Related papers: Sequential quantum processes with group symmetries
Group theory is extremely successful in characterizing the symmetries in quantum systems, which greatly simplifies and unifies our treatments of quantum systems. Here we introduce the concept of the symmetry for a quantum Boltzmann machine…
Quantum error correction and symmetries play central roles in quantum information science and physics. It is known that quantum error-correcting codes that obey (are covariant with respect to) continuous symmetries in a certain sense cannot…
Resource-efficient and high-precision approximate synthesis of quantum circuits expressed in the Clifford+T gate set is vital for Fault-Tolerant quantum computing. Efficient optimal methods are known for single-qubit RZ unitaries, otherwise…
The recent proposal (M Planat and M Kibler, Preprint 0807.3650 [quantph]) of representing Clifford quantum gates in terms of unitary reflections is revisited. In this essay, the geometry of a Clifford group G is expressed as a BN-pair, i.e.…
Optimal control techniques are applied for the decomposition of unitary quantum operations into a sequence of single-qubit gates and entangling operations. To this end, we modify a gradient-ascent algorithm developed for systems of coupled…
What is the structure of general quantum processes on composite systems that respect a global or local symmetry principle? How does the irreversible use of quantum resources behave under such symmetry principles? Here we employ an…
A novel family of exactly solvable quantum systems on curved space is presented. The family is the quantum version of the classical Perlick family, which comprises all maximally superintegrable 3-dimensional Hamiltonian systems with…
The problem of discriminating between many quantum channels with certainty is analyzed under the assumption of prior knowledge of algebraic relations among possible channels. It is shown, by explicit construction of a novel family of…
Practical success of quantum learning models hinges on having a suitable structure for the parameterized quantum circuit. Such structure is defined both by the types of gates employed and by the correlations of their parameters. While much…
For a symmetric positive semidefinite linear system of equations $\mathcal{Q} {\bf x} = {\bf b}$, where ${\bf x} = (x_1,\ldots,x_s)$ is partitioned into $s$ blocks, with $s \geq 2$, we show that each cycle of the classical block symmetric…
We develop an efficient algorithm for determining optimal adaptive quantum estimation protocols with arbitrary quantum control operations between subsequent uses of a probed channel. We introduce a tensor network representation of an…
We study classical structures in various categories of completely positive morphisms: on sets and relations, on cobordisms, on a free dagger compact category, and on Hilbert spaces. As an application, we prove that quantum maps with…
The quantum circuit model essentially treats every quantum algorithm as a straight-line program. While this view is universal, recent work has shown that it is inconvenient for using different-length quantum subroutines in superposition.…
Identifying symmetries in quantum dynamics, such as identity or time-reversal invariance, is a crucial challenge with profound implications for quantum technologies. We introduce a unified framework combining group representation theory and…
Quantum signal processing and quantum singular value transformation are powerful tools to implement polynomial transformations of block-encoded matrices on quantum computers, and has achieved asymptotically optimal complexity in many…
An arbitrary lossless transformation in high-dimensional quantum space can be decomposed into elementary operations which are easy to implement, and an effective decomposition algorithm is important for constructing high-dimensional…
From the set of operators for errors and its correction code, we introduce the so-called complete unitary transformation. It can be used for encoding while the inverse of it can be applied for correcting the errors of the encoded qubit. We…
The two-qubit canonical decomposition SU(4) = [SU(2) \otimes SU(2)] Delta [SU(2) \otimes SU(2)] writes any two-qubit quantum computation as a composition of a local unitary, a relative phasing of Bell states, and a second local unitary.…
Linear combination of unitaries (LCU for short) is one of the most important techniques in designing quantum algorithms. In this paper, we propose a new quantum algorithm in three different forms to achieve LCU. Different from previous…
In the context of $p$-adic quantum mechanics, we investigate composite systems of $p$-adic qubits and $p$-adically controlled quantum logic gates. We build on the notion of a single $p$-adic qubit as a two-dimensional irreducible…