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### Quantum computer vs supercomputer performance

I am an electrical engineer and have been learning about quantum computing for the last year, and I can hardly believe what I read and hear. It is becoming clearer to me, but it's a very difficult ...
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### What's the difference between observing in a given direction and operating in that same direction?

So starting with an up particle: $$\lvert \uparrow \rangle = \begin{bmatrix} 1 \\ 0 \\ \end{bmatrix}$$ My understanding is that you can measure $\lvert \uparrow \rangle$ in $X$ and have ...
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### Why can we forget about the ancilla bit in Grover's algorithm?

$\def\braket#1#2{\langle#1|#2\rangle}\def\bra#1{\langle#1|}\def\ket#1{|#1\rangle}$ When using Grover's algorithm to invert a function $f\colon \{0,1\}^m \rightarrow \{0,1\}$, an ancilla bit is used in ...
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Say we had a Hadamard-like gate with the -1 in the first entry instead of the last. Let's call it $H^1$. $$H = \begin{bmatrix}1&1\\1&-1\end{bmatrix}$$ $$H^1 = \begin{bmatrix}-1&1\\1&... 1answer 66 views ### Are 20 repetitions of Sycamore's one- and 2-qubit gates sufficient to produce a uniformly random state? In the answer to this question about random circuits, James Wootton states: One way to see how well we [fully explore the Hilbert space] is to focus on just randomly producing n qubit states. ... 1answer 39 views ### How many ancilla qubits to use with Multiple-Control Toffoli (mct) gate in Qiskit? The Multiple-Control Toffoli (mct) gate takes as input: 1. a register containing the control qubits, 2. the target qubits and 3. a register containing ancilla qubits. I don't know how many ... 0answers 47 views ### Who can give me a report about a simple calculate to show Quantum Computing's advantageous [duplicate] I really want to show something with others and try to do something for this 0answers 35 views ### 'ERROR: QasmSimulator: Circuit cannot be run using available methods.' I used the following code. Can anyone say what that error is about? ... 1answer 46 views ### IBM 53 qubit cloud access IBM announced a 53 qubit chip. Will the advertised chip be available for non-paying users, or only to IBM clients? 1answer 84 views ### How to prepare an initial state for variational quantum algorithms? I would like to prepare an initial state for variational quantum algorithms. The initial state should include the following states: |000\rangle, |010\rangle, |100\rangle, and |001\rangle. How ... 0answers 29 views ### Code for implementing MCT in qiskit [duplicate] I am trying to implement 7 control toffoli gate in qiskit . 1answer 68 views ### Why do quantum computation models based on open quantum systems receive so little attention? In almost all research on (universal) quantum computation the common models assumed from the outset are either the quantum circuit model with unitary gates, the measurement-based one-way model or the ... 2answers 52 views ### Physical Interpretation of Pauli Matrices as Polarization Check We know that the Pauli matrices are:$$\sigma_x = \begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}, \sigma_y = \begin{bmatrix}0 & -i \\ i & 0\end{bmatrix}, \sigma_z = \begin{bmatrix}1 & ...
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I cobbled together a few programs with Qiskit several months back which worked fine on both the BasicAer simulators and the actual IBMQ computers. However, when I tried to revisit them recently, ...
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### Input and output qubit notation in quantum gates

I am new to quantum computing and I am having trouble understanding the notation used for input/output qubits in quantum gates. I will use the CNOT gate as an example. In several (most) references I'...
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### Does a quantum computer have a clock signal and if yes how big is it?

I think there can't be a computer running software without having a clock signal. A fast classical computer has a clock rate between 4 to 5 GHz. If quantum computers are so much faster they must ...
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### History of anyon theory, braidings and tensor categories

What was the first paper/who was the first person to phrase anyon theory in terms of tensor categories? Going through Wilczek's book on fractional statistics, some of the reprinted papers anticipate ...
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### Is IBM Q composer using little-endian representation for multi-qubit states?

I am still confused when I am trying to use the IBM Q composer to reproduce some quantum circuits I found in different papers, and I am wondering if it is because there are two ways to represent a ...
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### How to define initial state $\rvert \Psi(0) \rangle \equiv \rvert 1, -1 \rangle \otimes \rvert 0 \rangle_{\text{cav}}$ of a system in QuTiP?

Say, we have a $\require{mhchem}\ce{^87Rb}$ atom having an electric dipole transition on the $D_{1}$ line and we have two hyperfine ground states, one on $F = 1$ and one on $F = 2$ level. So, we take ...
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### Can Eve manipulate the state in the following situation [closed]

Alice is sending a state to Bob via authenticated quantum channel. Can Eve apply a Unitary transform on the above state from Alice and send it back to Bob?
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### reversible operator that implements the unary gate 0-operator [closed]

Construct a reversible operator that implements the unary gate 0-operator (an operator that acts on one bit and returns 0 independently of the input.). How many bits are necessary?
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### Implement a reversible OR operator with less than three bits [closed]

Show that it is impossible to implement a reversible OR operator with less than three bits
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### Is there a way to develop a multiple controlled X or Z gate on Qiskit without using ancillary qubits?

