In this paper we present a new unified theoretical framework that describes the full dynamics of quantum computation. Our formulation allows any questions pertaining to the physical behavior of a quantum computer to be framed, and in principle, answered. We refer to the central organizing principle developed in this paper, on which our theoretical structure is based, as the *Quantum Computer Condition* (QCC), a rigorous mathematical statement that connects the irreversible dynamics of the quantum computing machine, with the reversible operations that comprise the quantum computation intended to be carried out by the quantum computing machine. Armed with the QCC, we derive a powerful result that we call the *Encoding No-Go Theorem*. This theorem gives a precise mathematical statement of the conditions under which fault-tolerant quantum computation becomes impossible in the presence of dissipation and/or decoherence. In connection with this theorem, we explicitly calculate a universal critical damping value for fault-tolerant quantum computation. In addition we show that the recently-discovered approach to quantum error correction known as "operator quantum error-correction" (OQEC) is a special case of our more general formulation. Our approach furnishes what we will refer to as "operator quantum fault-tolerance" (OQFT). In particular, we show how the QCC allows one to derive error thresholds for fault tolerance in a completely general context. We prove the existence of solutions to a class of time-dependent generalizations of the Lindblad equation. Using the QCC, we also show that the seemingly different circuit, graph- (including cluster-) state, and adiabatic paradigms for quantum computing are in fact all manifestations of a single, universal paradigm for all physical quantum computation.
We show that the time dependence of mean value of a physical quantity is related with the transition energies of a quantum system. In the case when the operator of a physical quantity anticommutes with the Hamiltonian of a system, studies of the evolution of its mean value allow determining the energy levels of the system. On the basis of the result, we propose a method for determining energy levels of physical systems on a quantum computer. The method opens a possibility to achieve quantum supremacy in solving the problem of finding minimal or maximal energy of Ising model with spatially anis…
A computational problem fed into a gate-model quantum computer identifies an objective function with a particular computational pathway (objective function connectivity). The solution of the computational problem involves identifying a target objective function value that is the subject to be reached. A bottleneck in a gate-model quantum computer is the requirement of several rounds of quantum state preparations, high-cost run sequences, and multiple rounds of measurements to determine a target (optimal) state of the quantum computer that achieves the target objective function value. Here, we …
One of the most promising applications of quantum computing is simulating quantum many-body systems. However, there is still a need for methods to efficiently investigate these systems in a native way, capturing their full complexity. Here, we propose variational quantum anomaly detection, an unsupervised quantum machine learning algorithm to analyze quantum data from quantum simulation. The algorithm is used to extract the phase diagram of a system with no prior physical knowledge and can be performed end-to-end on the same quantum device that the system is simulated on. We showcase its capab…
The field of quantum algorithms aims to find ways to speed up the solution of computational problems by using a quantum computer. A key milestone in this field will be when a universal quantum computer performs a computational task that is beyond the capability of any classical computer, an event known as quantum supremacy. This would be easier to achieve experimentally than full-scale quantum computing, but involves new theoretical challenges. Here we present the leading proposals to achieve quantum supremacy, and discuss how we can reliably compare the power of a classical computer to the po…
When a universal quantum computer is used by the public, it is assumed that it will be in the form of a quantum cloud server that exists in a few bases due to its cost. In this cloud server, privacy will be a crucial issue, and a blind quantum computation protocol will be necessary so that each user can use the server without the details of the calculations being revealed. It is also important to be able to verify that the server is performing calculations as instructed by the user, since quantum calculations cannot be verified by classical computation. In this paper, we put forward a protocol…
Physically Motivated Ansatz for Open Fermionic Systems on Quantum Computer
State Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China（中国科学技术大学精密与智能化学国家重点实验室）；Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）
An integrable anharmonic oscillator is presumably simulable by a classical computer and therefore by a quantum computer. An integrable anharmonic oscillator whose Hamiltonian is of normal type and quartic in the canonical coordinates is not quantizable. If, as argued here, quantum simulation of a finitely realizable classical physical system entails quantization of that system, then either there exist nonsimulable, integrable anharmonic oscillators or there are no obstructions to quantization by simulation. Simulation quantization implies further that any obstructions to quantization arise ent…
