25 pages of main text, 9 pages of appendices, 2 pages of references. No figures, no tables. Invited contribution to the Quantum Reports special issue "Relevance of Information Geometry in Quantum Information Science", C. Cafaro (ed.). Comments welcome. Published version (v2)
Gedanken experiments in quantum gravity motivate generalised uncertainty relations (GURs) implying deviations from the standard quantum statistics close to the Planck scale. These deviations have been extensively investigated for the non-spin part of the wave function but existing models tacitly assume that spin states remain unaffected by the quantisation of the background in which the quantum matter propagates. Here, we explore a new model of nonlocal geometry in which the Planck-scale smearing of classical points generates GURs for angular momentum. These, in turn, imply an analogous generalisation of the spin uncertainty relations. The new relations correspond to a novel representation of {\rm SU(2)} that acts nontrivially on both subspaces of the composite state describing matter-geometry interactions. For single particles each spin matrix has four independent eigenvectors, corresponding to two $2$-fold degenerate eigenvalues $\pm (\hbar + β)/2$, where $β$ is a small correction to the effective Planck's constant. These represent the spin states of a quantum particle immersed in a quantum background geometry and the correction by $β$ emerges as a direct result of the interaction terms. In addition to the canonical qubits states, $\ket{0} = \ket{\uparrow}$ and $\ket{1} = \ket{\downarrow}$, there exist two new eigenstates in which the spin of the particle becomes entangled with the spin sector of the fluctuating spacetime. We explore ways to empirically distinguish the resulting `geometric' qubits, $\ket{0'}$ and $\ket{1'}$, from their canonical counterparts.
We assume that space-time at the Planck scale is discrete, quantised in Planck units and "qubitsed" (each pixel of Planck area encodes one qubit), that is, quantum space-time can be viewed as a quantum computer. Within this model, one finds that quantum space-time itself is entangled, and can quantum-evaluate Boolean functions which are the laws of Physics in their discrete and fundamental form.
We illustrate the entanglement mechanism of quantum space-time itself. We consider a discrete, quantum version of de Sitter Universe with a Planck time-foliation, to which is applied the quantum version of the holographic principle (a Planckian pixel encodes one qubit rather than a bit). This results in a quantum network, where the time steps label the nodes. The quantum fluctuations of the vacuum are the connecting links of the quantum network, while the total number of pixels (qubits) of a spatial slice are the outgoing links from a node n. At each node n there is a couple of quantum gates, …
Dirac particle dynamics is encoded as a unitary path summation rule and implemented on a qubit array, where the qubit array represents both spacetime and the fermions contained therein. The unitary path summation rule gives a quantum algorithm to model a many-body system of Dirac particles in a gauge field with Lorentz invariance down to the grid scale (Planck scale)--the lattice-based model neither suffers the Fermi-sign problem nor breaks Lorentz invariance. Yet, for the Dirac Hamiltonian to generate the unitary evolution of the 4-spinor field at the Planck scale, there is time dilation betw…
A comparison of gate fidelities between different spin qubit types defined in quantum dots and a donor under different control errors is reported. We studied five qubit types, namely the quantum dot spin qubit, the double quantum dot singlet-triplet qubit, the double quantum dot hybrid qubit, the donor qubit and the quantum dot spin-donor qubit. For each one, we derived analytical time sequences that realize single qubit rotations along the principal axis of the Bloch sphere. We estimated the effects of control errors on the gate fidelity by using a Gaussian noise model. Then we compared the g…
In loop quantum gravity approach to Planck scale physics, quantum geometry is represented by superposition of the so-called spin network states. In the recent literature, a class of spin networks promising from the perspective of quantum simulations of quantum gravitational systems has been studied. In this case, the spin network states are represented by graphs with four-valent nodes, and two dimensional intertwiner Hilbert spaces (qubits of space) attached to them. In this article, construction of quantum circuits for a general intertwiner qubit is presented. The obtained circuits are simula…
We consider two qubit teleportation via quantum channel affected by amplitude damping noise. Addressing the same problem, X. Hu, Y. Gu, Q. Gong and G. Guo [Phys. Rev. A 81, 054302, (2010)] recently showed that in presence of noise, subjecting more qubits in quantum channel to amplitude damping can increase the fidelity of teleportation protocol. However, in this paper, by making some adjustments on quantum channel, we obtain teleportation fidelity which is even higher than one in the case of X. Hu et al. Moreover, our strategy is simpler than quantum distillation and compared to using weak mea…
A two-qubit quantum gate is realized using electronic excited states in a single ion with an energy separation on the order of a terahertz times the Planck constant as a qubit. Two phase locked lasers are used to excite a stimulated Raman transition between two metastable states $D_{3/2}$ and $D_{5/2}$ separated by 1.82 THz in a single trapped $^{40}$Ca$^+$ ion to construct a qubit, which is used as the target bit for the Cirac-Zoller two-qubit controlled NOT gate. Quantum dynamics conditioned on a motional qubit is clearly observed as a fringe reversal in Ramsey interferometry.