I know for instance I can derive a cccX gate using 2 Toffoli gates on 5 qubit wire or ccccX with 3 Toffoli gates and 7 qubits and so on. you will notice the depth is increasing as the number of ...
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### Can quantum computer perform classical computation? [duplicate]

I was going through a paper in which protocol said that the party computes modulo 'd' sum of other party secrets directly. It was not mentioned that the computation is classical. Can I assume that it ...
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### Quantum Supremacy: Some questions on cross-entropy benchmarking

I was skimming through the Google quantum supremacy paper but got stuck on this section: For a given circuit, we collect the measured bit-strings $\{x_i\}$ and compute the linear XEB fidelity [24-...
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### Quantum algorithms for Prolog or automated theorem proving?

Are there quantum algorithms for Prolog (SLD resolution - unification and depth-first-search) or for automated theorem proving in general (negation, resolution, and SAT)? Usually automated theorem ...
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### Applications of quantum computing for science popularization

I need to do some popularization of science for an event, and I would like to talk about the "best" applications of quantum computing. I know there is code-breaking (Shor algorithm), simulation of ...
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### Do pure states lie on a hypersphere in the Bloch representation?

It is known that every state $\rho$ of a $d$-level system (or if you prefer, qudits living in a $d$-dimensional Hilbert space) can be mapped into elements of $\mathbb R^{d^2-1}$ through the mapping ...
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### Unable to recognise little-endian format

I'm told that the input register is in little-endian format. But the vscode gives me error telling me that it is wrong argument for QFT even after using a suitable converter. Am I missing something ...
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### Transfer trained machine learning model

I know just the basics of quantum computer i.e. superposition, entanglement, gates and few other kinds of stuff. Now the question is it possible to transfer a trained machine learning model from IBM ...
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### What is the cost of implementing the Quantum Fourier transform in a classical computer?

What is the cost of implementing the Quantum Fourier transform (QFT) in a classical computer? We know we require at least $\log{n}$ depth quantum circuits to do a QFT in a quantum computer, with $n$ ...
A source constantly produces a stream of photons in one of the following states $$|\varphi_1\rangle=\dfrac{1}{\sqrt2}(a|00\rangle+ b|01\rangle+c|10\rangle+d|11\rangle)$$ $$|\varphi_2\rangle=\dfrac{1}... 1answer 100 views ### Exploring quantum computing with Qiskit [closed] I'm prepared to explore quantum computing which is completely new to me. Searching for a while on the Internet, I found IBM Qiskit which is an Open Source software necessitated for Quantum Computing. ... 1answer 65 views ### The solution when we transmit a qubit through a Pauli channel? A Pauli channel is defined as a convex combination of Pauli operators, i.e. \epsilon_{\text{Pauli}} (\rho)=\sum_{j} q_j\sigma_j\rho \sigma_j, where 0 \leq q_j \leq 1 and \sum_j q_j=1. Now, I ... 3answers 140 views ### Quantum operation that always produces output orthogonal to input I'm trying to show/convince myself the following statement is correct (I haven't been able to find any similar posts): "There is no reversible quantum operation that transforms any input state to a ... 1answer 45 views ### Would all quantum computing research be for naught if a powerful enough quantum computer is never built? Let's say 1000 years from now powerful quantum computers are still a matter of fiction and no useful calculations can be carried out using them. Would this mean that the entire industry of quantum ... 3answers 142 views ### Can everything in QM be described with degrees instead of matrices and vectors? I found this explanation. "The Hadamard gate can also be expressed as a 90º rotation around the Y-axis, followed by a 180º rotation around the X-axis. So H=XY^{1/2}H = X Y^{1/2}H=XY^{1/2}." Can ... 1answer 46 views ### How can classical computations be non-unitary? Given that classical physics emerges from quantum physics on a macroscopic scale, and all quantum operators are unitary, how are we able to perform non-unitary operations (such as setting a register ... 1answer 81 views ### Understanding the action of operators on vectors in tensor product spaces I'm studying Quantum Computing: A Gentle Introduction. On page 33, Section 3.1.2, after defining tensor product with 3 properties (distribution over addition on both left and right, scalar on both ... 1answer 64 views ### Trace of Hermitian Operator and Operator Function I am having trouble understanding the following step. From:$$\operatorname{trace}\left(\sum_z |z\rangle\langle z| \rho_A |z\rangle\langle z| * \log( \sum_z |z\rangle\langle z| \sum_x |\langle x|z \...
I'm trying to understand if there is some sort of formula or procedural way to determine if a vector is separable or entangled – aka whether or not a vector of size $m$ could be represented by the ...