相关论文: Qutrit ZX-calculus is Complete for Stabilizer Quan…
We demonstrate that it is possible to construct operators that stabilize the constraint-satisfying subspaces of computational problems in their Ising representations. We provide an explicit recipe to construct unitaries and associated…
Entanglement types of pure states of 3 qubits are classified by means of their stabilisers in the group of local unitary operations. It is shown that the stabiliser is generically discrete, and that a larger stabiliser indicates a…
We present a comprehensive and self-contained framework for the efficient classical simulation of Clifford circuits acting on $d$-dimensional qudits, including realistic Pauli/Weyl noise via stochastic simulation. Our approach uses the…
Efficient methods for the representation and simulation of quantum states and quantum operations are crucial for the optimization of quantum circuits. Decision diagrams (DDs), a well-studied data structure originally used to represent…
We study single-copy stabilizer learning, the problem of identifying a stabilizer group of dimension $n-t$ from an $n$-qubit quantum state $\rho$. We obtain two complementary results. First, in the average case, logarithmic-depth local…
We study the non-stabilizer resources required to achieve informational completeness in single-setting quantum state estimation scenarios. We consider fixed-basis projective measurements preceded by quantum circuits acting on $n$-qubit…
Large-scale quantum computation is likely to require massive quantum error correction (QEC). QEC codes and circuits are described via the stabilizer formalism, which represents stabilizer states by keeping track of the operators that…
Unitary t-designs are some of the most versatile tools in quantum information theory. Their applications range from randomized benchmarking and shadow tomography, to more fundamental ones such as emulating quantum chaos and establishing…
A quantum circuit may be strongly classically simulated with the aid of ZX-calculus by decomposing its $t$ T-gates into a sum of $2^{\alpha t}$ classically computable stabiliser terms. In this paper, we introduce a general procedure to find…
Conventional quantum mechanical qubits can be lifted to states as even three dimensional geometric algebra operators that act on observables. The operators may be implemented via the two types of Maxwell equation solution polarizations.…
We investigate the notion of uncertainty region using the variance based sum uncertainty relation for qubits and qutrits.We compare uncertainty region of the qubit (a 2-level system) with that of the qutrit (3-level system) by considering…
Quantum error-correcting codes can be used to protect qubits involved in quantum computation. This requires that logical operators acting on protected qubits be translated to physical operators (circuits) acting on physical quantum states.…
This paper defines coherent manifolds and discusses their properties and their application in quantum mechanics. Every coherent manifold with a large group of symmetries gives rise to a Hilbert space, the completed quantum space of $Z$,…
In this paper we investigate stabilizer quantum error correction codes using controlled phase rotations of strong coherent probe states. We explicitly describe two methods to measure the Pauli operators which generate the stabilizer group…
We develop a unified geometric framework for quantum circuit compilation based on quantized orbifold phases and their diagrammatic semantics. Physical qubit platforms impose heterogeneous phase resolutions, anisotropic Bloch-ball…
Verification of NISQ era quantum devices demands fast classical simulation of large noisy quantum circuits. We present an algorithm based on the stabilizer formalism that can efficiently simulate noisy stabilizer circuits. Additionally, the…
We use multidimensional circulant approach to construct new qutrit stabilizer $\dsb{\ell, 0, d}$ codes with parameters $(\ell, d) \in \{(51, 16), (52, 16), (54, 17), (55, 17), (57, 17)\}$ through symplectic self-dual additive codes over…
This paper explores the representation of quantum computing in terms of unitary reflections (unitary transformations that leave invariant a hyperplane of a vector space). The symmetries of qubit systems are found to be supported by…
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…
Quantum computers have steadily improved over the last decade, but developing fault-tolerant quantum computing (FTQC) techniques, required for useful, universal computation remains an ongoing effort. Key elements of FTQC such as…