One of the quantum theory concepts on which quantum information processing stands is superposition. Here we provide experimental evidence for the existence of classical analogues to the coherent superposition of energy states, which is made possible by the Hertz-type nonlinearity of the granules together with the external driving field. The granules' nonlinear vibrations are projected into the linear modes of vibration, which depend on one another through the phase and form a coherent superposition. We show that the amplitudes of the coherent states form the components of a state vector that spans a two-dimensional Hilbert space, and time enables the system to span its Hilbert space parametrically. Thus, the superposition of states can be exploited in two-state quantum-like computations without decoherence and wave function collapse. Finally, we demonstrate the experimental realization of applying a reversible Hadamard gate to a pure base state that brings the state into a superposition.
One of the quantum theory concepts on which quantum information processing stands is superposition. Here we provide experimental evidence for the existence of classical analogues to the coherent superposition of energy states, which is made possible by the Hertz-type nonlinearity of the granules together with the external driving field. The granules' nonlinear vibrations are projected into the linear modes of vibration, which depend on one another through the phase and form a coherent superposition. We show that the amplitudes of the coherent states form the components of a state vector that spans a two-dimensional Hilbert space, and time enables the system to span its Hilbert space parametrically. Thus, the superposition of states can be exploited in two-state quantum-like computations without decoherence and wave function collapse. Finally, we demonstrate the experimental realization of applying a reversible Hadamard gate to a pure base state that brings the state into a superposition.
In quantum information science and technology (QIST), the superposition of states is pivotal. Current qubits, formed by superposing two pure states, are foundational in QIST but are susceptible to decoherence, causing loss of superposed states. Addressing this, we introduced an "elastic bit" using the Hertz-type nonlinearity of elastic beads under external driving. These beads exhibit phase-dependent nonlinear vibrations, leading to coherent superpositions of energy states in linear vibration modes. The resulting amplitudes span a two-dimensional Hilbert space, with time allowing parametric spanning. We showcased the Hadamard gate, translating one state superposition to another through a unitary transformation. Remarkably, these elastic bits operate at room temperature and resist decoherence, making them apt for intermediate-scale quantum analogue computing. They offer solutions for challenges in supercomputing for artificial intelligence and autonomous vehicle data processing.
Among the fundamental phenomena that characterize a quantum system is coherent superposition between states, which we can write for a two-level system as: |ψ⟩ = α|0⟩ + e^(iφ) β|1⟩ A superposition is characterized by a phase φ which can be difficult to conceptualize with our physical intuition, trained only by experience in a classical world. Perhaps we can best approach it by considering the phase of classical waves, which we can concretely visualize, and which lead to some analogous phenomena like interference. In effect there is additional information in the system beyond the probability that it is measured in one state vs. the other. This phase is both a resource and a vulnerability of quantum systems. On one hand, it gives the system another degree of freedom which we can control. On the other hand, it can be easily lost, since the phase of a superposition tends to be very sensitive to fluctuations in the system's surrounding environment. The length of time that the phase remains known in a system (or equivalently, that the system maintains its information) is called the coherence time. In this thesis I will discuss two examples in which a coherent superposition of states is used to preserve information in a quantum system. In both cases the key laboratory tool used to access the quantum system is an AC field of classical amplitude which coherently drives the states, and in both cases we will see the beneficial properties of the stationary solutions of the combined system plus field, which are superposition states (in the basis that does not include the field). Chapter 1 will deal with an example of a coherent field extending the coherence time of a two-level system. I will show experimental data demonstrating this effect in the electron spin of the silicon vacancy in diamond, where the coherent driving field is a strain field in the carbon lattice. Chapter 2 will explain how the decay channels of a single atomic system can be controlled using superpositions of states, a phenomena which could be used to increase the fidelity of a state measurement. These results are computational rather than experimental, but I will suggest a real quantum system in which this phenomena could be demonstrated and calculate expected results.
