Search Results

There was a similar question asked here, but I feel like mine is even more basic. What's the easiest way to implement a circuit $U$ corresponding to a matrix-vector multiplication modulo 2? $$ |x_1x …

Is it correct that the following circuit can produce any two-qubit state with real amplitudes? (Meaning that for any set of the four real amplitudes there exists a set of angles...) If so, should …

I am trying to figure out what is the best way of dealing with registers while constructing circuits from abstract blocks. Consider the following subcircuit: \begin{equation} U|x\rangle|y\rangle|z\ran …

I would like to construct a quantum circuit s.t. It maps a certain (relatively small) subset of computational basis vectors onto a different subset of those, e.g. $$ |0101001\rangle \to |1000010\ran …

I apologize for a simple question, should be quite trivial. How do I construct a circuit for preparing such a state? $$ |0\rangle^n \mapsto \cos(\theta)|0...0\underset{i}{1}0...0\rangle + \sin(\theta) …

There exists a nice way of preparing any superposition (with real amplitudes — this is the case I'm interested in) of states $\{\ldots0001\rangle,\,|\ldots0010\rangle,\,|\ldots0100\rangle,\ldots\}$, e …

Consider a circuit acting on $n\geq2p+1$ qubits. The first $p$ qubits encode some unknown state $|\psi\rangle$. Next $p$ qubits encode a fixed given basis state $|\phi\rangle=|\ldots f_2f_1f_0\rangle$ …

How do I add an arbitrary overall phase to the circuit using standard gates? Yes, I know that the overall phase it irrelevant, yet this is only true until you control the circuit on extra qubits. Yes, …

I'm wondering what are the known/good/standard ways of exponentiating Pauli terms (i.e. constructing circuits, which implement $\exp(i\alpha XIIZYI...)$) using gates supported by trapped ion quantum c …

In this paper, the measurement of the real part of the matrix element of a Hermitian&unitary operator $G$ between the states $U|0\rangle$ and $V|0\rangle$ (i.e. $\langle 0| V^\dagger G U | 0\rangle$) …

What would be the simplest way to construct a block encoding circuit $U_A$ for a $2^n\times 2^n$ matrix $A$ proportional to $\operatorname{diag}(0,1,2,\ldots,2^n-1)$? A couple of options I can imagine …

One way or another, I would like to implement the action of the second-quantized creation operator on a quantum state: $|\psi\rangle\mapsto a^\dagger|\psi\rangle$. The motivation, of course, comes fro …

Is there a smart way to implement $e^{i\theta\,\Phi\,\rm{QFT} \, \Phi \, \rm{QFT}^\dagger}$, where both $\Phi \propto\sum_j2^jZ_j$ and $\rm{QFT}$ act on the same set of registers? Even an approximate …

I am wondering what a circuit should look like if I want to prepare the state of the following form: $$ |0\rangle^{\otimes n} \mapsto \dfrac{ |1000\ldots0\rangle + |0100\ldots0\rangle + |0010\ldots0\r …

For $2N$ qubits $\{i_1,j_1\ldots i_N,j_N\}$ I would like to have a circuit changing the value of an ancillary register from $0$ to $1$ if $i_1=j_1$ AND $i_2=j_2$ AND ... AND $i_N=j_N$. One way to cons …