Coherent Superposition Of Quantum States Research Articles

Coherence requirements for quantum communication from hybrid circuit dynamics

The coherent superposition of quantum states is an important resource for quantum information processing which distinguishes quantum dynamics and information from their classical counterparts. In this article we determine the coherence requirements to communicate quantum information in a broad setting encompassing monitored quantum dynamics and quantum error correction codes. We determine these requirements by considering hybrid circuits that are generated by a quantum information game played between two opponents, Alice and Eve, who compete by applying unitaries and measurements on a fixed number of qubits. Alice applies unitaries in an attempt to maintain quantum channel capacity, while Eve applies measurements in an attempt to destroy it. By limiting the coherence generating or destroying operations available to each opponent, we determine Alice’s coherence requirements. When Alice plays a random strategy aimed at mimicking generic monitored quantum dynamics, we discover a coherence-tuned phase transitions in entanglement and quantum channel capacity. We then derive a theorem giving the minimum coherence required by Alice in any successful strategy, and conclude by proving that coherence sets an upper bound on the code distance in any stabelizer quantum error correction code. Such bounds provide a rigorous quantification of the coherence resource requirements for quantum communication and error correction.

Stabilization of Multimode Schrödinger Cat States Via Normal-Mode Dissipation Engineering

Non-Gaussian quantum states have been deterministically prepared and autonomously stabilized in single- and two-mode circuit quantum electrodynamics architectures via engineered dissipation. However, it is currently unknown how to scale up this technique to multi-mode non-Gaussian systems. Here, we upgrade dissipation engineering to collective (normal) modes of nonlinear resonator arrays and show how to stabilize multi-mode Schrodinger cat states. These states are multi-photon and multi-mode quantum superpositions of coherent states in a single normal mode delocalized over an arbitrary number of cavities. We consider tailored dissipative coupling between resonators that are parametrically driven and feature an on-site nonlinearity, which is either a Kerr-type nonlinearity or an engineered two-photon loss. For both types of nonlinearity, we find the same exact closed-form solutions for the two-dimensional steady-state manifold spanned by superpositions of multi-mode Schrodinger cat states. We further show that, in the Zeno limit of strong dissipative coupling, the even parity multi-mode cat state can be deterministically prepared from the vacuum. Remarkably, engineered two-photon loss gives rise to a fast relaxation towards the steady state, protecting the state preparation against decoherence due to intrinsic single-photon losses and imperfections in tailored dissipative coupling, which sets in at longer times. The relaxation time is independent of system size making the state preparation scalable. Multi-mode cat states are naturally endowed with a noise bias that increases exponentially with system size and can thus be exploited for enhanced robust encoding of quantum information.

Using deep learning for digitally controlled STIRAP

Stimulated Raman Adiabatic Passage (STIRAP) is a technique for preparing atoms and molecules in an arbitrary preselected coherent superposition of quantum states, ordinarily controlled by Gaussian laser pulses. We search novel pulse sequences by exploiting deep reinforcement learning algorithms in order to achieve fast and flexible solutions for integer and fractional STIRAP. By using the robustness of the PPO algorithm, we impose the agent to exploit only digital pulses corresponding to on/off states of the control radiation instead of continuous amplitudes. Such method allows to adapt to detuning of the energy levels and disturbances such as dephasing.

Uncertainty Relations for the Number of Photons and the Phase Operator of an Electromagnetic Field for Phase Quantum Superpositions of Coherent States

We examine various uncertainty relations: (electromagnetic-field phase (the so-called “Pegg–Barnett operator”))–(number of photons), (trigonometric functions of the phase)–(number of photons), and (trigonometric functions of the phase)–(field phase). An electromagnetic field in quantum states of phase superpositions of coherent states, which are general superpositions of two coherent states with identical moduli but arbitrary phases, is considered. The rigorous uncertainty relation (Cauchy inequality) and the soft uncertainty relation (Heisenberg inequality) are examined and compared.

