Questions tagged [quantum-computer]

The quantum computing tag is relevant for computing that uses quantum states such as superposition and/or entanglement to locate low energy states as solutions to complex problems (rather than laboriously enumerating and checking solutions as would be done with non-quantum traditional computing).

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Quantum circuit that puts qubits in “equal” superposition

I would like to build a circuit that takes multiple qubit system states and puts them in a superposition with equal amplitudes. For example: Let's consider a 4 qubit system. I would like the circuit ...
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How do I compute the Hamiltonian generating the CNOT gate? [closed]

I have the matrix for the C-Not gate acting in a system of two qbits, $|q_{2}q_{1}\rangle$. In the basis $ \left[ |00\rangle, |10\rangle, |01\rangle, |11\rangle \right]$: $$ C_{N} = \left[ \begin{...
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Fundamental Understanding of Hamiltonians

First of all, my major is CS for several months I have been exploring the area Quantum Computing, therefore my background in Quantum Mechanics is a bit lacking. I know that a Hamiltonian is a self-...
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Bell State Measurement Algorithm

I'm relatively new to quantum computation and am taking a course in it. I was wondering if it is possible to code an algorithm which would be able to take an input of a 2 qubit state and perform a ...
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For what $\lambda$ is the channel $\mathcal E(\rho)=\lambda \rho^T + \frac{1-\lambda}{d}I$ CPT? [closed]

Consider the following channel: $\mathcal{E}(\rho) = \lambda\rho^T + \frac{1-\lambda}{d}I $ Which $\rho^T$ means transpose and $d$ is the dimension of the Hilbert space. My question is, for what ...
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What is the exponential form of Phase Shift Gate?

The Phase shift Gate is $$R(\theta) = \begin{pmatrix} 1 & 0 \\ 0 & e^{i\theta} \end{pmatrix} $$ Moreover, $$R^{\dagger}(\theta) = \begin{pmatrix} 1 &0 \\ 0 & e^{-i\theta}\end{pmatrix} ...
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How to explain to a second year undergrad what quantum computing is? [closed]

I work as a teaching assistant (TA), and I want to explain to my students what is quantum computing and its related fields. I could explain to them what quantum computing means and what research is ...
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How is the set of states $Q$ logically replaced by a Hilbert space?

Question is: How is the set of states $Q$ logically replaced by a Hilbert space if a classical Turing machine is described by a 7-tuple $M=\langle Q,\Gamma, b,\Sigma, \delta, q_ {0},F\rangle$? I read ...
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What makes a Quantum Computer Faster for solving specific problems?

I have an undergraduate understanding of Quantum Mechanics (or at least of whatever is covered in Griffith's) and the idea of a Quantum Computer sounds really interesting but I am having some trouble ...
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Can Schrödinger's Astronaut act as a quantum computer?

I am trying to reconcile Schrödinger's cat vs. quantum computing at the intuitive level. We all know that in the Schrödinger's cat thought experiment, the cat exists in a superposition of states, but ...
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What is the maximum amount of computation that can be performed in the future lifespan of the universe?

The ultimate question I have been trying to answer is the maximum universal population allowed by physical limits. Making some transhumanist assumptions I am perfectly happy with, I am equating this ...
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How is deterministic state transfer related to entanglement generation between two qubits?

From a quantum information theoretical point of view, how is deterministic state transfer related to entanglement generation between two qubits? Or, more specifically, how can you exploit the former ...
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Completely positive quantum channel

Let $\mathcal{E} \to CP(A \to B)$ (completely positive linear map) be a trace non-increasing $CP$ map. Show that any operator sum representation $\{M_x\}_{x=1}^{m}$ of $\mathcal{E}$ satisfes $\sum_{x=...
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Is it possible to count over the set of natural numbers on a quantum computing system? [closed]

On a classical computer, the maximum possible number you can count to is a finite number. I've asked around about this, and generally there has been opinion one way or another, but it seems to me that ...
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How can we “isolate” a qubit

From Wikipedia : In ion quantum computer, if the ions are not properly isolated, noise can result from ions interacting with external electromagnetic fields, which creates random movement and destroys ...
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About universal quantum computation by “quantum wires”?

