Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

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Advantage of Hadamard gate over rotation about the X axis for creating superpositions

When I look at most circuits (admittedly small sample as I'm a beginner), the Hadamard gate is used a lot to prepare a superposition from say the $\mid0\rangle$ state. But upon a little reflection, we can prepare a superposition using a…
Ntwali B.
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Can we perform quantum mechanical simulations using a quantum computer?

I'm a computer science major who's really keen on physics and quantum mechanics. I have started learning about Q# and D-Wave, but I just wanted to know if it's possible to test quantum mechanical theories using quantum computers. If so, then what…
Yashank
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Possibility of a "reset" quantum gate

I wish to have a "reset" gate. This gate would have an effect to bring a qubit to the $\mid0\rangle$ state. Clearly, such a gate is not unitary (and so I'm unable to find any reliable implementation in terms of universal gates). Now for my…
Ntwali B.
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What are the preferred numerical methods to simulate the evolution of a state through a time-dependent Hamiltonian?

Under the influence of a time-independent Hamiltonian $H$, a state $|\psi\rangle$ will evolve after a time $t$ to the final state $|\psi(t)\rangle=e^{-iH t}|\psi\rangle$, while in the most general case of a time-dependent Hamiltonian $H(t)$, the…
glS
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Resources for Quantum Communication Complexity

I recently came to know about this interesting topic of "communication complexity". In simple words, Wikipedia defines it as: In theoretical computer science, communication complexity studies the amount of communication required to solve a…
Sanchayan Dutta
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Are there any other companies besides Microsoft pursuing topological QC?

Also, why is Microsoft placing such an emphasis on topological qubits when most other companies seem to be focusing on other qubit technologies? I know topological qubits could handle noise far better than other systems, so they are appealing, but…
jman
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Number of gates required to approximate arbitrary unitaries

If I understand correctly, there must exist unitary operations that can be approximated to a distance $\epsilon$ only by an exponential number of quantum gates and no less. However, by the Solovay-Kitaev theorem, any arbitrary unitary operation in…
BlackHat18
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The process for transferring qubits between locations

I understand that right now qubits are physical entities in a Quantum Computer and I am playing around on the IBM Quantum Computer as well as the Q# language and dipping my toes into the Quantum world for the first time. I have read a lot of the…
Leigh Griffin
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Are non-secret-based quantum money mini-schemes susceptable to Jogenfors' "reuse attack?"

Aaronson and Christiano call public-key or private-key quantum mini-schemes $\mathcal M$ secret-based if a mint works by first uniformly generating a secret random classical strings $r$, and then generating a banknote $\$:=(s_r,\rho_r)$, where $s_r$…
Mark Spinelli
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Practical implementation of Hamiltonian Evolution

Following from this question, I tried to look at the cited article in order to simulate and solve that same problem... without success. Mainly, I still fail to understand how the authors managed to simulate the Hamiltonian evolution through the…
FSic
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Is it possible to realize CNOT gate in 3 dimension?

CNOT gates have been realized for states living in 2-dimensional spaces (qubits). What about higher-dimensional (qudit) states? Can CNOT gates be defined in such case? In particular, is this possible for three-dimensional states, for example, using…
Goat
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In Schur-Weyl's duality, why is the commutant of $\pi_k(S_k)$ spanned by $U(d)^{\otimes k}$ matrices?

I'm reading this tutorial paper about quantum state certification. However, I'm confused about the concept of Schur-Weyl duality, explicitly Theorem 35 of the paper. Let $S_k$ denotes the symmetric group and $\pi_k$ its unitary representation, i.e.,…
Sherlock
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Is there a fast sparse Hadamard transform?

Suppose I give you an $n$-qubit state vector as a classical list of numbers (or as an oracle that can query the amplitudes). I tell you this state vector will contain exactly $k$ non-zero amplitudes, after you apply a Hadamard transform to it. You…
Craig Gidney
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Can we avoid repetition in Shor's algorithm by using the quadratic formula?

Shor's algorithm is a quantum algorithm to find a non-trivial factor of a composite integer $N$. It is assumed that $N$ is odd and not a perfect power. The first step is to find the multiplicative order $r$ of $x$ modulo $N$, where $x$ is randomly…
Dave R
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Universal Gate Set, Magic States, and costliness of the T gate

The usual universal gate set is $\mathcal{C} + T$ where $\mathcal{C}$ is the Clifford group and $T = \begin{pmatrix} 1 & 0 \\ 0 & e^{i\pi/4} \end{pmatrix} $ is the $\pi/8$ rotation gate. In practice we find a code that has $\mathcal{C}$ transversal…
Eric Kubischta
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