Digitally stimulated Raman passage by deep reinforcement learning

Preparing an arbitrary preselected coherent superposition of quantum states finds widespread application in physics, including initialization of trapped ion and superconductor qubits in quantum computers. Both fractional and integer stimulated Raman adiabatic passage involve smooth Gaussian pulses, designed to grant adiabaticity, so to keep the system in an eigenstate constituted only of the initial and final states. We explore an alternative method for discovering appropriate pulse sequences based on deep reinforcement learning algorithms and by imposing that the control laser can be only either on or off instead of being continuously amplitude-modulated. Despite the adiabatic condition is violated, we obtain fast and flexible solutions for both integer and fractional population transfer. Such method, consisting of a Digital Stimulated Raman Passage (D-STIRaP), proves to be particularly effective when the system is affected by dephasing therefore providing an alternative path towards control of noisy quantum states, like trapped ions and superconductor qubits.

Quantum coherences reveal excited-state dynamics in biophysical systems

Ultrafast, multi-dimensional spectroscopic measurements of photosynthetic light-harvesting complexes have revealed quantum coherences with timescales comparable to those of energy-transfer processes. These observations have led to a debate regarding the states that give rise to the coherences and whether the presence of the coherences has implications for photosynthetic light harvesting. In these experiments, laser pulses create a coherent superposition of quantum states with a defined phase relationship across an ensemble, which gives rise to the quantum coherence and associated quantum beating signal. Dephasing of these quantum coherences, seen as a decay of the beating signal, is among the most sensitive probes of the interactions between a system and its surrounding environment. In this Review, we discuss the proposed origin and assignment of the observed quantum coherences in photosynthetic systems as electronic, vibronic or vibrational. We describe the latest experimental efforts towards unravelling the nature of the coherences, in particular ultrafast, two-dimensional electronic spectroscopy, as well as the accompanying theoretical and computational results. We discuss how measuring coherences can inform us about the excited-state dynamics of biophysical and chemical systems relevant to natural light harvesting and how these measurements reveal electronic structure beyond that captured by simplistic models. Femtosecond spectroscopy of photosynthetic systems reveals long-lived quantum coherences. This Review focuses on efforts to understand the microscopic origins of these signals and discusses how such coherences may be exploited to probe design principles of photosynthetic light harvesting.

Quantum Computation Based on Quantum Adiabatic Bifurcations of Kerr-Nonlinear Parametric Oscillators

Quantum computers with Kerr-nonlinear parametric oscillators (KPOs) have recently been proposed by the author and others. Quantum computation using KPOs is based on quantum adiabatic bifurcations of the KPOs, which lead to quantum superpositions of coherent states, such as Schrodinger cat states. Therefore, these quantum computers are referred to as "quantum bifurcation machines (QbMs)." QbMs can be used for qauntum adiabatic optimization and universal quantum computation. Superconducting circuits with Josephson junctions, Josephson parametric oscillators (JPOs) in particular, are promising for physical implementation of KPOs. Thus, KPOs and QbMs offer not only a new path toward the realization of quantum bits (qubits) and quantum computers, but also a new application of JPOs. Here we theoretically explain the physics of KPOs and QbMs, comparing them with their dissipative counterparts. Their physical implementations with superconducting circuits are also presented.

Quantum teleportation of qudits by means of generalized quasi-Bell states of light

Quantum superpositions of coherent states are produced both in microwave and optical domains, and are considered realizations of the famous “Schrödinger cat” state. The recent progress shows an increase in the number of components and the number of modes involved. Our work creates a theoretical framework for treatment of multicomponent two-mode Schrödinger cat states. We consider a class of single-mode states, which are superpositions of N coherent states lying on a circle in the phase space. In this class we consider an orthonormal basis created by rotationally-invariant circular states (RICS). A two-mode extension of this basis is created by splitting a single-mode RICS on a balanced beam-splitter. We show that these states are generalizations of Bell states of two qubits to the case of N-level systems encoded into superpositions of coherent states on the circle, and we propose for them the name of generalized quasi-Bell states. We show that using a state of this class as a shared resource, one can teleport a superposition of coherent states on the circle (a qudit). Differently from some other existing protocols of quantum teleportation, the proposed protocol provides the unit fidelity for all input states of the qudit. We calculate the probability of success for this type of teleportation and show that it approaches unity for the average number of photons in one component above N2. Thus, the teleportation protocol can be made unit-fidelity and deterministic at finite resources.

