相关论文: The Quantum Schur Transform: I. Efficient Qudit Ci…
All quantum gates with one and two qubits may be described by elements of $Spin$ groups due to isomorphisms $Spin(3) \simeq SU(2)$ and $Spin(6) \simeq SU(4)$. However, the group of $n$-qubit gates $SU(2^n)$ for $n > 2$ has bigger dimension…
The quantum Fourier transform (QFT) is a powerful tool in quantum computing. The main ingredients of QFT are formed by the Walsh-Hadamard transform H and phase shifts P(.), both of which are 2x2 unitary matrices as operators on the…
There are various gate sets that can be used to describe a quantum computation. A particularly popular gate set in the literature on quantum computing consists of arbitrary single-qubit gates and 2-qubit CNOT gates. A CNOT gate is however…
Many quantum information tasks use inputs of the form $\rho^{\otimes m}$, which naturally induce permutation and unitary symmetries. We classify all quantum channels that respect both symmetries - i.e. unitary-equivariant and…
Qudit is a multi-level computational unit alternative to the conventional 2-level qubit. Compared to qubit, qudit provides a larger state space to store and process information, and thus can provide reduction of the circuit complexity,…
The Quantum Fourier Transform (QFT) is required by hidden subgroup problem (HSP) algorithms, including Shor's algorithm for factoring. The circuit depth of the QFT remains challenging for near-term hardware. To find shallower alternatives…
Quantum noise in real-world devices poses a significant challenge in achieving practical quantum advantage, since accurately compiled and executed circuits are typically deep and highly susceptible to decoherence. To facilitate the…
Transversal gates are logical gate operations on encoded quantum information that are efficient in gate count and depth, and are designed to minimize error propagation. Efficient encoding circuits for quantum codes that admit transversal…
The Quantum Fourier transform (QFT) is a key ingredient in most quantum algorithms. We have compared various spin-based quantum computing schemes to implement the QFT from the point of view of their actual time-costs and the accuracy of the…
We show that several quantum circuit families can be simulated efficiently classically if it is promised that their output distribution is approximately sparse i.e. the distribution is close to one where only a polynomially small, a priori…
We address the question of efficient implementation of quantum protocols, with small communication and entanglement, and short depth circuit for encoding or decoding. We introduce two new methods to achieve this, the first method involving…
The Quantum Fourier Transform (QFT) is a key component of many important quantum algorithms, most famously as being the essential ingredient in Shor's algorithm for factoring products of primes. Given its remarkable capability, one would…
Each year, the gap between theoretical proposals and experimental endeavours to create quantum computers gets smaller, driven by the promise of fundamentally faster algorithms and quantum simulations. This occurs by the combination of…
Classical simulators play a major role in the development and benchmark of quantum algorithms and practically any software framework for quantum computation provides the option of running the algorithms on simulators. However, the…
Quantum information processing has witnessed significant advancements through the application of qubit-based techniques within universal gate sets. Recently, exploration beyond the qubit paradigm to $d$-dimensional quantum units or qudits…
Simulating large-scale coupled-oscillator systems presents substantial computational challenges for classical algorithms, particularly when pursuing first-principles analyses in the thermodynamic limit. Motivated by the quantum algorithm…
Quantum computers require quantum logic, something fundamentally different to classical Boolean logic. This difference leads to a greater efficiency of quantum computation over its classical counter-part. In this review we explain the basic…
We study representation theory of the partially transposed permutation matrix algebra, a matrix representation of the diagrammatic walled Brauer algebra. This algebra plays a prominent role in mixed Schur-Weyl duality that appears in…
Random quantum circuits are commonly viewed as hard to simulate classically. In some regimes this has been formally conjectured, and there had been no evidence against the more general possibility that for circuits with uniformly random…
Quantum computing has the potential to solve many complex algorithms in the domains of optimization, arithmetics, structural search, financial risk analysis, machine learning, image processing, and others. Quantum circuits built to…