We experimentally demonstrate the existence and control of coherent superpositions of elastic states in the direction of propagation of an ultrasonic pseudospin i.e., a φ-bit. The experimental realization of this mechanical pseudospin consists of an elastic aluminum rod serving as a waveguide sandwiched between two heavy steel plates. The Hertzian contact between the rod and the plates leads to restoring forces which couple the directions of propagation (forward and backward). This coupling generates the coherence of the superposition of elastic states. We also demonstrate φ-bit gate operations on the coherent superposition analogous to those used in quantum computing. In the case of a φ-bit, the coherent superposition of states in the direction of propagation are immune to wave function collapse upon measurement as they result from classical waves.
Decoherence represents one of the most fundamental problems in quantum mechanics since its birth. Interest in decoherence has been primarily academic until recently when the advances in experimental techniques in different fields of physics such as superconducting quantum interferometers; quantum optics and neutron interferometry sparked the practical interest in this quantum mechanical phenomenon. One particular field where decoherence is of crucial role is quantum computing, where decoherence stands as one of the main obstacles toward realizing practical progress in the field. On the other hand, the ability to manipulate linear superpositions of quantum states is expected to lead to considerable advances in that field. The purpose of this dissertation is to present a study of decoherence in nonlinear quantum systems. We started by studying the coherent superposition of distinct basis states in a single-degree-of-freedom model of SQUID with a variable potential barrier between the basis flux states. We numerically integrated Schrödinger equation of the system. We found that linear superpositions of the basis states, with relatively little residual excitation, can be formed by pulsed modulation of the potential barrier, provided the pulse duration exceeds the period of small oscillations of the flux. Two pulses applied in sequence exhibit strong interference effects, which we propose to use for an experimental determination of the decoherence time in SQUIDS. In addition, we developed, using quantum field theory techniques, a general formalism to study decoherence in a quantum system due to coupling to a non-linear environment. This formalism can be used to investigate decoherence in many of the existing two state quantum systems proposed for quantum computing and reveals important information about them such as decoherence time. Moreover, we used this formalism to compare decoherence induced in a simple two-state quantum system (qubit) for two different initial states of the environment: canonical (fixed temperature) and microcanonical (fixed energy), for the general case of a fully interacting oscillator environment. We found that even a relatively compact oscillator bath (with effective number of degrees of freedom as low as 10), initially in a microcanonical state, will typically cause decoherence almost indistinguishable from that caused by a macroscopic, thermal environment, except possibly at singularities of the environment's specific heat (critical points). In the latter case the precise magnitude of the difference between the canonical and microcanonical results depends on the critical behavior of the dissipative coefficient, characterizing the interaction of the two-state quantum system with the environment.
A quantum wave function can be a superposition of multiple waves. A double-well potential has a wave function with elements in each well. The lowest energy state has a symmetric wave function, and the next an antisymmetric wave function; a linear combination of these two energy states can be momentarily localized in one well, but will undergo quantum tunneling to the other side, within a time span that depends on the size of the central barrier; this type of tunneling occurs in the ammonia molecule. A spectacular example of superposition and wave–particle duality is given by the two-slit experiment: each particle has a probability of going through either slit, producing an interference pattern on a screen beyond the slits. Observing which slit has been used causes wave function collapse, destroying the interference pattern. Interference with very large molecules has been observed experimentally, demonstrating quantum effects in macroscopic objects.
In recent years coherent state qubits, |α〉 ± | - α〉 have gained much interest. The main reason is the promise to realize a universal set of coherent state quantum gates with a relative low overhead using, only linear optics and photon counters. A universal set of gates consists of a single mode and a two mode phase gate and a Hadamard gate. The Hadamard is the gate that transforms one set of basis states into the conjugate basis, e.g | ± α〉 - | - α〉. Here we present an experimental demonstration of a Hadamard gate for coherent state qubits. The implementation is based on the scheme proposed by Marek and Fiurasek (2010).