All Questions
Tagged with gate-synthesis universal-gates
30 questions
0
votes
1
answer
48
views
Is it possible to exactly compile Toffoli using H and CSWAP gates and ancilla qubits?
Question:
Given controlled-SWAP (CSWAP) and Hadamard (H) gates, is it possible to exactly compile the Toffoli (CCX) gate?
Note that I'm not looking for an encoded Toffoli gate. The answer should ...
- 551
1
vote
0
answers
40
views
Qiskit not efficiently compiling with new gate basis
I am using Qiskit to compile a small Qiskit circuit (shown below) with a gate basis consisting of Rigetti native gates:
RZ
...
0
votes
1
answer
158
views
Is there a tool to decompose 4-Qubit unitaries (aka 16x16 matrices)?
I was wondering if there is a tool that can decompose such a matrix in gates on 4 qubits?
I found one for 3-qubit gates (9x9 matrices) in Cirq but nothing for bigger matrices.
(The matrix is not ...
- 105
6
votes
1
answer
232
views
Universality with Toffoli + Hadamard
If I take the two gates Hadamard and Toffoli, then it is clear that I cannot simulate an arbitrary $n$ qubit unitary on $n$ qubits because both matrices are real, so there's no access to the complex ...
- 61.7k
1
vote
2
answers
1k
views
How to construct common classical gates with CNOT circuit?
How can I construct AND, OR, NAND, NOR with CNOT gates.
First off, this other question describes how to make them with matrices.
Theoretically I can construct all those gates already. I know how to ...
- 113
0
votes
1
answer
123
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Implementing Odd Permutations Without Ancilla Bit
The paper says that
The inversion $\alpha \mapsto \alpha^{-1} $ (where 0 is mapped to 0)
can be seen as a permutation on $\mathbb F_{256}$. This permutation is odd, while
quantum circuits with NOT, ...
- 1
4
votes
0
answers
100
views
What is the correct name of this quantum gate? Possibly state control gate
Let $\vec v \in \mathbb{C}^2 $ be the following quantum state:
$$
\vec v = \frac{1}{\sqrt{2}}\begin{bmatrix}
v_{1} \\
v_{2} \\
\end{bmatrix},\space \lvert v_1 \rvert = 1,...
- 41
2
votes
1
answer
85
views
Decompose bell measurement gate into combination of controlled-not gates and one-qubit gates
OPENQASM2.0 has only one two-qubit gate: controlled not. For a teleportation experiment, I need to perform a measurement in the Bell basis. That is, I need a two-qubit gate with matrix representation
$...
- 701
8
votes
1
answer
769
views
Is the Solovay-Kitaev theorem relevant for modern hardware?
The Solovay-Kitaev theorem (and more recent improvements) explains how to efficiently compile any 2-qubit unitary into any universal (dense) finite set of gates. My question is if this theorem is ...
- 1,695
4
votes
1
answer
169
views
Universality for reversible classical computation
Is there any way to check whether a set of gates (for example, take the set comprising of the CNOT gate and the Hadamard gate) is universal for reversible classical computation?
I can think of trial ...
- 1,515
3
votes
1
answer
471
views
How to create CNOT from an entangling gate and arbitrary single-qubit gates?
I am working on the classical simulation of quantum circuits. I know how to efficiently implement the following entangling gate, which -- in the following paper: https://arxiv.org/pdf/1803.02118 -- ...
2
votes
1
answer
97
views
Do we need to use an ancillary qubit when decomposing arbitrary $U(2^n)$ gates using Clifford+T universal gate sets?
As I know, we can decompose $U$ without ancilla if it's from special unitary group $SU(2^n)$. Do we need to use ancilla qubit on decomposing arbitrary $n$-qubit $U$ using Clifford+T universal gates ...
- 339
5
votes
2
answers
722
views
Are Toffoli gates actually used in designing quantum circuits?
In an actual quantum computer, are we designing circuits with Toffoli Gates and then using compilers or optimizers to remove redundancies so that we can use fewer qubits than a full Toffoli gates ...
- 651
2
votes
2
answers
410
views
How to construct a CU3 gate using only CX and U3 gates?
Knowing that CX and U3 (taking 3 parameters $\theta, \phi$ and $\lambda$) form a set of universal gates how can I construct an arbitrary CU3 gate using a decomposition of only CX and arbitrary U3 ...
- 45
7
votes
1
answer
435
views
What are the differences between the Toffoli and Fredkin gates (historical, practical, etc.)
