| Time | Speaker | Title |
| 10:00-10:30 | Morning Coffee |
| 10:30-11:30 | Mehdi Mhalla | "Finding optimal flows efficiently" |
| | Since a One-way QC is based on quantum measurement, which is a fundamentally nondeterministic evolution, a suffiicient condition of global determinism has been introduced as the existence of a causal flow in a graph that underlies the computation. We introduce a O(m)-algorithm for finding a causal flow (where m is the number of edges of the graph), if any, whatever the numbers of input and output vertices are. This answers the open question stated by Danos and Kashefi and by de Beaudrap . Moreover, we prove that our algorithm produces a flow of minimal depth.
Whereas the existence of a causal flow is a suffiicient condition for determinism, it is not a necessary condition. A weaker version of the causal fllow, called gfllow (generalised flow) has been introduced and has been proved to be a necessary and suffiicient condition for a family of deterministic computations. Moreover the depth of the quantum computation is upper bounded by the depth of the gflow. We provide here a polynomial time algorithm that outputs an optimal gfllow of a given graph and thus finds an optimal correction strategy to the nondeterministic evolution due to measurements.
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| 11:30-12:00 | Mio Murao | "Authorized Quantum computation based on gate shuffling" |
| | We present authorized quantum computation, where only a user with a non-cloneable quantum authorization key can perform a unitary operation created by an authenticated programmer. The security of our authorized quantum computation is based on the quantum computational complexity problem of forging the keys from an obfuscated quantum gate sequence based on gate shuffling. Under the assumption of the existence of a sufficiently-random gate shuffling algorithm, the problem is shown to be in the NQP (Non-deterministic Quantum Polynomial)-hard class by reducing it to a NQP-Complete problem, the exact non-identity check problem.
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| 12:30-13:30 | LUNCH |
| 13:30-14:30 | Elham Kashefi | "Twisted graph states for ancilla-driven universal quantum computation" |
| | E. Kashefi, D. K. L. Oi, D. Browne, J. Anders, E. Andersson
We introduce a new paradigm for quantum computing called Ancilla-Driven Quantum Computation (ADQC) which combines aspects both of the quantum circuit and the one-way model to overcome challenging issues in building large-scale quantum computers. Instead of directly manipulating each qubit to perform universal quantum logic gates or measurements, ADQC uses a fixed two-qubit interaction to couple the memory register of a quantum computer to an ancilla qubit. By measuring the ancilla, the measurement-induced back-action on the system performs the desired logical operations.
The underlying mathematical model is based on a new entanglement resource called generated from non-commuting operators, leading to a surprisingly powerful structure for parallel computation compared to graph states obtained from commuting generators. The ADQC model is formalised in an algebraic framework similar to the Measurement Calculus. Furthermore, we present the notion of causal flow for twisted graph states, based on the stabiliser formalism, to characterise the determinism. Finally we demonstrate compositional embedding between ADQC and both the one-way and circuit models which will allow us to transfer recently developed theory and toolkits of measurement-based quantum computing and quantum circuit models directly into ADQC.
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| 14:30-15:00 | Atsushi Tanaka | "Cheon's eigenvalue and eigenspace holonomies" |
| | An adiabatic change of a bound state along a loop in a parameter space can induces holonomies not only in the phase of the state, but also in associated eigenspace and eigenvalue. The former is known as the Berry phase and the latter is found a decade ago by Cheon. I will explain our recent result on Cheon's exotic holonomies. (1) Examples in finite-dimensional unitary matrices; (2) A unified theory for the phase and the eigenspace holonomies; (3) Degeneracies hidden in the complexified parameter space behind Cheon's holonomies. These are based on collaborations with M. Miyamoto (Waseda), T. Cheon (Kochi UT), and S.W. Kim (Pusan NU).
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| 15:00-15:30 | Afternoon Coffee |
| 15:30-16:00 | Toshio Oshima | "The single step quantum computer" |
| | It is widely believed that quantum computers need numerous
computational steps to perform a single quantum algorithm, e.g. factoring.
However, surprisingly, only a single step suffices for this purpose. I will
explain this new concept based on spin networks.
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| 16:00-17:00 | Damian Markham | "Stabiliser state quantum information in continuous variables" |
| | We present the continuous variable anaology to stabiliser states as developed by van Loock et al, and some examples of their use in quantum information. These states are defined with respect to a stabiliser group which and satisfy many analogous properties to the discrete case. For example, the analogy to clifford operators are the gaussian operations in CV and various similar no-go theorems hold. We focus on their use for secret sharing protocols.
*This talk is about some work with Peter.
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