We present a two-dimensional classical stochastic differential equation for a displacement field of a point particle in two dimensions and show that its components define real and imaginary parts of a complex field satisfying the Schroedinger equation of a harmonic oscillator. In this way we derive the discrete oscillator spectrum from classical dynamics. The model is then generalized to an arbitrary potential. This opens up the possibility of efficiently simulating quantum computers with the help of classical systems.
Universal quantum computers are the only general purpose quantum computers known that can be implemented as of today. These computers consist of a classical memory component which controls the quantum memory. In this paper, the space complexity of some data stream problems, such as PartialMOD and Equality, is investigated on universal quantum computers. The quantum algorithms for these problems are believed to outperform their classical counterparts. Universal quantum computers, however, need classical bits for controlling quantum gates in addition to qubits. Our analysis shows that the number…
Quantum Computers Speed Up Classical with Probability Zero
令$f$表示关于字的长度保持函数。经典算法可以被认为是表示$f$的黑盒的$T$迭代应用，从长度为$n$的输入字$x$开始。证明了如果随机选择$T=O(2^{n/(7+e)}), e >0$和$f$，则每个量子计算机以概率1需要对$f$进行不少于$T$次的计算，以获得经典计算的结果.这意味着允许量子加速的经典算法集的概率测度为零。第二个结果是，对于以概率1随机选择的任意经典时间复杂度$T$和$f$，经典计算的每个量子模拟至少需要$f$的$Ω(\sqrt {T})$评估。
Quantum inspired protocols e.g. [AAV13,AG17] attempt to achieve a single-prover interactive protocol where a classical machine can verify quantum computations in an information-theoretically secure manner. We define a family of protocols which seem natural for verifying quantum computations and generalizes such known protocols, namely those of [AAV13,AG17]. We show that any protocol from this family is bound to require an extremely powerful prover, much like the classical protocols of [LFKN92] and [Sha92]. Using our analysis, we also hint at possible ways one might try to realize a protocol wh…
In this article we describe a technique to transfer data from classical domain to quantum domain. We consider a set of $N (=2^n)$ classical data in the form of a column matrix and prepare a $n$-qubit quantum state, whose components correspond to the $N$ classical data. To prepare this $n$-qubit quantum vector we use Schmidt decomposition and singular value decomposition techniques respectively and construct the corresponding family of quantum circuits. To strengthen our argument we also give specific examples by considering a set of 4 and 16 classical data and constructing the corresponding 2 …
Quantum computing is an emerging field of science which will eventually lead us to new and powerful logic devices with capabilities far beyond the limits of current transistor-based technology. There are certain types of problems which quantum computers can solve fundamentally faster than the tradition digital computers. There are quantum algorithms which require both superposition and entanglement (e.g. Shor algorithm). But neither the Grover algorithm nor the very first quantum algorithm due to Deutsch and Jozsa need entanglement. Is it possible to utilize classical wave superposition to spe…
In the effort to develop useful quantum computers simulating quantum machines with conventional computing resources is a key capability. Such simulations will always face limits preventing the emulation of quantum computers of substantial scale but by pushing the envelope as far as possible through optimal choices of algorithms and hardware the value of the simulator tool is maximized. This work reviews the state-of-the-art numerical simulation methods i.e. the classical algorithms that emulate quantum computer evolution under specific operations. We focus on the mainstream state-vector and te…
In this paper we present a novel approach to emulating a universal quantum computer with a classical system, one that uses a signal of bounded duration and amplitude to represent an arbitrary quantum state. The signal may be of any modality (e.g., acoustic, electromagnetic, etc), but we focus our discussion here on electronic signals. Unitary gate operations are performed using analog electronic circuit devices, such as four-quadrant multipliers, operational amplifiers, and analog filters, although non-unitary operations may be performed as well. In this manner, the Hilbert space structure of …
This paper describes a novel approach to emulate a universal quantum computer with a wholly classical system, one that uses a signal of bounded duration and amplitude to represent an arbitrary quantum state. The signal may be of any modality (e.g. acoustic, electromagnetic, etc.) but this paper will focus on electronic signals. Individual qubits are represented by in-phase and quadrature sinusoidal signals, while unitary gate operations are performed using simple analog electronic circuit devices. In this manner, the Hilbert space structure of a multi-qubit quantum state, as well as a universa…
Investigating student interpretations of the differences between classical and quantum computers: Are quantum computers just analog classical computers?
Comments on `Stable Quantum Computation of Unstable Classical Chaos,' `Efficient Quantum Computing Insensitive to Phase Errors,' and `Quantum Computer Inverting Time Arrow for Macroscopic Systems'
最近，论文B。乔治和D.L. Shepelyansky，Phys. Rev. 86_，5393（2001）中提出的[C. Zalka，quant-ph/0110019; L. Di'osi，quant-ph/0110026]。这封信声称，当在量子计算机上执行Arnold猫映射下的相空间密度演化时，误差敏感性将呈指数级加速和降低。一方面，有些观点以前的答复者尚未提出。另一方面，作者的反应[quant-ph/0110142]提出了新的问题。本说明述及这两个问题。
Quantum Computer Can Not Speed Up Iterated Applications of a Black Box
让一个经典的算法是由执行该算法的一个步骤的黑盒的顺序应用程序确定。如果我们把这个黑盒看作一个预言机，它为任何查询a给出一个值F（a），我们可以在一台经典计算机上计算T个F在时间T上相对于这个预言机的顺序应用。证明了当T=O（2^{n/7}），其中n为输入长度时，F的T个顺序应用的结果不能在具有Oracle for F的量子计算机上以比时间Ω（T）更快的速度计算.这意味着没有一种量子加速经典算法的通用方法，在这种通用方法中，经典算法被视为给定黑盒的迭代应用。对于任意的时间复杂度T，量子模拟的时间下限为Ω（T^{1/2}）.
Magic states are the resource that allows quantum computers to attain an advantage over classical computers. This resource consists in the deviation from a property called stabilizerness which in turn implies that stabilizer circuits can be efficiently simulated on a classical computer. Without magic, no quantum computer can do anything that a classical computer cannot do. Given the importance of magic for quantum computation, it would be useful to have a method for measuring the amount of magic in a quantum state. In this work, we propose and experimentally demonstrate a protocol for measurin…
We introduce QRDM-NEVPT2: a hybrid quantum-classical implementation of strongly-contracted N-electron Valence State $2^{nd}$-order Perturbation Theory (SC-NEVPT2), in which the Complete Active Space Configuration Interaction (CASCI) step, capturing static correlation effects, is replaced by a simulation performed on a quantum computer. Subsequently, n-particle Reduced Density Matrices (n-RDMs) measured on a quantum device are used directly in a classical SC-NEVPT2 calculation, which recovers remaining dynamic electron correlation effects approximately. We also discuss the use of the cumulant e…
An accurate assessment of how quantum computers can be used for chemical simulation, especially their potential computational advantages, provides important context on how to deploy these future devices. In order to perform this assessment reliably, quantum resource estimates must be coupled with classical simulations attempting to answer relevant chemical questions and to define the classical simulation frontier. Herein, we explore the quantum and classical resources required to assess the electronic structure of cytochrome P450 enzymes (CYPs) and thus define a classical-quantum advantage bou…
