Noisy computation and reversible computation have been studied separately, and it is known that they are as powerful as unrestricted computation. We study the case where both noise and reversibility are combined and show that the combined model is weaker than unrestricted computation. In our noisy reversible circuits, each wire is flipped with probability p each time step, and all the inputs to the circuit are present in time 0. We prove that any noisy reversible circuit must have size exponential in its depth in order to compute a function with high probability. This is tight as we show that any circuit can be converted into a noise-resistant reversible one with a blow up in size which is exponential in the depth. This establishes that noisy reversible computation has the power of the complexity class NC^1.
We extend this to quantum circuits(QC). We prove that any noisy QC which is not worthless, and for which all inputs are present at time 0, must have size exponential in its depth. (This high-lights the fact that fault tolerant QC must use a constant supply of inputs all the time.) For the lower bound, we show that quasi-polynomial noisy QC are at least powerful as logarithmic depth QC, (or QNC^1). Making these bounds tight is left open in the quantum case.
We report optimal and asymptotically optimal reversible circuits composed of NOT, CNOT, and Toffoli (NCT) gates, keeping the count by the subsets of the gate types used. This study fine tunes the circuit complexity figures for the realization of reversible functions via reversible NCT circuits. An important consequence is a result on the limitation of the use of the $T$-count quantum circuit metric popular in applications.
Predictions for measurement outcomes in physical theories are usually computed by combining two distinct notions: a state, describing the physical system, and an observable, describing the measurement which is performed. In quantum theory, however, both notions are in some sense identical: outcome probabilities are given by the overlap between two state vectors - quantum theory is self-dual. In this paper, we show that this notion of self-duality can be understood from a dynamical point of view. We prove that self-duality follows from a computational primitive called bit symmetry: every logica…
We use entropy-energy arguments to assess the limitations on the running time and on the system size, as measured in qubits, of noisy macroscopic circuit-based quantum computers.
In this paper we consider adversarial noise models that will fail quantum error correction and fault-tolerant quantum computation. We describe known results regarding high-rate noise, sequential computation, and reversible noisy computation. We continue by discussing highly correlated noise and the "boundary," in terms of correlation of errors, of the "threshold theorem." Next, we draw a picture of adversarial forms of noise called (collectively) "detrimental noise." Detrimental noise is modeled after familiar properties of noise propagation. However, it can have various causes. We start by po…
Limitations of Noisy Geometrically Local Quantum Circuits
University of Maryland（马里兰大学）；Joint Center for Quantum Information & Computer Science, University of Maryland and NIST（马里兰大学与美国国家标准与技术研究院联合量子信息与计算中心）；IBM T. J. Watson Research Center（IBM托马斯·J·沃森研究中心）
The impressive progress in quantum hardware in the last years has raised the interest of the quantum computing community in harvesting the computational power of such devices. However, in the absence of error correction, these devices can only reliably implement very shallow circuits or comparatively deeper circuits at the expense of a nontrivial density of errors. In this work, we obtain extremely tight limitation bounds for standard NISQ proposals in both the noisy and noiseless regimes, with or without error-mitigation tools. The bounds limit the performance of both circuit model algorithms…
Recent technological developments have focused the interest of the quantum computing community on investigating how near-term devices could outperform classical computers for practical applications. A central question that remains open is whether their noise can be overcome or it fundamentally restricts any potential quantum advantage. We present a transparent way of comparing classical algorithms to quantum ones running on near-term quantum devices for a large family of problems that include optimization problems and approximations to the ground state energy of Hamiltonians. Our approach is b…
One of the simplest security proofs of quantum key distribution is based on the so-called complementarity scenario, which involves the complementarity control of an actual protocol and a virtual protocol [M. Koashi, e-print arXiv:0704.3661 (2007)]. The existing virtual protocol has a limitation in classical postprocessing, i.e., the syndrome for the error-correction step has to be encrypted. In this paper, we remove this limitation by constructing a quantum circuit for the virtual protocol. Moreover, our circuit with a shield system gives an intuitive proof of why adding noise to the sifted ke…
Transversality is a simple and effective method for implementing quantum computation fault-tolerantly. However, no quantum error-correcting code (QECC) can transversally implement a quantum universal gate set (Eastin and Knill, Phys. Rev. Lett., 102, 110502). Since reversible classical computation is often a dominating part of useful quantum computation, whether or not it can be implemented transversally is an important open problem. We show that, other than a small set of non-additive codes that we cannot rule out, no binary QECC can transversally implement a classical reversible universal ga…
Near-term quantum computers are noisy, and therefore must run algorithms with a low circuit depth and qubit count. Here we investigate how noise affects a quantum neural network (QNN) for state discrimination, applicable on near-term quantum devices as it fulfils the above criteria. We find that when simulating gradient calculation on a noisy device, a large number of parameters is disadvantageous. By introducing a new smaller circuit ansatz we overcome this limitation, and find that the QNN performs well at noise levels of current quantum hardware. We also show that networks trained at higher…
Heat-bath algorithmic cooling (AC) of spins is a theoretically powerful effective cooling approach, that (ideally) cools spins with low polarization exponentially better than cooling by reversible entropy manipulations alone. Here, we investigate the limitations and prospects of AC. For non-ideal and semioptimal AC, we study the impact of finite relaxation times of reset and computation spins on the achievable effective cooling. We derive, via simulations, the attainable cooling levels for given ratios of relaxation times using two semioptimal practicable algorithms. We expect this analysis to…
Noisy, intermediate-scale quantum computers come with intrinsic limitations in terms of the number of qubits (circuit "width") and decoherence time (circuit "depth") they can have. Here, for the first time, we demonstrate a recently introduced method that breaks a circuit into smaller subcircuits or fragments, and thus makes it possible to run circuits that are either too wide or too deep for a given quantum processor. We investigate the behavior of the method on one of IBM's 20-qubit superconducting quantum processors with various numbers of qubits and fragments. We build noise models that ca…
We propose one of the very few constructive consequences of the second law of thermodynamics. More specifically, we present protocols for secret-key establishment and multiparty computation the security of which is based fundamentally on Landauer's principle. The latter states that the erasure cost of each bit of information is at least kTln2 (where k is Boltzmann's constant and T is the absolute temperature of the environment). Albeit impractical, our protocols explore the limits of reversible computation, and the only assumption about the adversary is her inability to access a quantity of fr…
Real-time clustering of big performance data generated by the telecommunication networks requires domain-specific high performance compute infrastructure to detect anomalies. In this paper, we evaluate noisy intermediate-scale quantum (NISQ) computers characterized by low decoherence times, for K-means clustering and propose three strategies to generate shorter-depth quantum circuits needed to overcome the limitation of NISQ computers. The strategies are based on exploiting; i) quantum interference, ii) negative rotations and iii) destructive interference. By comparing our implementations on I…
The universal quantum computation model based on quantum walk by Childs has opened the door for a new way of studying the limitations and advantages of quantum computation, as well as for its intermediate-term simulation. In recent years, the growing interest in noisy intermediate-scale quantum computers (NISQ) has lead to intense efforts being directed at understanding the computational advantages of open quantum systems. In this work, we extend the quantum walk model to open noisy systems in order to provide such a tool for the study of NISQ computers. Our method does not use explicit purifi…