In this paper: A. Y. Kitaev, "Unpaired Majorana fermions in quantum wires", Phys.-Usp. 44 131 (2001), arXiv:cond-mat/0010440, it says: Unlimited quantum computation is possible if errors in ...
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Transmon implementation of qudit

With reference to this question, I would like to ask if there is any attempt to implement qudit with transmon. I can imagine using higher energy level than $|0\rangle$ and $|1\rangle$ used in transmon ...
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How to physically understand 'qudit'?

I've heard that a qudit is a unit of quantum information described by a superposition of $d$ states (more general than qubit). However, I haven't found a formal introduction about what it is and how ...
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Quantum Computing: Preparation of the Bell state Notation [closed]

I was watching some lectures on qubits. They were talking about how to generate a Bell state. They described it as follows: Prepare state 00: $$\left |0 \right> \otimes \left |0 \right>$$ Apply ...
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What is going on inside quantum gates physically?

What are the physical realities of the different quantum gates? I am particularly interested in how the CNOT gate works on the inside as well as how the Hadamard gate works. The Hadamard gate to me is ...
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Is there an unentangled electron pair in the universe?

How can we be sure that there are two electrons in the universe whose spins are uncorrelated (their joint state is the tensor product of their individual projections) but each of them has nonzero ...
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How to implement a derivative of a unitary gate in a quantum circuit?

I was reading this paper1, which says in Eqn(15) that the derivative of a unitary gate with respect to the parameter $\mu$ can be decomposed into linear combinations of unitary gates. However, I didn'...
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What is the construction of Charge Qubit - Cooper pair box?

I have to dive deeper into the construction and architecture of quantum computers but I am stuck with how a charge qubit is manufactured. I know the basic circuit but I am unable to understand the ...
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What are the units of time in the Quantum Adiabatic Theorem?

To preface my question, I'm coming to adiabatic quantum computing from a background in classical computer science with little knowledge of quantum physics, so simple, step-by-step explanations or ...
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Are quantum computers able to simulate every physical process that a classical one can simulate?

I edited the question since this comment was (rightly) made: There are few things that are more annoying than questions where the question text is not self-contained. So: Quantum supremacy has been ...
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On Google's Sycamore chip showing quantum supremacy, have they published the values of Josephson critical current and capacitance?

I notice that they discuss a 6 GHz resonance, and show diagrams with 5 or 6 quantum states in a cosine potential, but I could not find any other specific values of their Josephson parameters.
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Number of degrees of freedom in a unitary transformation on a $n$-qubit register

I was going thorough paper Transformation of quantum states using uniformly controlled rotation by Mottonen et al. In that it says The configuration space of the $n$-qubit quantum register is $2^n$-...
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Quantum Computing without Complex Numbers

p.s. I am trying to get a handle on what actual computing operations a quantum computer program does. Any information on that would be appreciated [noting the issue that that might count as a ...
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What methods can I use to find the minimum of a tranverse field Ising model?

I am trying to solve for the minimum of the hamiltonian of the form: $$ H = \sum_{i,j} J_{ij}q(i)q(j) + g_i\sum_i x(i) $$ where q(i) is the operator (I + z(i))/2 and z(i) and x(i) are pauli operators ...
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Two CNOT gates on two Two qubits [closed]

Suppose we have two qubits in the state $(a|0⟩+b|1⟩)|0⟩ $, to which we apply the following circuit. Specify the state of each qubit after we applied the circuit to the state (a|0⟩+b|1⟩)|0⟩ . Let the ...
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Is a qutrit an example of tripartite entanglement? [closed]

Is a qutrit considered to be in a state of tripartite entanglement?
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Proof that $U$ is an unitary operator [closed]

I have a function $f$ mapping a bit onto another bit, i.e. $f : \{0, 1\} \rightarrow \{0, 1\} $. The function f is either constant, so f(0) = f(1) or balanced, so f(0) $\neq$ $f$(1). The quantum gate ...
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Can human brain do quantum computation?

