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What's the most efficient decomposition in terms of T-count of the 4-qubit Toffoli with 1 ancilla?
When decomposing the 4-qubit Toffoli in the Clifford+T universal gate set with 1 ancilla qubit, what is the most efficient implementation one can get in terms of T-count? I can only find papers that handle the problem for general n-qubit Toffoli…
Ocelot
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6
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Example non-stabilizer code?
A code is a non-stabilizer code if it is not equivalent by local unitaries to a stabilizer code.
What is an example of a non-stabilizer code with distance $ d \geq 2 $?
Are there any non-stabilizer codes that are known to have especially good…
Ian Gershon Teixeira
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What's new in Quantum Natural Language Processing (QNLP) w.r.t classical NLP?
I recently discovered Cambridge Quantum people have developed lambeq, a quantum natural language processing high-level library. Before diving into it, I'd like to understand more in detail what quantum computers can do better when it comes to NLP.…
mpro
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6
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Is effective quantum cloning possible, given that any classical function can be implemented as a quantum circuit?
As in Compiling a classical function to a quantum circuit in practice, as far as my understanding goes, it is known that any classical function can be implemented as a quantum circuit. So given $f(x)=x$, there should be some quantum circuit $Q_f$…
Paulske
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6
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Can a merchant who accepts a knot-based quantum coin mint her own knot-based coin?
Referring to Farhi, Gosset, Hassidim, Lutomirski, and Shor's "Quantum Money from Knots," a mint $\mathcal{M}$ generates a run of coins, including, say, $(s,|\$\rangle)$, using a quantum computer to mint $|\$\rangle$ while publishing the public…
Mark Spinelli
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6
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4 answers
Finite subgroup of $U(4)$ containing a non-Clifford gate and all local Cliffords
Background
I denote the $n$-qubit Clifford group as $C_n$ and the $n$-qubit group of all `local Clifford' (LC) unitaries as $C_1^{\otimes n}$ where $C_1 = \langle H, S\rangle$.
It is well known that $C_n$ is a maximal finite group in $U(2^n)$. That…
Jonas Anderson
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Is 216 qumodes photonic quantum processor equivalent to 216 qubits superconducting quantum processor, in terms of computational power?
Xanadu just launched borealis, 216 qumodes photonic quantum computer, this week.
https://xanadu.ai/blog/beating-classical-computers-with-Borealis
Its number of qubits is very interesting because it has twice the number of qubits of IBM Quantum…
Natchapol Patamawisut
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6
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1 answer
Non-universal gate sets
Imagine that I have the gate $T=\text{diag}(1,e^{i\pi/4})$ and want to add to it some two-qubit gate $U$ such that the set $\{U,T\}$ is not universal for quantum computation. What limits are there on the choice of $U$?
I already know that $U$ could…
DaftWullie
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6
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How is entanglement achieved between two particles in quantum computing?
Many texts (especially meant for public consumption) discussing quantum mechanics tend to skim over exactly how entanglement is achieved. Even the Wikipedia article on quantum entanglement describes the phenomenon as follows:
"Quantum entanglement…
Ebony Maw
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What methods exist for cooling superconducting quantum computers?
Existing superconducting quantum computers need to be cooled near absolute zero. For example, some of D-Wave's machines are cooled to about $20 \ \mathrm {mK}$. Their design uses a dilution refrigerator.
Are there any other cooling methods for…
user4574
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1 answer
Can W gate be written only using H,T?
I want to write the decompose the gate $W=(X+Y)/\sqrt{2}$ using only $H$ and $T$ (and all the derived Clifford gates basically). I know $H=(X+Z)/\sqrt{2}$ is it possible to obtain exactly $W$ from this set (no approximation)?
Mauricio
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T-depth in Qiskit
How to find T-depth in Qiskit? Is there any inbuilt function or some method to find T-depth? I know that the .depth() function exists which returns circuit depth (i.e., length of critical path), but is there any method for T-depth?
Gopal Dahale
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6
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How accurate must QM be for applications of quantum computing?
The Tale of One-Way Functions (section 2.4) claims that quantum mechanics would have to be accurate to an remarkable (absurd?) degree for an application such as factoring large numbers. So, orthogonal to the thousands of qubits and billions of…
yoyo
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6
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2 answers
Confusion regarding Neumark's/Naimark's extension of POVM
Starting with the definitions used.
A PVM is a set $\mathcal{P} = \{P_i: P_i^2 = P_i, P_iP_j = \delta_{ij}P_j, \sum{P_i} = \mathbf{I}\}_{i,j=1}^n$, where $n\leq d$ on a Hilbert space $\mathcal{H}^d$ of dimension $d$
A POVM is a set $\mathcal{M} =…
Abhishek Banerjee
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6
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2 answers
Investigating the scaling of the error of a Trotter-Suzuki-approximation
I am doing an assignment and I am being asked to investigate the scaling of the error with the number of repetions $n$ of a approximation of the Hadamard with $R_x$ and $R_y$.
This is the approximation, where $\theta = \frac {\pi} {\sqrt2}$:
$$ H…
tommasopeduzzi
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