A. E. Shalyt-Margolin, V. I. Strazhev, A. Ya. Tregubovich
The Halting problem of a quantum computer is considered. It is shown that if halting of a quantum computer takes place the associated dynamics is described by an irreversible operator.
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The halting of universal quantum computers is shown to be incompatible with the constraint of unitarity of the dynamics.
We argue that the halting problem for quantum computers which was first raised by Myers, is by no means solved, as has been claimed recently. We explicitly demonstrate the difficulties that arise in a quantum computer when different branches of the computation halt at different, unknown, times.
It has been shown (Arxiv: quant-ph/0507236) that a universal quantum computer could be powerful enough to solve efficiently the quantum search problem, and the reversible and unitary halting protocol based on the state-locking pulse field is the key component to construct the efficient quantum search processes, while the state-locking pulse field is the key component to generate the reversible and unitary halting protocol. In this paper the reversible and unitary halting protocol and the generalized state-locking pulse field have been extensively investigated theoretically. The basic principle…
Fluctuations and Irreversibility: Historical and Modern Perspectives
本文综述了量子波动理论与线性响应理论的联系，探讨了量子系统中耗散功对非经典效应的影响，以及其在量子技术发展中的重要性。
According to Deutsch, a universal quantum Turing machine (UQTM) is able to perform, in repeating a fixed unitary transformation on the total system, an arbitrary unitary transformation on an arbitrary data state, by including a program as another part of the input state. We note that if such a UQTM really exists, with the program state dependent on the data state, and if the prescribed halting scheme is indeed valid, then there would be no entanglement between the halt qubit and other qubits, as pointed out by Myers. If, however, the program is required to be independent of the data, the conce…
Measuring out-of-time-order correlators on a quantum computer based on an irreversibility-susceptibility method
本文通过三种协议在量子计算机上实验测量反时间序相关函数，首次演示了不可逆性-易变性方法，并比较了三种方法的性能与局限性。
For decades, researchers have sought to understand how the irreversibility of the surrounding world emerges from the seemingly time symmetric, fundamental laws of physics. Quantum mechanics conjectured a clue that final irreversibility is set by the measurement procedure and that the time reversal requires complex conjugation of the wave function, which is overly complex to spontaneously appear in nature. Building on this Landau-Wigner conjecture, it became possible to demonstrate that time reversal is exponentially improbable in a virgin nature and to design an algorithm artificially reversin…
We show in some detail how to implement Shor's efficient quantum algorithm for discrete logarithms for the particular case of elliptic curve groups. It turns out that for this problem a smaller quantum computer can solve problems further beyond current computing than for integer factorisation. A 160 bit elliptic curve cryptographic key could be broken on a quantum computer using around 1000 qubits while factoring the security-wise equivalent 1024 bit RSA modulus would require about 2000 qubits. In this paper we only consider elliptic curves over GF($p$) and not yet the equally important ones o…
Voltage peaks on a conventional computer's power lines allow for the well-known dangerous DPA attacks. We show that measurement of a quantum computer's transient state during a computational step reveals information about a complete computation of arbitrary length, which can be extracted by repeated probing, if the computer is suitably programmed. Instant computing, as we name this mode of operation, recognizes for any total or partial recursive function arguments lying in the domain of definition and yields their function value with arbitrary small error probability in probabilistic linear ti…
Experimental simulation of non-equilibrium quantum piston on a programmable photonic quantum computer
本研究利用可编程光子量子计算机实验模拟双玻色子量子活塞的非平衡动力学，揭示了不可区分性和多体干涉对量子功、耗散和熵生产的影响。
Uncovering the origin of the arrow of time remains a fundamental scientific challenge. Within the framework of statistical physics, this problem was inextricably associated with the second law of thermodynamics, which declares that entropy growth proceeds from the system's entanglement with the environment. It remains to be seen, however, whether the irreversibility of time is a fundamental law of nature or whether, on the contrary, it might be circumvented. Here we show that, while in nature the complex conjugation needed for time reversal is exponentially improbable, one can design a quantum…
A legend tells that once Loschmidt asked Boltzmann on what happens to his statistical theory if one inverts the velocities of all particles, so that, due to the reversibility of Newton's equations, they return from the equilibrium to a nonequilibrium initial state. Boltzmann only replied ``then go and invert them''. This problem of the relationship between the microscopic and macroscopic descriptions of the physical world and time-reversibility has been hotly debated from the XIXth century up to nowadays. At present, no modern computer is able to perform Boltzmann's demand for a macroscopic nu…
High-order splitting of non-unitary operators on quantum computers
该研究提出了一种高阶算子分裂方法，利用复系数产品公式在量子计算机上高效模拟耗散动力学，通过实时间与虚时间的哈密顿演化实现高精度，适用于近期量子处理器。
We employ quantum mechanical principles in the computability exploration of the class of classically noncomputable Hilbert's tenth problem which is equivalent to the Turing halting problem in Computer Science. The Quantum Adiabatic Theorem enables us to establish a connection between the solution for this class of problems and the asymptotic behaviour of solutions of a particular type of time-dependent Schrödinger equations. We then present some preliminary numerical simulation results for the quantum adiabatic processes corresponding to various Diophantine equations.
We explore in the framework of Quantum Computation the notion of computability, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm that exploits the quantum adiabatic processes is considered for the Hilbert's tenth problem, which is equivalent to the Turing halting problem and known to be mathematically noncomputable. Generalised quantum algorithms are also considered for some other mathematical noncomputables in the same and of different noncomputability classes. The key element of all these algorithms is the measurability of both the values of…
We explore in the framework of Quantum Computation the notion of {\em Computability}, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm for Hilbert's tenth problem, which is equivalent to the Turing halting problem and is known to be mathematically noncomputable, is proposed where quantum continuous variables and quantum adiabatic evolution are employed. If this algorithm could be physically implemented, as much as it is valid in principle--that is, if certain hamiltonian and its ground state can be physically constructed according to the propo…
Quantum Random Self-Modifiable Computation
该研究提出可执行图灵机指令、量子随机指令与元指令的ex-machine模型，证明其可计算图灵不可计算语言且存在能逐步判定停机问题的演化路径，为希尔伯特的有限过程构想提供了新的实现思路。
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