Related papers: Classical programmability is enough for quantum ci…
Quantum computers and quantum algorithms have made great strides in the last few years and promise improvements over classical computing for specific tasks. Although the current hardware is not yet ready to make real impacts at the time of…
Understanding the boundary between classical simulatability and the power of quantum computation is a fascinating topic. Direct simulation of noisy quantum computation requires solving an open quantum many-body system, which is very costly.…
Quantum computers are poised to radically outperform their classical counterparts by manipulating coherent quantum systems. A realistic quantum computer will experience errors due to the environment and imperfect control. When these errors…
Recently an algorithm has been constructed that shows the binary icosahedral group $\2I$ together with a $T$-like gate forms the most efficient single-qubit universal gate set. To carry out the algorithm fault tolerantly requires a code…
Universal approximation theorems are the foundations of classical neural networks, providing theoretical guarantees that the latter are able to approximate maps of interest. Recent results have shown that this can also be achieved in a…
This research applies concepts from algorithmic probability to Boolean and quantum combinatorial logic circuits. A tutorial-style introduction to states and various notions of the complexity of states are presented. Thereafter, the…
Instead of producing quantum languages that are fit for current quantum computers, we build a language from standard classical assembler and augment it with quantum capabilities so that quantum algorithms become a subset of it. This paves…
A quantum computer consists of a set of quantum bits upon which operations called gates are applied to perform computations. In order to perform quantum algorithms, physicists would like to design arbitrary gates to apply to quantum bits.…
It is well known that a quantum circuit on $N$ qubits composed of Clifford gates with the addition of $k$ non Clifford gates can be simulated on a classical computer by an algorithm scaling as $\text{poly}(N)\exp(k)$[1]. We show that, for a…
The Gottesman-Knill theorem asserts that quantum circuits composed solely of Clifford gates can be efficiently simulated classically. This theorem hinges on the fact that Clifford gates map Pauli strings to other Pauli strings, thereby…
In this work, we study distributions of unitaries generated by random quantum circuits containing only symmetry-respecting gates. We develop a unified approach applicable to all symmetry groups and obtain an equation that determines the…
Quantum computers promise to efficiently solve important problems classical computers never will. However, in order to capitalize on these prospects, a fully automated quantum software stack needs to be developed. This involves a multitude…
A formalism is developed for describing approximate classical behaviour in finite (but possibly large) quantum systems. This is done in terms of a structure common to classical and quantum mechanics, viz. a Poisson space with a transition…
We define and construct efficient depth-universal and almost-size-universal quantum circuits. Such circuits can be viewed as general-purpose simulators for central classes of quantum circuits and can be used to capture the computational…
The architecture of circuital quantum computers requires computing layers devoted to compiling high-level quantum algorithms into lower-level circuits of quantum gates. The general problem of quantum compiling is to approximate any unitary…
Uniformly controlled one-qubit gates are quantum gates which can be represented as direct sums of two-dimensional unitary operators acting on a single qubit. We present a quantum gate array which implements any n-qubit gate of this type…
A proof that continuous time quantum walks are universal for quantum computation, using unweighted graphs of low degree, has recently been presented by Childs [PRL 102 180501 (2009)]. We present a version based instead on the discrete time…
We have shown that quantum systems on finite-dimensional Hilbert spaces are equivalent under local transformations. Using these transformations give rise to a gauge group that connects the hamiltonian operators associated with each quantum…
Quantifying quantum states' complexity is a key problem in various subfields of science, from quantum computing to black-hole physics. We prove a prominent conjecture by Brown and Susskind about how random quantum circuits' complexity…
The correspondence between the integrability of classical mechanical systems and their quantum counterparts is not a 1-1, although some close correspondencies exist. If a classical mechanical system is integrable with invariants that are…