First of all, I know that any math (or computation) a classical computer can do, we human can do with pen and paper at same type of efficiency. Obviously, that is because we tell a classical computer ...
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Computations and physical processes

Can computation be accomplished using any physical process? For simplicity let me restrict myself to the computation of performing addition. I am aware that mechanical calculators just use Newtonian ...
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Representing Quantum Gates in Tensor Product Space

I want to write the matrix form of a single or two qubit gate in the tensor product vector space of a many qubit system. Ill outline a simple example: Both qubits, $q_0$ and $q_1$ start in the ground ...
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Is partial trace method valid for highly entangled state? [closed]

Suppose there are four wires of qubits and the state vector is highly entangled. I want to know the density matrix (or state vector) of wire-$1$ only. In this case, is it available to use partial ...
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Confusion regarding bra-ket notation and proof of a ket equation

My question is two-part. First, imagine a bipartite quantum state $|\Phi \rangle_{AB}$, made of $2n$-qubits, shared between Alice and Bob (with $n$-qubits each). Alice performs some unitary operation $...
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Why would and when do Qubits collapse into one state upon observation?

Something like an electron would act like a particle upon observation because the high energy light waves interfere with it. But what about Qubits? Why do they collapse into one state? And when do ...
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How to check if a qubit in a circuit is equal to another qubit?

If we have a set of qubits q1 ,q2 and q3 for example, $$ \vert{q_1}\rangle = a \vert{0}\rangle +b \vert{1}\rangle\\ \vert{q_2}\rangle=\vert{0}\rangle\\ \vert{q_3}\rangle=\vert{0}\rangle $$ the state ...
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If superposition is just uncertainty, then how come quantum computers work? [closed]

If superposition is just uncertainty due to a particle changing on observation and not literally 2 things at once, how come quantum computers work while having qubits that are literally 1 and 0 at the ...
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What is the present state of research on quantum networks? [closed]

I recently came across the article The Quantum Internet Is Emerging, One Experiment at a Time in Scientific American where it was discussed how quantum networks could provide a level of privacy and ...
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How many parallel processes does a Quantum Computer Have?

I know that quantum computers have a extremely large capacity to do many different calculations at once, but how many different calculations? Is it infinite, like I've heard some articles say, or is ...
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Is there a way to go from the continuous variable quantum computer model to the qubit model?

There are some papers such as https://arxiv.org/abs/quant-ph/0008040 and https://arxiv.org/abs/1907.09832 that discuss going from qubit to the continuous model. But I'm curious if there is a way to ...
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Why can photons be used as qubits?

I've been studying quantum computers and while it's apparent to me how electrons are used as qubits, through their spin number, it's not as clear what makes a photon a viable candidate to be used as a ...
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How to experimentally perform a POVM measurement?

Reading through Nielsen and Chuang, I came across the following example. Consider a POVM containing three elements, $$ E_1 \equiv \frac{\sqrt{2}}{1 + \sqrt{2}} |1⟩⟨1|,\\ E_2 \equiv \frac{\sqrt{2}}...
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Applying a rotation on an entangled state

I want to understand an experiment but I am struggling with the (basic) math/braket notation. In the experiment two ions are entangled and separated into two wells $A$ and $B$. The spin state of the ...
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Smallest Distance-5 Quantum Error Correction Code? [closed]

Is it known/proven what the smallest quantum error correction code is that can correct arbitrary two-qubit Pauli errors? I can think of the nested/concatenated 5-qubit code or a 25-qubit version of ...
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Does the spatial part of the wavefunction need to be antisymmetric in the singlet and symmetric in the triplet?

Two spin-1/2 particles either are part of a spin-1 triplet or a spin-0 singlet. The singlet is antisymmetric but bosons need to be symmetric wave functions. So does the spatial part of the wave ...
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Quantum computer measurement

Hello Stackexchange physics, This question is mostly a request for a source of information on quantum measurement and decoherence that is consistent and independent of the particular context. When I ...
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How do entangled states increase computational space for quantum computers compared when only using product states? [duplicate]

My question is: n-qubit product state. $$|\psi\rangle=(a_1|0\rangle+a_2|1\rangle)\otimes(b_1|0\rangle+b_2|1\rangle)\otimes \cdots$$ n-qubit Entangled state $$|\psi\rangle=(a_1|000\cdots000\rangle)+...

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