Questions tagged [gate-synthesis]

Question 1

I want to implement a unitary operation $U$ on $n$ qubits, which performs the following mapping on computational basis states: $$U|i\rangle = |2^i\rangle,\quad \forall i \in [0, n-1]$$ When $i\geq n$, ...

Question 2

Currently writing a QASM parser and wondering if this is the proper way to parse a program using a DAG (Deutsch's from QASMBench in this example). The output from Deutsch's would be: ...

Question 3

The paper mentions that the following state can be prepared efficiently (in terms of parameter $L$). (Page 7 of this paper) $$|{\eta}\rangle = \frac{1}{\sqrt{L+1}}\sum_{j=0}^{L} U_j\cdots U_1\Big(|{\...

Question 4

Can a gate sequence approximating a given single-qubit rotation up to precision $\epsilon$ be compiled in time $O(\log(1/\epsilon))$ (i.e., time strictly logarithmic and not polylog)?

Question 5

I recently noticed that some quantum computers supply native gate $$iSWAP_{\theta} = e^{-i \theta (XX + YY)}.$$ I wonder, how do I build a circuit for $$e^{-i \theta Z\otimes(XX + YY)}$$ Is this one ...

Question 6

What I'm looking for is something that takes a standard gate (simple paulis for example) and give its fusion based (FBQC) equivalent; this would be two sets of pauli strings on n qubits : the first ...

Question 7

I'm reading through this recent survey paper and on page 18 it states that "every quantum circuit can be transformed into a canonical form : product of (clifford gate)* ($\pi/8$ pauli-product ...

Question 8

Given a stabilizer code, there are several ways to transform it to an equivalent code (same n,k,d). The "standard form" is one option and it seems to have lower CX and CZ gate count needed ...

Question 9

Let $U$ be a unitary operator acting on $d$ qubits constructed by taking tensor products of single-qubit rotation gates. Let $C^nU$ denote a controlled-$U$ operation, where the control is implemented ...

Question 10

Clifford+Toffoli+M is a universal gate set. What's a cheap way to approximately (or exactly) get a T state using this gate set? I know that once I have a T state I can catalyze more very easily, but ...

Question 11

I know that a Givens rotation is the product of a $X\otimes X$ and a $Y\otimes Y$ rotation. Each Pauli string rotation can be reduced to a single qubit rotation (see Fig. 2 in [1] or Fig 12. in [2] ...

Question 12

I have a quantum computer that cannot implement the gate $U$ by itself, and needs help in the form of a magic state $|U\rangle$ held in another register. Is there a general-purpose procedure for ...

Question 13

I want to create a gate that, given a sequence of qbits that encode n, transforms that sequence in n+1, in other words the successor function. I managed to do it in qiskit by writing this: ...

Question 14

Consider the unitary matrix $A \in \mathbb{R}^{n^2\times n^2}$ which has only the first $n$ rows explicitly defined, with the remaining rows having some flexibility. $A$ can be written in block form ...

Question 15

There are (at least) two conventions for single-qubit, arbitrary-angle Z rotations in quantum computing, which I will call Rz(theta) and Z^t. $$ R_Z(\theta) = \exp(-i \theta Z/2) = \mathrm{diag}(e^{-i ...

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Questions tagged [gate-synthesis]

How to implement $U|i\rangle=|2^i\rangle$ without ancilla qubits?

Is this a correct DAG from parsing QASM?

Is there a more efficient/better way to prepare the History-State using poly(n)-depth circuit?

Synthesis of single-qubit rotation in time $O(\log(1/\epsilon))$

What is the circuit for $e^{-i \theta Z\otimes (X X + Y Y)}$?

Are there tools to generate fusion based (FBQC) gates

does every quantum circuit have a "canonical form"

does the standard form of a stabilizer code minimize the number of CX/CZ gates needed to encode it?

Depth and Width Bounds for Controlled Unitaries in Quantum Circuits

Short way to create a good |T> state using Clifford+Toffoli+M

Can an arbitrary angle Givens rotation be implemented with a single arbitrary angle 1-qubit rotation?

Procedure for constructing magic state gate injection gadgets

Simple successor gate

Can I efficiently decompose this flexible unitary matrix into 1 and 2 qubit gates?

Is Controlled$(R_z(\theta))$ more expensive than Controlled$(Z^t)$ on the surface code?

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