Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

Questions tagged [circuit-construction]

For questions about the construction of complex circuits using elementary quantum gates.

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Minimum number of T gates needed to perform two overlapping Toffolis

Consider this circuit: How many T gates are needed to implement it, in the stabilizer+T gate set? The circuit can use cliffords, measurement, classical feedback, ancilla qubits, and T gates. Only T gates cost. I know how to do it with 8 T gates,…
Craig Gidney
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How to do quantum circuit arithmetic?

I'm looking at a circuit from this paper on quantum machine learning. So to introduce my own notation: we start with $|\psi_0⟩ = |0,a,b⟩ = a_0b_0|000⟩ + a_0b_1|001⟩ + a_1b_0|010⟩ + a_1b_1|011⟩$ after the first $H$-gate we have $|\psi_1⟩$ after the…
Alexander Soare
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Showing the equivalence of two simple {NOT, CNOT} circuits

As a beginner, for exercise purpose, I’ve studied this two quantum circuits. They are equivalent, and for 2 qubits it’s easy to write the unitary transformation matrix. Looking for another method I wrote what follows, but I’m not sure about…
Fabrizio R.
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How to construct the unitary representation of the function $f(x, y, z) = (x \oplus y, y \oplus z)$?

Consider the function $f:\{0, 1\}^3\to\{0, 1\}^2$ with $f(x, y, z) = (x \oplus y, y \oplus z)$. How would you construct its standard unitary representation?
David
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How to generate the following $n$-level $n$-particle singlet state?

Could you please give a direction/reference towards realising the following using any set of realisable quantum gates $$\boxed{|S_{n}\rangle = \frac{1} {\sqrt{n!}} \sum_{S\in P_n^{n}} ( \,-1) \,^{\Gamma(S)}|s_{0}\rangle |s_{1}\rangle…
qcnoob
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Does delaying measurements change the complexity of the circuit?

It's often said that for any quantum circuit with intermediate measurements, there exists an equivalent circuit where all measurements are at the end of the circuit. Is anything ever argued about the complexity of the circuit with delayed…
Ethan
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Prepare superposition of quantum states weighted by fidelity with reference state

Given a list of $m$ quantum states $$|\phi_0\rangle, |\phi_1\rangle, ... |\phi_{m-1}\rangle$$ each on $n$ qubits, with unitaries to prepare these ($U_0, U_1, ...$), I'd like to prepare a superposition of these states weighted by their overlap with…
Nikhil Khatri
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Circuit for controlled rotations conditioned on a $d$ bit precision estimate of $\theta$ for $O(d)$ gates

Suppose I have a $d$-bit estimate of $\theta \in (0, 2 \pi]$, say a register of qubits $|\tilde{\theta} \rangle = |z_1 \rangle \ldots |z_d \rangle$ for $|z_i \rangle \in \{|0 \rangle, |1 \rangle \}$ where $\theta \approx \sum_{i=1}^{d} z_i \pi…
IntegrateThis
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Can someone walk us through Nielsen's proof on a circuit for quantum teleportation?

Michael Nielsen posted on Twitter about a proof on a circuit for quantum teleportation. Had some fun this afternoon re-analyzing the circuit for quantum teleportation. Here's a proof I found that the circuit works. The circuit to be verified: top…
0x90
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Matrix mod 2 multiplication

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_2x_3\ldots x_n\rangle \mapsto |y_1y_2y_3\ldots…
mavzolej
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Minimum number of ancilla qubits required to make a transformation unitary?

Background The counterpart of a NOT gate is the CNOT gate. They make use of ancilla qubits to achieve this. Question Given an arbitrary non-unitary transformation what are the minimum number of ancilla qubits required to make a transformation…
More Anonymous
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What's my computational basis if I want to define a unitary operator that implements a function such as $f(i) = 2^{i+1} \text{mod 21}$?

I know I must define $U_f$, the unitary operator, on the computational basis. But what's my computational basis here?
R. Chopin
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Reasons for Google's calibration policy of fitting to Alternating Single/Two-qubit gate pattern

In Cirq document that describes 'best practices' for manually optimizing circuits, they recommend to construct a circuit in a pattern that alternate 'single-qubit gates with two-qubit gates in each layer'. Regarding this, I have few questions: (1)…
Changu Kang
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Preparing arbitrary two- and multi-qubit states with real amplitudes

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 generally expect that arbitrary state…
mavzolej
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Is it possible to simulate any classical algorithm with the same efficiency on quantum computer?

Consider any data structure based on the binary search trees, e.g. set. Classical computers can make queries (insert, remove, test if element present), into this structure in $O(\log n)$ time, where $n$ is the number of elements. Using the quantum…
user7988
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