So try to get familiar to this labeling.I want to write the matrix form of a single or two qubit gate in the tensor product vector space of a many qubit system. Putting together all the examples shown in previous section, the labels on the coordinate left side can be renamed as shown on right ? In many technical document about Bloch Sphere uses the labels shown on right. In many documents, you would see this function is represented to be |-i> for simplicity. If you plug these values into Bloch sphere state function you will get the function with the same proability of |0> and |1>, but the probability of |1> is imaginary number as shown below. ![]() In spherical coordinate, this point is where theta = pi/2 and phi = pi. It will flip the components for 0> and 1> (exchanging their probabilities). X gate X, or bit-flip, is another simple gate. Now Let's take the point on the circumference that crosses the -y axis. Just put in a single qubit a H-gate and measure it. Using CryptoCompares mining calculator, we find out that a device with 108 H/s can. How to calculate the depth of a quantum circuit in Qiskit The depth of a circuit is a metric that calculates the longest path between the data input and the output. In many documents, you would see this function is represented to be |+i> for simplicity. MiSTer uses field-programmable gate array (FPGA) technology to. Now Let's take the point on the circumference that crosses the +y axis. In many documents, you would see this function is represented to be |-> for simplicity. If you plug these values into Bloch sphere state function you will get the function with the same proability of |0> and |1> as shown below. In spherical coordinate, this point is where theta = pi/2 and phi = pi. Now Let's take the point on the circumference that crosses the -x axis. In many documents, you would see this function is represented to be |+> for simplicity. In spherical coordinate, this point is where theta = pi/2 and phi = 0. Now Let's take the point on the circumference that crosses the -z axis. Init: 0, 0, 0, 0, 0 For each gate in sequence (consistent with the input/output dependencies of the gates), take the maximum depth d to that point on. Initialise the depth ending at each qubit to 0. If you plug these values into Bloch sphere state function you will get |1> as shown below. Here is how you can compute the circuit depth, adding one gate at a time, to compute the length of the longest path that ends at a given qubit. A quantum gate is an operation applied to a qubit that changes the quantum state of. In spherical coordinate, this point is where theta = pi and phi = 0. An algorithm is a step-by-step procedure to perform a calculation. If you plug these values into Bloch sphere state function you will get |0> as shown below. It allows us to move away from the poles of the Bloch sphere and create a superposition of 0 0 and 1 1. In spherical coordinate, this point is where theta = 0 and phi = 0. The Hadamard gate (H-gate) is a fundamental quantum gate. Let's take the point on the circumference that crosses the +z axis. Now for practice, let's think of some of the important points in the coordinate and how it is expressed in state function. Here you would notice that the probability of |1> can be expressed in complex number. The probability of |0> and |1> (alpha and beta) is transformed into a little bit complicated form in Bloch sphere as shown below. In case not familiar with Euler form of the equation and for easy calculation, we can rewrite the above formula as the equation shown below.Įven though the qbit state function on Bloch sphere looks a little bit complicated, it is still in the form of probability for two qbit state |0> and |1>. ![]() The qbit state function in the Bloch Sphere is defined as follows. As you know, Spherical Coordinates is a system defined by R (radius), theta and phi. Simply put, Bloch Sphere is a way to respresent a qbit states in a 3D spherical coordinates.
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