Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

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Shortest sequence of universal quantum gates that correspond to a given unitary

Question: Given a unitary matrix acting on $n$ qubits, can we find the shortest sequence of Clifford + T gates that correspond to that unitary? For background on the question, two important references: Fast and efficient exact synthesis of single…
user120404
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What is the status of quantum computing compared with other (photonic) quantum technologies?

There is a number of emerging quantum technologies, among which we find the category of photon-based quantum technologies, including quantum key distribution or quantum random number generators. The question is: what is the short-term viability of…
agaitaarino
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How to keep track of entanglements when emulating quantum computation?

I am trying to build a quantum computation library as my university project. I am still learning all the aspects of the Quantum Computing field. I know there are efficient libraries already for quantum emulation. I just want to make my own, which…
Midhun XDA
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In Grover's Algorithm, why does the optimal number of iterations involve a floor?

On page 157 of Kaye, Laflamme and Mosca they write that in Grover's algorithm we need to apply Grover's iterate a total of: $$\Big\lfloor \frac{\pi}{4} \sqrt{N}\Big\rfloor$$ (They actually wrote $\Big\lfloor \frac{\pi}{4}…
Quantum spaghettification
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What is the difference between a qubit and a quantum state?

In general, a qubit is mathematically represented as a quantum state of the form $\lvert \psi\rangle = \alpha \lvert 0\rangle + \beta \lvert 1\rangle$, using the basis $\{ \lvert 0\rangle, \lvert 1\rangle \}$. It seems to me that a qubit is just a…
user72
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What happens if two separately entangled qubits are passed through a C-NOT gate?

Suppose I transform a state as follows: I start with the state $\lvert 0\rangle \otimes \lvert0\rangle \otimes \lvert0\rangle \otimes \lvert 0 \rangle$. I entangle the 1st and 2nd qubits (with an H gate and C-NOT). I then then entangle the 3rd and…
Midhun XDA
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Is there an intuitive way to conceptualize the ground and excited states of a transmon qubit?

I understand how a transmon qubit is analogous to an LC circuit, but has an anharmonic energy spectrum due to the nonlinearity of the Josephson junction. I also understand how to write out the Hamiltonian and the significance of the contributing…
taryn3194
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Is BQP only about time? Is this meaningful?

The complexity class BQP (bounded-error quantum polynomial time) seems to be defined only considering the time factor. Is this always meaningful? Do algorithms exist where computational time scales polynomially with the input size but other…
Daniel Tordera
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How efficient is Qiskit's unitary decomposition?

In Qiskit's extension package we have the UnitaryGate module that you can initialize using a unitary matrix and then add it to your circuit. How efficiently is this decomposition done under the hood? Also, if I wanted to do the decomposition myself,…
Dani007
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How do you apply a CNOT on polarization qubits?

I read that a qubit can be encoded in a polarization state (horizontal or vertical polarization of a photon). How do you perform two-qubit operations on a polarization qubit?
Daniel Tordera
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Understanding the $M$ upper bound in the paper: "Multipartite entanglement and high-precision metrology"

This paper is a paper in 2012 and cited by a lot of papers. And there does not exist comment in arxiv or error statement in PRA. But when I reading this paper, I think the right part of the eq(23) should be $2M+(N-M)(N-M+2)$ instead of…
narip
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Entanglement transfer of spin-entangled triplet-pair states between flying qubits and stationary qubits

The context: We are in the solid state. After a photon absortion by a system with a singlet ground state, the system undergoes the spin-conserving fission of one spin singlet exciton into two spin triplet excitons (for context, see The entangled…
agaitaarino
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What would be the simplest addition that would make the D-Wave architecture universal?

The D-Wave system, as I understand it, allows us to program Ising models and to find their ground states. In this form, it is not universal for quantum computation: it can not simulate a circuit model quantum computer. What would be the simplest…
James Wootton
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Consequences of SAT ∈ BQP

"Quantum magic won't be enough" (Bennett et al. 1997) If you throw away the problem structure, and just consider the space of $2^n$ possible solutions, then even a quantum computer needs about $\sqrt{2^n}$ steps to find the correct one (using…
Didix
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Quantum implementation of arcsin

I am looking to implement a quantum version of the arcsinus function. Such a problem is motivated by the HHL algorithm where $x\mapsto 1/x$ and $\arcsin$ can be used to get $1/x$ from the computational basis state into the amplitude. My questions…
SRichoux
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