Related papers: Optimal T depth quantum circuits for implementing …
Random quantum circuits are a central concept in quantum information theory with applications ranging from demonstrations of quantum computational advantage to descriptions of scrambling in strongly-interacting systems and black holes. The…
In this paper, we investigate an approach to circuit lower bounds via bounded width circuits. The approach consists of two steps: (i) We convert circuits to (deterministic or nondeterministic) bounded width circuits. (ii) We prove lower…
Quantum Error Correction (QEC) is the cornerstone of practical Fault-Tolerant Quantum Computing (FTQC), but incurs enormous resource overheads. Circuits must decompose into Clifford+T gates, and the non-transversal T gates demand costly…
The efficient execution of fault-tolerant quantum algorithms is fundamentally limited by the production rate of magic states required for non-Clifford operations. While circuit optimization typically targets T-depth, static T-depth does not…
Electronic structure simulation is an anticipated application for quantum computers. Due to high-dimensional quantum entanglement in strongly correlated systems, the quantum resources required to perform such simulations are far beyond the…
The aim of this paper is to build quantum circuits that implement discrete-time quantum walks having an arbitrary position-dependent coin operator. The position of the walker is encoded in base 2: with $n$ wires, each corresponding to one…
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…
Quantum computing has gained attention in recent years due to the significant progress in quantum computing technology. Today many companies like IBM, Google and Microsoft have developed quantum computers and simulators for research and…
Standard quantum amplitude estimation algorithms provide quadratic speedup to Monte-Carlo simulations but require a circuit depth that scales as inverse of the estimation error. In view of the shallow depth in near-term devices, the…
Implementing quantum algorithms on realistic hardware requires translating high-level global operations into sequences of native elementary gates, a process known as quantum compiling. Physical limitations, such as constraints in…
In this paper, we show that for every constant $0 < \epsilon < 1/2$ and for every constant $d \geq 2$, the minimum size of a depth $d$ Boolean circuit that $\epsilon$-approximates Majority function on $n$ variables is…
The quantum Toffoli gate allows universal reversible classical computation. It is also an important primitive in many quantum circuits and quantum error correction schemes. Here we demonstrate the realization of a Toffoli gate with three…
Quantum state preparation, also known as encoding or embedding, is a crucial initial step in many quantum algorithms and often constrains theoretical quantum speedup in fields such as quantum machine learning and linear equation solvers.…
Clique problem has a wide range of applications due to its pattern matching ability. There are various formulation of clique problem like $k$-clique problem, maximum clique problem, etc. The $k$-Clique problem, determines whether an…
We examine the number T of queries that a quantum network requires to compute several Boolean functions on {0,1}^N in the black-box model. We show that, in the black-box model, the exponential quantum speed-up obtained for partial functions…
The Toffoli gate serving as a basic building block for reversible quantum computation, has manifested its great potentials in improving the error-tolerant rate in quantum communication. While current route to the creation of Toffoli gate…
A variety of quantum algorithms employ Pauli operators as a convenient basis for studying the spectrum or evolution of Hamiltonians or measuring multi-body observables. One strategy to reduce circuit depth in such algorithms involves…
In fault-tolerant quantum circuit synthesis, T gates supplied via magic states dominate space-time cost, while Clifford gates incur negligible overhead. Conventional flows minimize AND count in an {XOR, AND, NOT} basis as a proxy for T,…
We study a natural complexity measure of Boolean functions known as the rational degree. Denoted $\textrm{rdeg}(f)$, it is the minimal degree of a rational function that is equal to $f$ on the Boolean hypercube. For total functions $f$, it…
We show that the depth of quantum circuits in the realistic architecture where a classical controller determines which local interactions to apply on the kD grid Z^k where k >= 2 is the same (up to a constant factor) as in the standard…