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 computers are emerging as a viable alternative to tackle certain computational problems that are challenging for classical computers. With the rapid development of quantum hardware such as those based on trapped ions, there is practical motivation for identifying risk management problems that are efficiently solvable with these systems. Here we focus on network partitioning as a means for analyzing risk in critical infrastructures and present a quantum approach for its implementation. It is based on the potential speedup quantum computers can provide in the identification of eigenvalue…
Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. Quantum computational algorithms have the potential to be an exciting new way of studying quantum cosmology. In quantum cosmology, we learn about the dynamics of the universe without constructing a complete theory of quantum gravity. Since the universal wavefunction exists in an infinite-dimensional superspace over all possible 3D metrics and modes of matter configurations, we take minisuperspaces for our work by constraining the degrees of freedom to particular 3D metrics and uni…
Solving for molecular excited states remains one of the key challenges of modern quantum chemistry. Traditional methods are constrained by existing computational capabilities, limiting the complexity of the molecules that can be studied or the accuracy of the results that can be obtained. Several quantum computing methods have been suggested to address this limitation. However, these typically have hardware requirements which may not be achieved in the near term. We propose a variational quantum machine learning based method to determine molecular excited states aiming at being as resilient as…
Although the current information revolution is still unfolding, the next industrial revolution is already rearing its head. A second quantum revolution based on quantum technology will power this new industrial revolution with quantum computers as its engines. The development of quantum computing will turn quantum theory into quantum technology, hence release the power of quantum phenomena, and exponentially accelerate the progress of science and technology. Building a large-scale quantum computing is at the juncture of science and engineering. Even if large-scale quantum computers become real…
First quantum computers very recently have demonstrated "quantum supremacy" or "quantum advantage": Executing a computation that would have been impossible on a classical machine. Today's quantum computers follow the NISQ paradigm: They exhibit error rates that are much higher than in conventional electronics and have insufficient quantum resources to support powerful error correction protocols. This raises questions which relevant computations are within the reach of NISQ architectures. Several "NISQ-era algorithms" are assumed to match the specifics of such computers; for instance, variation…
Fault-tolerant quantum error correction (QEC) is crucial for unlocking the true power of quantum computers. QEC codes use multiple physical qubits to encode a logical qubit, which is protected against errors at the physical qubit level. Here we use a trapped ion system to experimentally prepare $m$-qubit GHZ states and sample the measurement results to construct $m\times m$ logical states of the $[[m^2,1,m]]$ Shor code, up to $m=7$. The synthetic logical fidelity shows how deeper encoding can compensate for additional gate errors in state preparation for larger logical states. However, the opt…
Sandia National Laboratories（桑迪亚国家实验室）；DAMTP, Centre for Mathematical Sciences, University of Cambridge（剑桥大学数学科学中心 DAMTP）；Department of Physics and Astronomy, Dartmouth College（达特茅斯学院物理与天文学系）；Joint Center for Quantum Information and Computer Science, University of Maryland（马里兰大学量子信息与计算科学联合中心）；School of Physics, University of Sydney（悉尼大学物理学院）；Department of Chemistry, Rice University（莱斯大学化学系）；Department of Physics and Astronomy, Rice University（莱斯大学物理与天文学系）；Department of Computer Science, University of Oxford（牛津大学计算机科学系）
We present a comprehensive architectural analysis for a proposed fault-tolerant quantum computer based on cat codes concatenated with outer quantum error-correcting codes. For the physical hardware, we propose a system of acoustic resonators coupled to superconducting circuits with a two-dimensional layout. Using estimated physical parameters for the hardware, we perform a detailed error analysis of measurements and gates, including CNOT and Toffoli gates. Having built a realistic noise model, we numerically simulate quantum error correction when the outer code is either a repetition code or a…
Quantum computers have an exponential speed-up advantage over classical computers. One of the most prominent utilities of quantum computers is their ability to study complex quantum systems in various fields using quantum computational algorithms. Quantum computational algorithms can be used to study cosmological systems and how they behave with variations in the different parameters of the system. Here, we use the variational quantum eigensolver (VQE) algorithm to simulate the Hawking radiation phenomenon. VQE algorithm is a combination of quantum and classical computation methods used to obt…
