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More efficient implementation of $4$-qubit gate

While working on an error detection algorithm, I stumbled upon the problem of simplifying the following implementation Here, the $S$ gate is defined by $$S=\left( \begin{array}{cc} \frac{\sqrt{3}}{2} & -\frac{1}{2} e^{\frac{i \pi }{3}} \\ …
QC_QAOA
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What matrix operations have better known time complexity on a quantum computer?

I'm exploring quantum computers for a semester project. I'm mainly interested in making faster matrix calculations than a regular computer. I was wondering what arithmetic operations (irrespective of how simple or complex they are) are faster on a…
adiboi
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Does the no-hiding theorem suggest that quantum information is never destroyed?

According to Wikipedia: The no-hiding theorem proves that if information is lost from a system via decoherence, then it moves to the subspace of the environment and it cannot remain in the correlation between the system and the environment. This is…
Nick ODell
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Q# Simulation Behavior

I am attempting to run a series of tests on a Q# program I'm running on the local simulator, but I'm not seeing any way to use >1 shot and collect the results of those shots at once, as in essentially every other quantum language/system I've seen.…
Xavier McCaig
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Why can I not apply a control gate/function to a gate like T, S, S dagger, ... (using IBM Quantum Experience)? Is there another option?

I am trying to use the circuit composer of the IBM QE. I am doing the inverse QFT on 3 qubits and therefore need a control on T and S dagger gates, but it won't let me. Does anyone know why or know a way around it? I've been stuck on this for a…
Natasha
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Topology graphs of IBM's quantum computers

What is the meaning of the topology graphs of IBM's quantum computers? How should it be interpreted? For example, how should I understand the following graph?
AL_P
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Do there exist problems known to be computationally intractable for quantum computer, but tractable for classical computer?

Or alternatively phrased, is it believed that the complexity class P is a complete subset of BQP? Consider the following diagram à la MIT OpenCourseWare, which seems to explicitly state as much.
Eoin Dowling
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What makes representing qubits in a 3D real vector space possible?

Qubits exist in a 2D complex vector space, but we can represent qubits on the Bloch sphere as a 3D real vector space. Mathematically, what makes this possible – why don't we need 4 real dimensions?
Marc Bacvanski
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Run VQE for parametrized quantum circuit with ancilla qubits

Let's say we have the following circuit (picture and code shown below), and now the $q_0$ is an ancilla qubit. If the system of interest has only two qubits, Is there a way to use only $q_{1,2}$ as my ansatz and plug it into the built-in VQE in…
fagd
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Positive semidefinite relationship after partial trace

Let $\rho_{ABC}$ and $\sigma_{C}$ be arbitrary quantum states and $\lambda\in \mathbb{R}$ be minimal such that $$\rho_{ABC}\leq \lambda \rho_{AB}\otimes\sigma_C$$ We assume there are no issues with support in the above statement to avoid infinities.…
JRT
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Is Gaussian boson sampling (used for showing quantum advantage) a subcategory of the continuous variable approach?

I read about the photonic QC Jiŭzhāng that showed quantum advantage by Gaussian boson sampling. I read that boson sampling itself is a sub-universal technique of QC (where they use single-photon states as input states). In the paper, the scientists…
ile2N
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What is the matrix for a SWAP operation on two qubits?

Say we want to swap qubits $a$, $b$ in the same register, where $a,b \in \left \{ 0, 1,\cdots, n-1 \right \}$. What would be the corresponding matrix. For those interested, I'm curious about this matrix because I'm implementing the QFT, which by…
LPenguin
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Get state vector of a single qubit in a circuit in Qiskit

I have two quantum circuits, and I would like to compare state vector of the first qubit and check if equals, what is the best way to do that in qiskit ? Let's say I have : psi = QuantumCircuit(5) psi.ry(np.pi/4.,0) psi.x(0) psi.x(1) psi2 =…
user12910
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Qubit Connectivity of IBM Quantum Computer

When simulating a quantum circuit using the qiskit qasm_simulator, the qubits that you assign to the quantum circuit may be connected to all other qubits. In other words, if there are $n$ qubits in the quantum circuit, a single qubit can interact…
Yitian Wang
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Decomposing gates resembling exponentiated members of desired gateset

Suppose I have access to a pretty typical gate set, for example $\{\text{CNOT}, \text{SWAP}, \text{R}_{x}, \text{R}_{y}, \text{R}_{z}, \text{CR}_x, \text{CR}_y, \text{CR}_z\}$ where $\text{CR}$ is a controlled single-qubit rotation. I'm curious…
forky40
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