Robust coherent superposition of states using quasiadiabatic inverse engineering

We use the invariant-based inverse engineering subject to the quasiadiabatic condition to produce robust and high fidelity coherent superposition of quantum states. The inverse engineering provides shortcuts to the desired quantum-state evolution while the quasiadiabaticity provides robustness with respect to errors. We derive simple pulses with low areas which are robust with respect to pulse area and detuning.

Fluctuations and a rigorous uncertainty relation of trigonometric operators of the phase and the number of photons of an electromagnetic field for general quantum superpositions of coherent states

The quantum-statistical properties of states of an electromagnetic field of general superpositions of coherent states of the form of N α,β(α⌤+e iξ β⌤ are investigated. Formulas for the fluctuations (variances) of Hermitian trigonometric phase field operators Ŝ ≡ cos φ, Ĉ ≡ sin φ (the so-called “Susskind–Glogower operators”) are found. Expressions for the rigorous uncertainty relations (Cauchy inequalities) for operators of the number of photons and trigonometric phase operators, as well as for operators Ŝ and Ĉ, are found and analyzed. The states of amplitude $${N_{\alpha ,\beta }}\left( {\left| {{{\sqrt {ne} }^{i\varphi }}\rangle + {e^{i\xi }}\left| {{{\sqrt {{n_\beta }e} }^{i\varphi }}\rangle } \right.} \right.} \right)$$ , φ = φα = φβ, and phase $${N_{\alpha ,\beta }}\left( {\left| {{{\sqrt {ne} }^{i{\varphi _\alpha }}}\rangle + {e^{i\xi }}\left| {{{\sqrt {ne} }^{i{\varphi _\beta }}}\rangle } \right.} \right.} \right)$$ , n = n α = n β, superpositions of coherent states are considered separately. The types of quantum superpositions of meso- and macroscales (n α, n β » 1) are found for which the sines and/or cosines of the phase of the field can be measured accurately, since, under certain conditions, the quantum fluctuations of these quantities are close to zero. A simultaneous accurate measurement of cosφ and sinφ is possible for amplitude superpositions, while an accurate measurement of one of these trigonometric phase functions is possible in the case of certain phase superpositions. Amplitude superpositions of coherent states with a vacuum state are quantum states of the field with a “maximum” level of the quantum uncertainty both in the case of a mesoscopic scale and in the case of a macroscopic scale of the field with an average number of photons n α/β ≈ 0, n β/α » 1.

Electromagnetic field fluctuations and uncertainty relation for general quantum superpositions of coherent states

Quantum statistical properties of general superpositions of coherent states of the type have been studied. Formulas for fluctuations (variances) of the coordinate and momentum quadratures and fluctuations of the number of photons in these states are obtained. The amplitude and phase superpositions of coherent states are considered separately. In the case of amplitude superpositions, a field under certain conditions occurs in a quadrature-squeezed state. At the same time, the photon distribution in the case of amplitude superpositions is always super-Poissonian. In the case of phase superpositions, a field under certain conditions occurs in quadrature-squeezed states for small average numbers of photons. For certain parameters of coherent states, the photon statistics in phase superpositions is sub-Poissonian. Using amplitude superpositions, it is possible to generate a microscopic electromagnetic field with the average photon number below or on the order of unity, as well as mesoscopic and even macroscopic fields with arbitrary large average photon numbers, characterized by significant quadrature squeezing. Using phase superpositions, it is possible to create under certain conditions the electromagnetic field states with sub-Poissonian statistics (squeezed distribution of photon numbers) for an arbitrary large average photon number. Expressions for a ‘strict’ coordinate–momentum uncertainty relation (Cauchy inequality) are obtained and analysed in cases of general, amplitude and phase superpositions of coherent states.

