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Consider two noisy quantum channels (CPTP maps), $\Phi_1^A$ and $\Phi_2^A$, acting on a system $A$. Suppose that for any pure state $\left|\psi\right>\in \mathcal H_A$, $$F\big(\psi, \Phi_1^A(\psi)... 15 votes 0 answers 305 views ### Reference that explains how to read 3d topological diagrams for surface code computations I like making diagrams to describe computations. For the surface code, an excellent tool is 3d topological diagrams. Here is an example diagram (made by me in SketchUp): The basic idea is that white ... 13 votes 0 answers 224 views ### Does the Curry-Howard correspondence have a quantum-specific type system? In Wikipedia we can read that the Curry–Howard correspondence is a correspondence between formal proof calculi and type systems for models of computation. In particular, it splits into two ... 12 votes 0 answers 224 views ### Are all quantum algorithms hidden subgroup algorithms? I am reading the paper "Quantum Hidden Subgroup Algorithms: An Algorithmic Toolkit" by Samuel Lomonaco and Louis Kauffman from the book, "Mathematics of Quantum Computation and Quantum ... 12 votes 0 answers 335 views ### Relation between quantum entanglement and quantum state complexity Both quantum entanglement and quantum state complexity are important in quantum information processing. They are usually highly correlated, i.e., roughly a state with a higher entanglement corresponds ... 12 votes 0 answers 98 views ### Active improving of nanodiamond surfaces for NV centers? This question is related (and complementary) to "Passive improving of nanodiamond surfaces for NV centers?". Nitrogen-Vacancy centers (NVs) have astonishing quantum properties, which make them ... 11 votes 0 answers 174 views ### Status of hidden shift and hidden subgroup problems We know that solving a hidden subgroup problem over a non-commutative group is a long standing problem in quantum computing even for groups like D_{2n} (alternatively can be written as \mathbb{Z}_n ... 11 votes 0 answers 170 views ### Estimate/determine Bures separability probabilities making use of corresponding Hilbert-Schmidt probabilities For two-qubit states, represented by a 4\times 4 density matrix, the generic state is described by 15 real parameters. For ease of calculation, it can help to consider restricted families of states, ... 10 votes 0 answers 241 views ### What is stopping FACTORING from being BQP-complete? Classical complexity theory makes much of the study of so-called intermediate problems - that is, problems that are in \mathsf{NP} but are nonetheless not known to be in \mathsf{P} and further not ... 10 votes 0 answers 199 views ### Is HHL still BQP-complete when the matrix entries are only in {0,1}? I'm studying BQP-completeness proofs of a number of interesting problems of Janzing and Wocjan, and Wocjan and Zhang. Janzing and Wocjan show that estimating entries of matrix powers (A^m)_{ij} with ... 10 votes 0 answers 78 views ### Strong vs weak simulations and the polynomial hierarchy collapse (Edited to make the argument and the question more precise) An argument for quantum computational "supremacy" (specifically in Bremner et al. and the Google paper) assumes that there exists a ... 10 votes 0 answers 126 views ### Anti-symmetrization on the lattice Assume, I'm using a system of qubits to simulate a fermionic system. If I'm using the second-quantized formalism (e.g. orbitals in quantum chemistry), the anti-symmetric nature of the fermionic wave ... 10 votes 0 answers 171 views ### Entanglement transfer of spin-entangled triplet-pair states between flying qubits and stationary qubits The context: We are in the solid state. After a photon absortion by a system with a singlet ground state, the system undergoes the spin-conserving fission of one spin singlet exciton into two spin ... 9 votes 0 answers 123 views ### Calculate the period (like in Shor's algorithm) from the factors? One of the fundamental elements of Shor's algorithm is the calculation of the function:$$ f_a(r) = a^r (mod \ N)  where $N$ is the number to be factored and $a$ is a number chosen with some ...
Introduction Consider a state $\vert\psi\rangle$ such as below, which is in a superposition of a difference between a Rubik's cube in a solved state and a Rubik's cube in the "superflip" ...