Related papers: Completeness for Prime-Dimensional Phase-Affine Ci…
In this paper, we study the affine phase retrieval problem, which aims to recover signals from the magnitudes of affine measurements. We develop second-order optimization methods based on Newton and Gauss-Newton iterations and establish…
In quantum computing the decoherence time of the qubits determines the computation time available and this time is very limited when using current hardware. In this paper we minimize the execution time (the depth) for a class of circuits…
High-efficiency quantum information processing is equivalent to the fewest quantum resources and the simplest operations by means of logic qubit gates. Based on the reflection geometry of a single photon interacting with a three-level…
By exploiting a symmetric scheme for coupling $N$ spin-1/2 constituents (the physical qubits) to states with total angular momentum $N/2-1$, we construct rotationally invariant logical qudits of dimension $d=N-1$. One can encode all qudit…
Although quantum circuits have been ubiquitous for decades in quantum computing, the first complete equational theory for quantum circuits has only recently been introduced. Completeness guarantees that any true equation on quantum circuits…
We present some basic integer arithmetic quantum circuits, such as adders and multipliers-accumulators of various forms, as well as diagonal operators, which operate on multilevel qudits. The integers to be processed are represented in an…
There is a bijection between odd prime dimensional qudit pure stabilizer states modulo invertible scalars and affine Lagrangian subspaces of finite dimensional symplectic $\mathbb{F}_p$-vector spaces. In the language of the stabilizer…
Affine forms are a common way to represent convex sets of $\mathbb{R}$ using a base of error terms $\epsilon \in [-1, 1]^m$. Quadratic forms are an extension of affine forms enabling the use of quadratic error terms $\epsilon_i \epsilon_j$.…
We introduce the first complete equational theory for quantum circuits. More precisely, we introduce a set of circuit equations that we prove to be sound and complete: two circuits represent the same unitary map if and only if they can be…
We introduce the qudit ZH-calculus and show how to generalise all the phase-free qubit rules to qudits. We prove that for prime dimensions d, the phase-free qudit ZH-calculus is universal for matrices over the ring Z[e^2(pi)i/d]. For…
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…
Current proposals for quantum compilers require the synthesis and optimization of linear reversible circuits and among them CNOT circuits. Since these circuits represent a significant part of the cost of running an entire quantum circuit,…
Quantum Compiling Algorithms decompose (exactly, without approximations) an arbitrary $2^\nb$ unitary matrix acting on $\nb$ qubits, into a sequence of elementary operations (SEO). There are many possible ways of decomposing a unitary…
We present a framework for the synthesis of phase polynomials that addresses both cases of full connectivity and partial connectivity for NISQ architectures. In most cases, our algorithms generate circuits with lower CNOT count and CNOT…
Qubits, which are quantum counterparts of classical bits, are used as basic information units for quantum information processing, whereas underlying physical information carriers, e.g. (artificial) atoms or ions, admit encoding of more…
Lithium niobate photonic circuits have the salutary property of permitting the generation, transmission, and processing of photons to be accommodated on a single chip. Compact photonic circuits such as these, with multiple components…
We introduce a complete equational theory for the fragment of quantum circuits generated by the real Clifford gates plus the two-qubit controlled-Hadamard gate. That is, we give a simple set of equalities between circuits of this fragment,…
Quantum computers are a revolutionary class of computational platforms with applications in combinatorial and global optimization, machine learning, and other domains involving computationally hard problems. While these machines typically…
Planar quadratic differential systems occur in many areas of applied mathematics. Although more than one thousand papers have been written on these systems, a complete understanding of this family is still missing. Classical problems, and…
Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional $N=2$ supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra.…