How to create a circuit with multiple qubits?

How to create a circuit with multiple qubits?

Create a quantum circuit that produces the Bell state: 1 √2 (|01⟩+|10⟩) 1 2 ( | 01 ⟩ + | 10 ⟩) . Use the statevector simulator to verify your result. The circuit you created in question 1 transforms the state |00⟩ | 00 ⟩ to 1 √2 (|01⟩+|10⟩) 1 2 ( | 01 ⟩ + | 10 ⟩), calculate the unitary of this circuit using Qiskit’s simulator.

What is the unitary matrix for two qubits?

In general, a unitary transformation on n n qubits is a matrix U U of size 2n ×2n 2 n × 2 n (so that it acts on vectors of size 2n 2 n ), such that U −1 = U † U − 1 = U † . For example, the CNOT (controlled-NOT) gate is a commonly used two-qubit gate and is represented by the following unitary matrix:

How is the quantum state of multiple qubits represented?

More generally, you can see that the quantum state of n n qubits is represented by a unit vector v1 ⊗v2 ⊗⋯⊗vn v 1 ⊗ v 2 ⊗ ⋯ ⊗ v n of dimension 2⋅2⋅2⋯ = 2n 2 ⋅ 2 ⋅ 2 ⋯ = 2 n using this construction. Just as with single qubits, the quantum state vector of multiple qubits holds all the information needed to describe the system’s behavior.

Where do qubits start in a Qiskit circuit?

First, we need to import all the tools we will need: In Qiskit, we use the QuantumCircuit object to store our circuits, this is essentially a list of the quantum operations on our circuit and the qubits they are applied to. In our quantum circuits, our qubits always start out in the state |0⟩ | 0 ⟩.

How to calculate the quantum Count of qubits?

This code implements the QFT on n qubits: Again, note we have chosen to return another QuantumCircuit object, this is so we can easily invert the gate. We create the gate with t = 4 qubits as this is the number of counting qubits we have chosen in this guide: We now have everything we need to complete our circuit! Let’s put it together.

How to calculate single qubit unitary in Qiskit?

We can see Qiskit has performed the tensor product: X⊗I = [0 I I 0] = ⎡ ⎢ ⎢ ⎢⎣0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0⎤ ⎥ ⎥ ⎥⎦ X ⊗ I = [ 0 I I 0] = [ 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0] Calculate the single qubit unitary ( U U) created by the sequence of gates: U = XZH U = X Z H. Use Qiskit’s unitary simulator to check your results.

How are multiple qubits and entangled states represented?

1. Representing Multi-Qubit States We saw that a single bit has two possible states, and a qubit state has two complex amplitudes. Similarly, two bits have four possible states: And to describe the state of two qubits requires four complex amplitudes. We store these amplitudes in a 4D-vector like so:

Can a qubit be 0 or 1 at the same time?

Like a normal bit, a qubit can be either 0 or 1, but unlike a normal bit, which can only be 0 or 1, a qubit can also be in a state where it is both at the same time. When extended to systems of many qubits, this ability to be in all possible binary states at the same time gives rise to the potential computational power of quantum computing.

Can a combined state be written as two separate qubits?

We can see this in Qiskit: This combined state cannot be written as two separate qubit states, which has interesting implications. Although our qubits are in superposition, measuring one will tell us the state of the other and collapse its superposition.

How are qubit control pulses generated in a microwave?

Convention- ally, qubit control pulses are generated by single-sideband modulation of a microwave carrier tone; accurate control of both the in-phase and quadrature pulse amplitudes allows arbitrary rotations on the Bloch sphere [5{8].

How does a SFQ pulse affect a qubit?

For typical parameters, SFQ pulse amplitudes are of or- der 1 mV and pulse durations are around 2 ps, roughly two orders of magnitude shorter than the typical qubit oscillation period. As a result, the SFQ pulse imparts a delta function-like kick to the qubit that induces a coher- ent rotation in the qubit subspace [15].

How is single flux used to control qubits?

An alternative approach involves irradiation of the qubits with trains of Single Flux Quantum (SFQ) pulses, pulses of voltage whose time integral is precisely equal to the superconducting ux quantum.

How are qubits stored in a Qiskit circuit?

In Qiskit, we use the QuantumCircuit object to store our circuits, this is essentially a list of the quantum operations on our circuit and the qubits they are applied to. In our quantum circuits, our qubits always start out in the state | 0⟩|0⟩. We can use the initialize () method to transform this into any state.

How many qubits are in a quantum gate?

Definition: A quantum gate is a unitary map where is at most 3, (recall, is the state space for 3 qubits). Now let’s see how to implement AND and OR for two qubits.

How is joint state represented in a quantum circuit?

Then we’ll define some basic quantum gates, and present the definition of a quantum circuit. In a classical system, if you have two bits with values , then the “joint state” of the two bits is given by the concatenated string . But if we have two qubits , which are vectors in , how do we represent their joint state?

How to show that a two qubit state is an entangled state?

A two-qubit state | ψ ⟩ ∈ C 4 is an entangled state if and only if there not exist two one-qubit states | a ⟩ = α | 0 ⟩ + β | 1 ⟩ ∈ C 2 and | b ⟩ = γ | 0 ⟩ + λ | 1 ⟩ ∈ C 2 such that | a ⟩ ⊗ | b ⟩ = | ψ ⟩, where ⊗ denotes the tensor product and α, β, γ, λ ∈ C.

How to represent the state of a qubit?

Either the qubit definitely outputs a 0, or it definitely outputs a 1. There is no overlap. One way to represent this with mathematics is to use two orthogonal vectors. |0⟩ = [1 0] |1⟩= [0 1]. | 0 ⟩ = [ 1 0] | 1 ⟩ = [ 0 1]. This is a lot of notation to take in all at once.

Why are quantum computers difficult to simulate with large numbers of qubits?

If we have n n qubits, we will need to keep track of 2n 2 n complex amplitudes. As we can see, these vectors grow exponentially with the number of qubits. This is the reason quantum computers with large numbers of qubits are so difficult to simulate.

Which is an entangled state of a qubit?

This state is very interesting to us, because it is entangled. This leads us neatly on to the next section. We saw in the previous section we could create the state: This is known as a Bell state. We can see that this state has 50% probability of being measured in the state |00⟩ | 00 ⟩, and 50% chance of being measured in the state |11⟩ | 11 ⟩.

How many possible states does a qubit have?

We saw that a single bit has two possible states, and a qubit state has two complex amplitudes. Similarly, two bits have four possible states: 00 01 10 11 And to describe the state of two qubits requires four complex amplitudes.