# Questions tagged [circuit-construction]

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

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### Constructing a two 3-qubit state involving either X, Y or Z rotation gate

The goal is to construct the state $|\psi\rangle = \frac{1}{2}|010\rangle + \frac{\sqrt{3}}{2}|101\rangle$ Two issues I am facing: What is a good choice for initial state? What is a good choice for ...
1 vote
43 views

### Construct of a quantum circuit for the projection $|0\rangle\langle0| + |1\rangle\langle1|$ and its generalizations

We can construct a projection over $|0\rangle \langle 0|$ using a quantum circuit with two qubits via the Hadamard test circuit $$U = H_1 X_2 CZ_{1,2} X_2 H_1 X_1\,, \tag{1}$$ and by performing ...
24 views

### What is the mathematical rationale for the decompose() function of qiskit?

The decompose() function decomposes the encapsulated quantum module into sets of elementary quantum gates. But what is the math behind its operation? For example how is a diag[1,1,1,1,1-1,1,1,1,1] ...
73 views

### Quantum error correction circuit from stabilizer codes

I am trying to familiarize myself with QEC codes and their use in quantum communication. Right now, I am trying to implement some more widely known codes in Qiskit. My main problem is I cannot wrap my ...
1 vote
83 views

### How to interpret the circuit that measures stabilizers in the 5-qubit error correcting code

I would like to understand the exact role of the following circuit (By Vtomole - Own work, CC BY-SA 4.0) in the 5-qubit QECC. The image attached (from Wikipedia) is captioned "Quantum Circuit ...
1 vote
55 views

### Implementing $n$-bit Toffoli gate with $(2n-5)$ and $(4n-12)$ CCNOT gates

Papers such as Diao et al. "A Quantum Circuit Design for Grover’s Algorithm" implement an $n-1$ bit Toffoli gate with $2n-7$ gates and $n-3$ scratch bits. I want to know if there is a way to ...
1 vote
59 views

### How to interpret the encoding circuit for the 5-qubit QECC

I have a question on circuit which constitutes the sydnrome measurement for the 5-qubit error correcting code. If I focus on just a portion of the circuit: Reference for image. The full circuit can ...
46 views

### Efficient gate executing the time evolution of a Hamiltonian using Runge-Kutta method

You can find a minimal working example below. In particular, I want to replace the scipy.linalg.expm() matrix exponential by a Runge Kutta time evolution method as ...
74 views

### How to apply rotation about X and Z in stim?

I have a quantum circuit illustrated in the provided image, where I perform a series of quantum operations followed by a projective measurement.. Using Qiskit, I've already written the code for this ...
76 views

### Help debugging implementation of Draper QFT adder

I am attempting to implement the adder found in this paper. Here is the code: ...
46 views

1 vote
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### Superposition on a subset of integers [duplicate]

Assuming I have $n$ qubits and I want to create a superposition out of a subset of integers:$$k∈\{1,...,2^n\},$$ how can I create a circuit that creates a uniform superposition of, for example, $k = 3$...
73 views

### Can the oracle for $f:\{0,1\}^n \rightarrow \{0,1\}^m$ be implemented with only $n+m$ qubits?

(Part 1: Required ancilla qubits for a given function's oracle) The question is that given a Boolean function $f:\{0,1\}^n \rightarrow \{0,1\}^m$, how many ancilla qubits are required to build its ...
274 views

### Given $f: \{0, 1\}^n\to\{0, 1\}^m$, how many qubits are needed to implement the oracle $\mathcal U|x,0\rangle^{\otimes m}=|x,f(x)\rangle$?

Suppose I am given a function $f: \{0, 1\}^n \to \{0, 1\}^m$. A standard oracle would be of the form $\mathcal{U}|x\rangle|0\rangle^{\otimes m} = |x\rangle|f(x)\rangle$. I would suspect that this ...
44 views

### Understanding circuit to Hamiltonian embedding where we do not have a separate clock register

I am trying to understand the clock construction given in this paper, to embed a circuit to a Hamiltonian, which doesn't need to access a separate clock register. The construction, at a high level, ...
50 views

### How to alter the result of (somewhat) randomly generated circuits?

I create randomly generated circuits by iterating through a list of the gate set (in my case [$CX,SX,RZ,X$]) and adding the gate to the circuit. (In the case of the $CX$ gate we look at the topology ...
41 views

### Quantum Crosstalk in gate scheduling with different gates

I am working on quantum crosstalk, specifically on CNOT and SWAP gate operations that lead to crosstalk. I have encountered works that decompose CNOT and SWAP with iSWAP and CZ gates. I would like to ...
62 views

1 vote
75 views

### Are there low T-count measurement and Clifford correction protocols for diagonal CNOT+T gates other than CCZ?

Famously, the CCZ gate requires 7 T gates to construct unitarily whereas using an ancilla, measurement, and classically-controlled Clifford gates, it can be constructed with only 4 T gates [1212.5069]....
1 vote