# Questions tagged [solovay-kitaev-algorithm]

For questions about the Solovay-Kitaev theorem (and algorithm), a proof that quantum computers can efficiently simulate any 1-qubit quantum gate using a restricted set of quantum gates, as well as the generalisation allowing for the efficient creation of gates with some arbitrarily number of dimensions.

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### a question about quantum gate decomposition on simulator or emulator

I have read a paper about "approximated decomposition" of a unitary single gate (Solovay-Kitaev algorithm) which told us a any unitary single gate can be decomposed into {Hadamard, Phase} with any ...
83 views

### Understanding the length of the sequence obtained via Solovay-Kitaev decomposition

I have downloaded two codes of SK algorithm from GitHub and try to understand how to decompose a unitary single qubit gate. These code are https://github.com/DEBARGHYA4469/Quantum-Compiler and https:/...
75 views

### Why is phase gate a member of universal gate set?

According to Solovay-Kitaev theorem it is possible to approximate any unitary quantum gate by sequence of gates from small set of another gates. The approximation can be done with an arbitrary ...
40 views

### Is there an analog for the Solovay-Kitaev Theorem for approximating quantum states?

The Solovay-Kitaev theorem shows that we can approximate arbitrary unitary transformations with polynomially many quantum gates. Can we approximate the resulting state vectors in the same way by ...
130 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 ...
102 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 ...
198 views

### Status of software packages for quantum compiling

By "quantum compiling", what I mean is classical algorithms to solve the following problem: given a $SU(D)$ matrix $U$ (the goal) and a set of $SU(D)$ unitary matrices $V_1 \cdots V_N$ (the gates), ...
1k views

### Approximating unitary matrices

I currently have 2 unitary matrices that I want to approximate to a good precision with the fewer quantum gates possible. In my case the two matrices are: The square root of NOT gate (up to a global ...
170 views

### Does the GLOA have any advantage over the Solovay-Kitaev algorithm?

The Solvay Kitaev algorithm was discovered long before the Group Leaders Optimization algorithm and it has some nice theoretical properties. As far as I understand, both have exactly the same goals: ...
313 views

### Number of gates required to approximate arbitrary unitaries

If I understand correctly, there must exist unitary operations that can be approximated to a distance $\epsilon$ only by an exponential number of quantum gates and no less. However, by the Solovay-...