# Questions tagged [quantum-state]

Quantum systems can mathematically be described by their 'quantum state'. When the system is closed/isolated, the state is 'pure' and can be written as a sum (i.e. 'superposition') of basis vectors. When the system is a subsystem of an open system, the state is instead usually 'mixed' and cannot be written as a pure state, so has to be written as a density matrix. Consider using the density-matrix tag when relevant

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### What is the IQ plane?

I struggle to find any information on Nielsen and Chuang or similar texts on the exact definition of the so-called IQ plane (I think this is a notion closely related to solid state quantum computers ...
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### Is Grover's algorithm suitable for this search problem?

I wonder if we can utilize Grover's algorithm to solve the following search problem. Leetcode 33. Search in Rotated Sorted Array Example 1: Input: nums = [4,5,6,7,0,1,2], target = 0 Output: true ...
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### Quantum hardness of XQUATH conjecture

Consider the XQUATH conjectures, as defined here (https://arxiv.org/abs/1910.12085, Definition 1). (XQUATH, or Linear Cross-Entropy Quantum Threshold Assumption). There is no polynomial-time ...
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### Can we use space to achieve absolute zero for a quantum computer?

Why can't we use space to maintain absolute zero temperature required by the qubit chips and connect it to a satellite to perform computations?
For any linear operator $A$, the support of $A$ is the orthogonal complement of its kernel. Hence when we say, $supp(A)\subset supp(B)$, we have that for any vector $v$ in the kernel of $B$ i.e. $Bv = ... 1answer 70 views ### Minimal output dimension of a quantum channel Consider quantum channels$\Phi : M_n \rightarrow M_{d_1}$and$\Psi : M_n \rightarrow M_{d_2}$with$d_1\leq d_2$. We say that$\Phi$is isometrically extended by$\Psi$(denoted$\Phi \leq_{\text{...
Consider a quantum channel $\Phi : M_n \rightarrow M_m$ and let $\frac{\mathbb{I}_n}{n}$ be the maximally mixed input state. For all input states $\rho\in M_n$, is it true that \quad \text{rank} \, \...