Beyond Ansätze: Learning Quantum Circuits as Unitary Operators
This paper explores the advantages of optimizing quantum circuits on $N$ wires as operators in the unitary group $U(2^N)$. We run gradient-based optimization in the Lie algebra $\mathfrak u(2^N)$ and use the exponential map to parametrize unitary matrices. We argue that $U(2^N)$ is not only more general than the search space induced by an ansatz, but in ways easier to work with on classical computers. The resulting approach is quick, ansatz-free and provides an upper bound on performance over all ans\"atze on $N$ wires.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Structured Unitary Tensor Network Representations for Circuit-Efficient Quantum Data Encoding
Encoding classical data into quantum states is a central bottleneck in quantum machine learning: many widely used encodings are circuit-inefficient, requiring deep circuits and substantial quantum resources, which limits…
Quantum Machine LearningArchitectures and random properties of symplectic quantum circuits
Parametrized and random unitary (or orthogonal) $n$-qubit circuits play a central role in quantum information. As such, one could naturally assume that circuits implementing symplectic transformation would attract simila…
Gaussian ProcessesLearning unitaries with quantum statistical queries
We propose several algorithms for learning unitary operators from quantum statistical queries (QSQs) with respect to their Choi-Jamiolkowski state. Quantum statistical queries capture the capabilities of a learner with l…
Quantum Machine LearningParameterized quantum comb and simpler circuits for reversing unknown qubit-unitary operations
Quantum combs play a vital role in characterizing and transforming quantum processes, with wide-ranging applications in quantum information processing. However, obtaining the explicit quantum circuit for the desired quan…
Quantum Machine LearningSuper Quantum Mechanics
We introduce Super Quantum Mechanics (SQM) as a theory that considers states in Hilbert space subject to multiple quadratic constraints. Traditional quantum mechanics corresponds to a single quadratic constraint of wavef…