficult part is to create a universal resource state on which the measurements are made. We propose to use continuous-variable (CV) entanglement in the optical frequency comb of a single optical parametric oscillator with a multimode pump to produce a very large CV graph state with a special 4-regular graph. This scheme is interesting because of its potential for scalability, although issues of error correction and fault tolerance are yet to be fully addressed. Other possible physical configurations that are achievable with this scheme are related to the existence of certain bipartite edge-weighted graphs with circulant support having orthogonal adjacency matrices. If the above description fails to move you, don\'t worry, there will be pretty pictures. Joint work with N. Menicucci and O. Pfister, and with S. Severini