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Register a new userOptical analogy to quantum computation based on classical fields modulated pseudorandom phase sequences
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We demonstrate that a tensor product structure and optical analogy of quantum entanglement can be obtained by introducing pseudorandom phase sequences into classical fields with two orthogonal modes. Using the classical analogy, we discuss efficient simulation of several typical quantum states, including product state, Bell states, GHZ state, and W state. By performing quadrature demodulation scheme, we propose a sequence permutation mechanism to simulate certain quantum states and a generalized gate array model to simulate quantum algorithm, such as Shors algorithm and Grovers algorithm. The research on classical simulation of quantum states is important, for it not only enables potential beyond quantum computation, but also provides useful insights into fundamental concepts of quantum mechanics.
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We propose an optical parallel computation similar to quantum computation that can be realized by introducing pseudorandom phase sequences into classical optical fields with two orthogonal modes. Based on the pseudorandom phase sequences, we first propose a theoretical framework of phase ensemble model referring from the concept of quantum ensemble. Using the ensemble model, we further demonstrate the inseparability of the fields similar to quantum entanglement. It is interesting that a N2^N dimensional Hilbert space spanned by N optical fields is larger than that spanned by N quantum particles. This leads a problem for our scheme that is not the lack of resources but the redundancy of resources. In order to reduce the redundancy, we propose a special sequence permutation mechanism to efficiently imitate certain quantum states, including the product state, Bell states, GHZ state and W state. For better fault tolerance, we further devise each orthogonal mode of optical fields is measured to assign discrete values. Finally, we propose a generalized gate array model to imitate some quantum algorithms, such as Shors algorithm, Grovers algorithm and quantum Fourier algorithm. The research on the optical parallel computation might be important, for it not only has the potential beyond quantum computation, but also provides useful insights into fundamental concepts of quantum mechanics.
An effective simulation of quantum entanglement is presented using classical fields modulated with n pseudorandom phase sequences (PPSs) that constitute a n2^n-dimensional Hilbert space with a tensor product structure. Applications to classical fields are examplied by effective simulation of both Bell and GHZ states, and a correlation analysis was performed to characterize the simulation. Results that strictly comply with criteria of quantum entanglement were obtained and the approach was also shown to be applicable to a system consisting of n quantum particles.
The key to optical analogy to a multi-particle quantum system is the scalable property. Optical elds modulated with pseudorandom phase sequences is an interesting solution. By utilizing the properties of pseudorandom sequences, mixing multiple optical elds are distinguished by using coherent detection and correlation analysis that are mature methods in optical communication. In this paper, we utilize the methods to investigate optical analogies to multi-particle quantum states. In order to demonstrate the feasibility, numerical simulations are carried out in the paper, which is helpful to the experimental verication in the future.
Quantum optimal control represents a powerful technique to enhance the performance of quantum experiments by engineering the controllable parameters of the Hamiltonian. However, the computational overhead for the necessary optimization of these control parameters drastically increases as their number grows. We devise a novel variant of a gradient-free optimal-control method by introducing the idea of phase-modulated driving fields, which allows us to find optimal control fields efficiently. We numerically evaluate its performance and demonstrate the advantages over standard Fourier-basis methods in controlling an ensemble of two-level systems showing an inhomogeneous broadening. The control fields optimized with the phase-modulated method provide an increased robustness against such ensemble inhomogeneities as well as control-field fluctuations and environmental noise, with one order of magnitude less of average search time. Robustness enhancement of single quantum gates is also achieved by the phase-modulated method. Under environmental noise, an XY-8 sequence constituted by optimized gates prolongs the coherence time by $50%$ compared with standard rectangular pulses in our numerical simulations, showing the application potential of our phase-modulated method in improving the precision of signal detection in the field of quantum sensing.
For space-based laser communications, when the mean photon number per received optical pulse is much smaller than one, there is a large gap between communications capacity achievable with a receiver that performs individual pulse-by-pulse detection, and the quantum-optimal joint-detection receiver that acts collectively on long codeword-blocks of modulated pulses; an effect often termed superadditive capacity. In this paper, we consider the simplest scenario where a large superadditive capacity is known: a pure-loss channel with a coherent-state binary phase-shift keyed (BPSK) modulation. The two BPSK states can be mapped conceptually to two non-orthogonal states of a qubit, described by an inner product that is a function of the mean photon number per pulse. Using this map, we derive an explicit construction of the quantum circuit of a joint-detection receiver based on a recent idea of belief-propagation with quantum messages (BPQM) (arXiv:1607.04833). We quantify its performance improvement over the Dolinar receiver that performs optimal pulse-by-pulse detection, which represents the best classical approach. We analyze the scheme rigorously and show that it achieves the quantum limit of minimum average error probability in discriminating 8 (BPSK) codewords of a length-5 binary linear code with a tree factor graph. Our result suggests that a BPQM-receiver might attain the Holevo capacity of this BPSK-modulated pure-loss channel. Moreover, our receiver circuit provides an alternative proposal for a quantum supremacy experiment, targeted at a specific application that can potentially be implemented on a small, special-purpose, photonic quantum computer capable of performing cat-basis universal qubit logic.
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