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We define QSE, a symbolic execution framework for quantum programs by integrating symbolic variables into quantum states and the outcomes of quantum measurements. The soundness of QSE is established through a theorem that ensures the…
Quantum simulation is a potentially powerful application of quantum computing, holding the promise to be able to emulate interesting quantum systems beyond the reach of classical computing methods. Despite such promising applications, and…
Suppose $\boldsymbol{y}$ is a real random variable, and one is given access to ``the code'' that generates it (for example, a randomized or quantum circuit whose output is $\boldsymbol{y}$). We give a quantum procedure that runs the code…
We present an efficient quantum algorithm to simulate nonlinear differential equations with polynomial vector fields of arbitrary degree on quantum platforms. Models of physical systems that are governed by ordinary differential equations…
Stochastic processes play a fundamental role in physics, mathematics, engineering and finance. One potential application of quantum computation is to better approximate properties of stochastic processes. For example, quantum algorithms for…
Quantum parameter estimation promises a high-precision measurement in theory, however, how to design the optimal scheme in a specific scenario, especially under a practical condition, is still a serious problem that needs to be solved case…
We study the computation complexity of Boolean functions in the quantum black box model. In this model our task is to compute a function $f:\{0,1\}\to\{0,1\}$ on an input $x\in\{0,1\}^n$ that can be accessed by querying the black box.…
Variational Quantum Algorithms (VQAs) are expected to be promising algorithms with quantum advantages that can be run at quantum computers in the close future. In this work, we review simple rules in basic quantum circuits, and propose a…
We study minimum-error identification of an unknown single-bit Boolean function given black-box (oracle) access with one allowed query. Rather than stopping at an abstract optimal measurement, we give a fully constructive solution: an…
Quantum computing, an innovative computing system carrying prominent processing rate, is meant to be the solutions to problems in many fields. Among these realms, the most intuitive application is to help chemical researchers correctly…
New technologies such as Quantum-dot Cellular Automata (QCA), Single Electron Tunneling (SET), Tunneling Phase Logic (TPL) and all-spin logic (ASL) devices have been widely advocated in nanotechnology as a response to the physical limits…
The search task is one of the most difficult when it comes to execution speed, and reducing the latter is important both when working with large data and with small samples, if they need to be processed frequently and in a limited time.…
We propose a method for performing software pipelining on quantum for-loop programs, exploiting parallelism in and across iterations. We redefine concepts that are useful in program optimization, including array aliasing, instruction…
Quantum computers are promising tools for simulating many-body quantum systems due to their potential scaling advantage over classical computers. While significant effort has been expended on many-fermion systems, here we simulate a model…
Computer-aided engineering techniques are indispensable in modern engineering developments. In particular, partial differential equations are commonly used to simulate the dynamics of physical phenomena, but very large systems are often…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…
In this paper we propose a new approach to quantum neural networks. Our multi-layer architecture avoids the use of measurements that usually emulate the non-linear activation functions which are characteristic of the classical neural…
Boolean functions can be represented in many ways including logical forms, truth tables, and polynomials. Additionally, Boolean functions have different canonical representations such as minimal disjunctive normal forms. Other canonical…
With advances in quantum computing, researchers can now write and run many quantum programs. However, there is still a lack of effective methods for debugging quantum programs. In this paper, quantum symbolic execution (QSE) is proposed to…
We prove a general lower bound on the bounded-error entanglement-assisted quantum communication complexity of Boolean functions. The bound is based on the concept that any classical or quantum protocol to evaluate a function on distributed…