A rigorous uncertainty relation (Cauchy Inequality) for an electromagnetic field in quantum superpositions of coherent states and in a two-photon coherent state

It is shown that the Heisenberg uncertainty relation (or soft uncertainty relation) determined by the commutation properties of operators of electromagnetic field quadratures differs significantly from the Robertson–Schrodinger uncertainty relation (or rigorous uncertainty relation) determined by the quantum correlation properties of field quadratures. In the case of field quantum states, for which mutually noncommuting field operators are quantum-statistically independent or their quantum central correlation moment is zero, the rigorous uncertainty relation makes it possible to measure simultaneously and exactly the observables corresponding to both operators or measure exactly the observable of one of the operators at a finite measurement uncertainty for the other observable. The significant difference between the rigorous and soft uncertainty relations for quantum superpositions of coherent states and the two-photon coherent state of electromagnetic field (which is a state with minimum uncertainty, according to the rigorous uncertainty relation) is analyzed.

Quantum ballistic experiment on antihydrogen fall

We propose an approach to measuring gravitational mass of antihydrogen () based on interferometry of time distribution of free-fall events of antiatoms. Our method consists of preparing a coherent superposition of quantum states of localized near a material surface in the gravitational field of the Earth, and then observing the time distribution of annihilation events after the free-fall of the initially prepared superposition from a given height to a detector plate. We show that the time distribution of interest is mapped to a precisely predictable velocity distribution of the initial wave packet. This approach is combined with production of a coherent superposition of gravitational states by inducing a resonant transition using an oscillating gradient magnetic field. We show that the relative accuracy of measuring the atom gravitational mass can be achieved with this approach is 10−4, with 103 antiatoms settled in lowest gravitational states.

Observation of Atom-Wave Beats Using a Kerr Modulator for Atom Waves.

A phase modulation puts the atom in a coherent superposition of quantum states with different kinetic energies. We have detected the interference of such modulated waves at the output of our atom interferometer, and we have observed beats at the difference of the modulation frequencies and its harmonics, in good agreement with theory. The phase modulations were produced by a Kerr phase modulator, i.e., by the propagation of the atom wave in a time-dependent electric field. An extension of this technique to electron interferometry should open the way to very high temporal resolution in electron microscopy.

Effectively Calculable Quantum Mechanics

According to mathematical constructivism, a mathematical object can exist only if there is a way to compute (or construct) it; so, what is non-computable is non-constructive. In the example of the quantum model, whose Fock states are associated with Fibonacci numbers, this paper shows that the mathematical formalism of quantum mechanics is non-constructive since it permits an undecidable (or effectively impossible) subset of Hilbert space. On the other hand, as it is argued in the paper, if one believes that testability of predictions is the most fundamental property of any physical theory, one needs to accept that quantum mechanics must be an effectively calculable (and thus mathematically constructive) theory. With that, a way to reformulate quantum mechanics constructively, while keeping its mathematical foundation unchanged, leads to hypercomputation. In contrast, the proposed in the paper superselection rule, which acts by effectively forbidding a coherent superposition of quantum states corresponding to potential and actual infinity, can introduce computable constructivism in a quantum mechanical theory with no need for hypercomputation.

Robust coherent superposition of states by single-shot shaped pulse

We adapt a single-shot shaped pulse technique to produce robust coherent superpositions of quantum states with a high fidelity of control. We derive simple pulses of low areas for the corresponding Rabi frequency which are robust with respect to pulse area imperfections. Such features of robustness, high-fidelity, and low Rabi frequency area are crucial steps towards the experimental implementation of scalable quantum gates.

