# Tag Info

### Why can quantum walks not approach a stationary distribution

Suppose for contradiction that there is some limiting state $|f\rangle$ that an initial state $|s_1\rangle \neq |f\rangle$ approaches as a unitary operation $U$ is repeatedly applied. So there is ...
• 28.6k
Accepted

### Quantum simulation of environment-assisted quantum walks in photosynthetic energy transfer

One major idea there seems to be that the "environment" (quantum decoherence) assists or optimizes the transport of a signal The idea that photosynthetic systems are doing a Grover search or ...
• 12.7k

### Why can quantum walks not approach a stationary distribution

That's an interesting point and I suppose reversibility, interpreted as bijectivity, is not enough. But unitarity implies a lot more. More specifically, unitary operators preserve distance. So we can ...
• 1,752
Accepted

• 13.1k
1 vote

### Use of Position Hilbert Space in Quantum Walk

Now, my question is what is the use of above representation, if all the operation are defined on initial state. This means very little. Like in any kind of dynamics, you start with an initial state ...
• 21.2k
1 vote

### Why, in a discrete-time quantum walk,we first apply the tensor product of the coin operation with the identity?

The idea is that by applying Hadamard just to the coin and doing nothing to the position state, this is the equivalent of tossing the coin. To see this in a very crude way, imagine applying Hadamard ...
• 51k
1 vote

### Why, in a discrete-time quantum walk,we first apply the tensor product of the coin operation with the identity?

A (discrete-time) quantum walk can be thought of as the direct "quantization" of a classical random walk. In a classical random walk, at each iteration, you flip a coin and move the walker ...
• 21.2k

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