Related papers: Lower bounds on the non-Clifford resources for qua…
Given a pure state transformation $\psi\mapsto\phi$ restricted to entanglement-assisted local operations with classical communication, we determine a lower bound for the dimension of a catalyst allowing that transformation. Our bound is…
Quantum error correction is the art of protecting fragile quantum information through suitable encoding and active interventions. After encoding $k$ logical qubits into $n>k$ physical qubits using a stabilizer code, this amounts to…
Measurement-based quantum computing enables universal quantum computing with only adaptive single-qubit measurements on certain many-qubit states, such as the graph state, the Affleck-Kennedy-Lieb-Tasaki (AKLT) state, and several…
Quantum error correction and fault-tolerance have provided the possibility for large scale quantum computations without a detrimental loss of quantum information. A very natural class of gates for fault-tolerant quantum computation is the…
Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
Measuring the closest distance between two states is an alternative and significant approach in the resource quantification, which is the core task in the resource theory. Quite limited progress has been made for this approach even in…
Given a finite dimensional pure state transformation restricted by entanglement assisted local operations and classical communication (ELOCC), we derive minimum and maximum bounds on the entanglement of an ancillary catalyst that allows…
There are various physical scenarios in which one can only implement operations with a certain symmetry. Under such restriction, a system in a symmetry-breaking state can be used as a catalyst, e.g. to prepare another system in a desired…
Quantum entanglement and quantum nonstabilizerness are fundamental resources that characterize distinct aspects of a quantum state: entanglement reflects non-local correlations, while nonstabilizerness quantifies the deviation from…
We derive an upper bound for the time needed to implement a generic unitary transformation in a $d$ dimensional quantum system using $d$ control fields. We show that given the ability to control the diagonal elements of the Hamiltonian,…
Efficient constructions for quantum logic are essential since quantum computation is experimentally challenging. This thesis develops quantum logic synthesis as a paradigm for reducing the resource overhead in fault-tolerant quantum…
We study the complexity of learning quantum states in various models with respect to the stabilizer formalism and obtain the following results: - We prove that $\Omega(n)$ $T$-gates are necessary for any Clifford+$T$ circuit to prepare…
We develop a procedure for distilling magic states used in universal quantum computing that requires substantially fewer initial resources than prior schemes. Our distillation circuit is based on a family of concatenated quantum codes that…
In this paper we estimate the fidelity of stabilizer and CSS codes. First, we derive a lower bound on the fidelity of a stabilizer code via its quantum enumerator. Next, we find the average quantum enumerators of the ensembles of finite…
Random quantum states have various applications in quantum information science. We discover a new ensemble of quantum states that serve as an $\epsilon$-approximate state $t$-design while possessing extremely low entanglement, magic, and…
Manipulation and quantification of quantum resources are fundamental problems in quantum physics. In the asymptotic limit, coherence distillation and dilution have been proposed by manipulating infinite identical copies of states. In the…
The performance of quantum resource manipulation protocols, including key examples such as distillation of quantum entanglement, is measured in terms of the rate at which desired target states can be produced from a given noisy state.…
The adiabatic theorem provides sufficient conditions for the time needed to prepare a target ground state. While it is possible to prepare a target state much faster with more general quantum annealing protocols, rigorous results beyond the…
Catalysis refers to the possibility of enabling otherwise inaccessible quantum state transitions by supplying an auxiliary system, provided that the auxiliary is returned to its initial state at the end of the protocol. We show that…
Many proposals for fault-tolerant quantum computation require injection of 'magic states' to achieve a universal set of operations. Some qubit states are above a threshold fidelity, allowing them to be converted into magic states via 'magic…