Quantum coherence over the noisy quantum channels

The coherent superposition of quantum states is one of the characteristic features of quantum mechanics, and it is also physical resource of quantum information processing. The coherence of quantum system can not last a long time as the effect of the noise. How well has the noisy channel preserved the quantum coherence of the quantum system? Based on the relative entropy of coherence, in this paper, we discuss the coherence, entanglement and quantum correlations in the bipartite quantum system. To discuss the effect of the noise, we then give a definition of the decayed amount of the maximal quantum coherence, i.e., the decay of coherence. Then we obtain that the uncertainty relations between entanglement and the coherence with respect to the noisy models. Finally, we used the measure of the decay of coherence to discuss how well several noisy channels preserves the coherence.

Two quantum Simpson’s paradoxes

The so-called Simpson’s ‘paradox’, or Yule–Simpson (YS) effect, occurs in classical statistics when the correlations that are present among different sets of samples are reversed if the sets are combined together, thus ignoring one or more lurking variables. Here we illustrate the occurrence of two analog effects in quantum measurements. The first, which we term the quantum–classical YS effect, may occur with quantum limited measurements and with lurking variables coming from the mixing of states, whereas the second, here referred to as the quantum–quantum YS effect, may take place when coherent superpositions of quantum states are allowed. By analyzing quantum measurements on low-dimensional systems (qubits and qutrits), we show that the two effects may occur independently and that the quantum–quantum YS effect is more likely to occur than the corresponding quantum–classical one. We also found that there exist classes of superposition states for which the quantum–classical YS effect cannot occur for any measurement and, at the same time, the quantum–quantum YS effect takes place in a consistent fraction of the possible measurement settings. The occurrence of the effect in the presence of partial coherence is discussed as well as its possible implications for quantum hypothesis testing.

On genetic information uncertainty and the mutator phenotype in cancer

Recent evidence supports the existence of a mutator phenotype in cancer cells, although the mechanistic basis remains unknown. In this paper, it is shown that this enhanced genetic instability is generated by an amplified measurement uncertainty on genetic information during DNA replication. At baseline, an inherent measurement uncertainty implies an imprecision of the recognition, replication and transfer genetic information, and forms the basis for an intrinsic genetic instability in all biological cells. Genetic information is contained in the sequence of DNA bases, each existing due to proton tunnelling, as a coherent superposition of quantum states composed of both the canonical and rare tautomeric forms until decoherence by interaction with DNA polymerase. The result of such a quantum measurement process may be interpreted classically as akin to a Bernoulli trial, whose outcome X is random and can be either of two possibilities, depending on whether the proton is tunnelled (X=1) or not (X=0). This inherent quantum uncertainty is represented by a binary entropy function and quantified in terms of Shannon information entropy H(X)=−P(X=1)log2P(X=1)−P(X=0)log2P(X=0). Enhanced genetic instability may either be directly derived from amplified uncertainty induced by increases in quantum and thermodynamic fluctuation, or indirectly arise from the loss of natural uncertainty reduction mechanisms.

Coherent control of three-spin states in a triple quantum dot

Spin qubits involving individual spins in single quantum dots or coupled spins in double quantum dots have emerged as potential building blocks for quantum information processing applications. It has been suggested that triple quantum dots may provide additional tools and functionalities. These include the encoding of information to either obtain protection from decoherence or to permit all-electrical operation, efficient spin busing across a quantum circuit, and to enable quantum error correction utilizing the three-spin Greenberger-Horn-Zeilinger quantum state. Towards these goals we demonstrate for the first time coherent manipulation between two interacting three-spin states. We employ the Landau-Zener-St\"uckelberg approach for creating and manipulating coherent superpositions of quantum states. We confirm that we are able to maintain coherence when decreasing the exchange coupling of one spin with another while simultaneously increasing its coupling with the third. Such control of pairwise exchange is a requirement of most spin qubit architectures but has not been previously demonstrated.