Related papers: Efficient quantum circuits for high-dimensional re…
This thesis presents an efficient quantum algorithm and explicit circuits for generating eigenstates of arbitrary SU(2) and SU(3) representations. These include a wide variety of highly entangled states. The algorithm uses Schur transform…
We present an efficient family of quantum circuits for a fundamental primitive in quantum information theory, the Schur transform. The Schur transform on n d-dimensional quantum systems is a transform between a standard computational basis…
The design of efficient quantum circuits is an important issue in quantum computing. It is in general a formidable task to find a highly optimized quantum circuit for a given unitary matrix. We propose a quantum circuit design method that…
Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum…
Geometric phases induced in quantum evolutions have built-in noise-resilient characters, and thus can find applications in many robust quantum manipulation tasks. Here, we propose a feasible and fast scheme for universal quantum computation…
We discuss efficient quantum logic circuits which perform two tasks: (i) implementing generic quantum computations and (ii) initializing quantum registers. In contrast to conventional computing, the latter task is nontrivial because the…
We propose a method for the efficient quantum simulation of fermionic systems with superconducting circuits. It consists in the suitable use of Jordan-Wigner mapping, Trotter decomposition, and multiqubit gates, be with the use of a quantum…
Qutrit offers the potential for enhanced quantum computation by exploiting an enlarged Hilbert space. However, the synthesis of high-fidelity and fast qutrit gates, particularly for single qutrit, remains an ongoing challenge, as it…
We extend quantum circuit cutting to heterogeneous registers comprising mixed-dimensional qudits. By decomposing non-local interactions into tensor products of local generalised Gell-Mann matrices, we enable the simulation and execution of…
In the age of noisy quantum processors, the exploitation of quantum symmetries can be quite beneficial in the efficient preparation of trial states, an important part of the variational quantum eigensolver algorithm. The benefits include…
Quantum control in large dimensional Hilbert spaces is essential for realizing the power of quantum information processing. For closed quantum systems the relevant input/output maps are unitary transformations, and the fundamental challenge…
Quantum computation offers the potential to solve fundamental yet otherwise intractable problems across a range of active fields of research. Recently, universal quantum-logic gate sets - the building blocks for a quantum computer - have…
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…
Representations of quantum computations are almost always based on a tensor product $\otimes$-structure. This coincides with what we are able to execute in our experiments, as well as what we observe in Nature, but it makes certain familiar…
Non-Hermitian (NH) quantum systems demonstrate striking differences from their Hermitian counterparts, leading to claims of NH advantage in areas ranging from metrology to entanglement generation. We show that in the context of quantum…
We show that higher-dimensional versions of qubits, or qudits, can be encoded into spin systems and into harmonic oscillators, yielding important advantages for quantum computation. Whereas qubit-based quantum computation is adequate for…
Large scale quantum computing is highly anticipated, and quantum circuit design automation needs to keep up with the transition from small scale to large scale problems. Methods to support fast quantum circuit manipulations (e.g.~gate…
Because of the importance of unitarity in quantum physics, work on the representations of the de Sitter group has focussed on the unitary case, which necessarily means infinite dimensional matrices for this non-compact group. Here we…
Modeling non-Hermitian Hamiltonians is increasingly important in classical and quantum domains, especially when studying open systems, $PT$ symmetry, and resonances. However, the quantum simulation of these models has been limited by the…
We present a novel set of reversible modular multipliers applicable to quantum computing, derived from three classical techniques: 1) traditional integer division, 2) Montgomery residue arithmetic, and 3) Barrett reduction. Each multiplier…