6 votes
Accepted

Is 216 qumodes photonic quantum processor equivalent to 216 qubits superconducting quantum processor, in terms of computational power?

My name is Isaac and I work at Xanadu. That’s a really good question! Generally speaking, you can argue that 216 qumodes are more powerful than 216 superconducting (SC) qubits since qumodes encode ...
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  • 76
5 votes

Is there a quantum gate that can turn any superposition $|\varphi \rangle $ into a unit column vector $|00\cdots 1\cdots 0\rangle $

It depends on what you mean. For a given state $|\varphi\rangle$, it is always possible to find a gate $U_\varphi$ such that $U_\varphi|\varphi\rangle=|i\rangle_{10}$ for some given $i$. However, it ...
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4 votes

Are the SDG and TDG gates hermitian?

A matrix $A$ is a Hermitian if and only if $$ A = A^\dagger$$ So if $A^\dagger$ is Hermitian then that means $A^\dagger = (A^\dagger)^\dagger = A$ and so of course $A$ is hermitian. By the way, by ...
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  • 12.5k
4 votes

Finite subgroup of $U(4)$ containing a non-Clifford gate and all local Cliffords

This partial answer places additional restrictions on $U$. Constructing unitaries with infinite order By KAK decomposition, $U$ can be written as $$ U=(A_1\otimes A_0)e^{i\alpha X\otimes X + i\beta Y\...
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  • 13.5k
4 votes

Definitions of a quantum circuit's depth and connectivity

The traditional definitions of classical Boolean circuits work perfectly well here: https://en.wikipedia.org/wiki/Boolean_circuit. This is the definition that gives you Niel de Beaudrap's definition. ...
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  • 1,661
4 votes
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Is there a name for a gate that 'moves' one qubit to a new position via multiple SWAP gates?

Note that the first SWAP places qubit $i+1$ at position $i$. The second one places qubit $i+2$ at position $i+1$. Eventually, the qubit number $k$ will be at place $k-1$ for $k>i$, while qubit $i$ ...
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4 votes

Non-universal gate sets

Yes, there are other cases. Superposition and entanglement The proposed rule $$ \text{if $U$ has an element $U_{ij}$ such that $|U_{ij}|\notin\{0,1\}$},\\ \text{then the set $\{T,U\}$ is universal}\...
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2 votes
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what's the point of the first barrier in this circuit?

Correct, quoting What is a "barrier" in Qiskit Circuits?: The barrier acts as a directive for circuit compilation to separate pieces of a circuit so that any optimizations or re-writes are ...
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  • 1,833
2 votes
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Can someone explain to me what is T gate and tdg like im five?

tdg is the method used to apply $T^\dagger$ (read T dagger). Thus, there are no differences between these two. For a quantum gate $U$, $U^\dagger$ is the inverse of ...
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2 votes
Accepted

Quantum gates with 1 qubit output

Indeed, it is useful to consider these types of situations. Sometimes we might measure a qubit and throw it away, leaving us one less qubit than before in our system. The issue you bring up is, what ...
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  • 332
2 votes

How can I write if conditions on quantum registers using qiskit

If "some operations" in your question means quantum operations, then you can use Gate.c_if() to apply a gate based on a value in a classical register as ...
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2 votes

Definitions of a quantum circuit's depth and connectivity

Let me try to provide a more precise definition of connectivity in a quantum circuit. Every quantum circuit defines a graph (network), with vertices (nodes) given by qubits. There is an edge $q_1 q_2$ ...
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  • 332
2 votes

How does a Hadamard gate impact the initial/previous values of a Qubit?

I think you might just be misunderstanding the Hadamard gate slightly. In the computational basis, $H= \frac{1}{\sqrt{2}}\begin{pmatrix} 1 & 1 \\ 1 & -1\end{pmatrix}$ maps $|0\rangle \...
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  • 226
2 votes

Is there a general way to parametrize 2-qubit unitaries?

There is some parametrized matrix form for a 2-qubit unitary, but it would be extremely inconvenient to work with. An $n$-qubit gate is an element of the group $SU(2^n)$, which has dimension $2^{2n} - ...
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  • 393
1 vote

Is there a general way to parametrize 2-qubit unitaries?

What I propose here could possibly be simplified further, but that's at least a first direction. First, any unitary can be written as $U=e^{-it/\hbar \widetilde{H}}$ for some $t$ and $\widetilde{H}$ (...
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1 vote

Finite subgroup of $U(4)$ containing a non-Clifford gate and all local Cliffords

Here's an example for the real Pauli and Clifford groups : $$P_1=<X_1,Z_1>; |P_1|=8;$$ $$P_2=<X_1,Z_1,X_2,Z_2>; |P_2|=32;$$ $$C_1=<X_1,Z_1,H_1>; |C_1|=16;$$ $$C_1^{\otimes 2}=<X_1,...
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  • 910
1 vote
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Definitions of a quantum circuit's depth and connectivity

I would like to give explicit definitions of the circuit depth and connectivity. I assume that the meaning of terms like vector state, quantum circuit, wires, and 1- and 2-qubit gates is understood. I'...
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  • 196
1 vote
Accepted

Speed of Superconducting Qubit Architectures

Google's Sycamore processor for which they claimed quantum supremacy (https://doi.org/10.1038/s41586-019-1666-5) performs two-qubit operations in 12 ns, so that would be some 80 MHz. Of course ...
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  • 161
1 vote

How to write a code to separate two qubits?

Maybe it should be useful tu use qutip to better understand what you desire (if you are familiar with python) by visualizing exactly the 2 qubits and its state vectors (which I believe is what you ...
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1 vote

Is there a gate sending $|0\rangle^{\otimes n}$ to a state where some amplitudes are zero?

you can check out qiskit textbook, https://qiskit.org/textbook/ch-gates/phase-kickback.html https://qiskit.org/textbook/ch-quantum-hardware/density-matrix.html#5.-Mixed-States-in-the-Bloch-Sphere-- ...
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  • 423
1 vote

Is digital quantum computing more powerful than the analog one?

As someone else said, you're right depending on how you define "analog quantum computing" because it's a bit of an overloaded term. Quantum annealers work by slowly changing a Hamiltonian ...
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