I'm trying to understand the historical ordering and the practical differences between the Toffoli Gate and the Fredkin Gate.
Toffoli's February 1980 tech report MIT/LCS/TM-151 states:
Where ...
- 651
1
vote
0
answers
56
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How can I prove the universality of this set of gates?
I was reading this article. A brief explanation: Here we have a circuit, the registers are a stepfunction state, an single photon state and a function state. The first two have position operators $X$ ...
9
votes
3
answers
1k
views
How can I see, without math, the action of a gate in matrix form?
Suppose we have the Fredkin gate with
$$
F=
\left( {\begin{array}{cc}
1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 ...
- 878
1
vote
0
answers
931
views
How to implement controlled u3 gate from Qiskit using simpler gates?
I am trying to implement the u3 controlled gate (able to rotate the qubit in any specified direction in 3 dimensions if the control is 1, for two qubits) using simpler gates. The simpler gates ...
12
votes
1
answer
396
views
Sampling random circuits vs Solovay-Kitaev compiler
Suppose I want to obtain a gate sequence representing a particular 1 qubit unitary matrix.
The gate set is represented by a discrete universal set, e.g. Clifford+T gates or $\{T,H\}$ gates.
A well ...
- 141
4
votes
1
answer
197
views
Rewrite circuit with measurements with unitaries
In quantum physics, because of the no-cloning theorem, lots of classical proofs of cryptographic problems cannot be turned into quantum proofs (rewinding is usually not possible quantumly). A dream ...
- 676
2
votes
1
answer
907
views
What quantum gate is XNOR equivalent to?
The standard way to implement a reversible XOR gate is by means of a controlled-NOT gate or CNOT; this is the "standard quantum XOR operation". Physics.Stackexchange
Is there a "standard quantum XNOR ...
- 3,342
5
votes
1
answer
370
views
How can I decompose a gate into $\{\mathrm{CNOT}, \mathrm{H}, \mathrm{P}(\theta)\}$?
I am working with the set $\{\mathrm{CNOT}, \mathrm{H}, \mathrm{P}(\theta)\}$
where $\mathrm{H}$ is the Hadamard gate, and $\mathrm{P}(\theta)$ is the phase gate with angle $\theta$.
I want to build ...
- 313
26
votes
1
answer
1k
views
Explicit Conversion Between Universal Gate Sets
I'm interested in the conversion between different sets of universal gates. For example, it is known that each of the following sets is universal for quantum computation:
$\{T,H,\textrm{cNOT}\}$
$\{H,...
- 61.7k
7
votes
1
answer
631
views
Quantum XOR Linked List Construction
After getting help here with XNOR & RCA gates I decided to dive into XOR Swaps & XOR linked lists. I was able to find this explanation for quantum XOR Swapping which seems sufficient for the ...
- 3,342
6
votes
1
answer
785
views
Quantum Ripple Carry Adder Construction
There is an excellent answer to How do I add 1+1 using a quantum computer? that shows constructions of the half and full adders. In the answer, there is a source for the QRCA. I have also looked at ...
- 3,342
13
votes
2
answers
887
views
Quantum XNOR Gate Construction
Tried asking here first, since a similar question had been asked on that site. Seems more relevant for this site however.
It is my current understanding that a quantum XOR gate is the CNOT gate. Is ...
- 3,342
10
votes
2
answers
694
views
Shortest sequence of universal quantum gates that correspond to a given unitary
Question: Given a unitary matrix acting on $n$ qubits, can we find the shortest sequence of Clifford + T gates that correspond to that unitary?
For background on the question, two important ...
- 405
14
votes
2
answers
6k
views
Given a decomposition for a unitary $U$, how do you decompose the corresponding controlled unitary gate $C(U)$?
Suppose we have a circuit decomposition of a unitary $U$ using some universal gate set (for example CNOT-gates and single qubit unitaries). Is there a direct way to write down the circuit of the ...
- 2,457
19
votes
2
answers
2k
views
What is the mathematical justification for the "universality" of the universal set of quantum gates (CNOT, H, Z, X and π/8)?
In this answer I mentioned that the CNOT, H, X, Z and $\pi/8$ gates form a universal set of gates, which given in sufficient number of gates can get arbitrarily close to replicating any unitary ...
- 17.8k
15
votes
1
answer
480
views
How does approximating gates via universal gates scale with the length of the computation?
I understand that there is a constructive proof that arbitrary gates can be approximated by a finite universal gate set, which is the Solovay–Kitaev Theorem.
However, the approximation introduces an ...
- 2,457