We consider cosmological evolution from the perspective of quantum information. We present a quantum circuit model for the expansion of a comoving region of space, in which initially-unentangled ancilla qubits become entangled as expansion proceeds. We apply this model to the comoving region that now coincides with our Hubble volume, taking the number of entangled degrees of freedom in this region to be proportional to the de Sitter entropy. The quantum circuit model is applicable for at most 140 $e$-folds of inflationary and post-inflationary expansion: we argue that no geometric description …
Almost all theories of Quantum Gravity predict modifications of the Heisenberg Uncertainty Principle near the Planck scale to a so-called Generalized Uncertainty Principle (GUP). Recently it was shown that the GUP gives rise to corrections to the Schrodinger and Dirac equations, which in turn affect all non-relativistic and relativistic quantum Hamiltonians. In this paper, we apply it to superconductivity and the quantum Hall effect and compute Planck scale corrections. We also show that Planck scale effects may account for a (small) part of the anomalous magnetic moment of the muon. We obtain…
In this paper we study the influence of Dzyaloshinskii-Moriya (DM) interaction on quantum correlations in two qubit Werner states and maximally entangled mixed states (MEMS). We consider our system as a closed system of a qubits pair and one auxiliary qubit which interact with any one of the qubit of the pair through DM interaction. We show that DM interaction, taken along any direction (x or y or z), does not affect two qubit Werner states. On the other hand the MEMS are affected by x and z components of DM interaction and remain unaffected by the y component. Further, we find that the state …
Contextuality is a necessary resource for universal quantum computation and non-contextual quantum mechanics can be simulated efficiently by classical computers in many cases. Orders of Planck's constant, $\hbar$, can also be used to characterize the classical-quantum divide by expanding quantities of interest in powers of $\hbar$---all orders higher than $\hbar^0$ can be interpreted as quantum corrections to the order $\hbar^0$ term. We show that contextual measurements in finite-dimensional systems have formulations within the Wigner-Weyl-Moyal (WWM) formalism that require higher than order …
The presence of valley states is a significant obstacle to realizing quantum information technologies in Silicon quantum dots, as leakage into alternate valley states can introduce errors into the computation. We use a perturbative analytical approach to study the dynamics of exchange-coupled quantum dots with valley degrees of freedom. We show that if the valley splitting is large and electrons are not properly initialized to valley eigenstates, then time evolution of the system will lead to spin-valley entanglement. Spin-valley entanglement will also occur if the valley splitting is small an…
We consider measurement disturbance tradeoffs in quantum machine learning protocols which seek to learn about quantum data. We study the simplest example of a binary classification task, in the unsupervised regime. Specifically, we investigate how a classification of two qubits, that can each be in one of two unknown states, affects our ability to perform a subsequent classification on three qubits when a third is added. Surprisingly, we find a range of strategies in which a non-trivial first classification does not affect the success rate of the second classification. There is, however, a non…
Error-corrected quantum computers can only work if errors are small and uncorrelated. Here I show how cosmic rays or stray background radiation affects superconducting qubits by modeling the phonon to electron/quasiparticle down-conversion physics. For present designs, the model predicts about 57\% of the radiation energy breaks Cooper pairs into quasiparticles, which then vigorously suppress the qubit energy relaxation time ($T_1 \sim$ 160 ns) over a large area (cm) and for a long time (ms). Such large and correlated decay kills error correction. Using this quantitative model, I show how this…
Symmetries of the initial state of a quantum system and the quantum channels, which simultaneously affect parts of the system, can significantly simplify the description of the entanglement evolution. Using concurrence as the entanglement measure, we study the entanglement evolution of few qubit systems, when each of the qubits is affected by a local channel independently of the others. We show that, for low-rank density matrices of the final quantum state, such complex entanglement dynamics can be completely described by a combination of independent factors representing the evolution of entan…
We demonstrate, in the context of Loop Quantum Gravity, the Quantum Holographic Principle, according to which the area of the boundary surface enclosing a region of space encodes a qubit per Planck unit. To this aim, we introduce fermion fields in the bulk, whose boundary surface is the two-dimensional sphere. The doubling of the fermionic degrees of freedom and the use of the Bogoljubov transformations lead to pairs of spin network's edges piercing the boundary surface with double punctures, giving rise to pixels of area encoding a qubit. The proof is also valid in the case of a fuzzy sphere.
We describe a direct method to determine the negativity of an arbitrary two-qubit state in experiments. The method is derived by analyzing the relation between the purity, negativity, and a universal entanglement witness for two-qubit entanglement. We show how the negativity of a two-qubit state can be calculated from just three experimentally accessible moments of the partially transposed density matrix of a two-photon state. Moreover, we show that the negativity can be given as a function of only six invariants, which are linear combinations of nine invariants from the complete set of 21 fun…
Interaction of solid state qubits with environmental degrees of freedom strongly affects the qubit dynamics, and leads to decoherence. In quantum information processing with solid state qubits, decoherence significantly limits the performances of such devices. Therefore, it is necessary to fully understand the mechanisms that lead to decoherence. In this review we discuss how decoherence affects two of the most successful realizations of solid state qubits, namely, spin-qubits and superconducting qubits. In the former, the qubit is encoded in the spin 1/2 of the electron, and it is implemented…
We report on the coherence of Greenberger-Horne-Zeilinger (GHZ) states comprised of up to 8 qubits in the IBM ibmqx5 16-qubit quantum processor. In particular, we evaluate the coherence of GHZ states with $N=1,\ldots,8$ qubits, as a function of a delay time between state creation and measurement. We find that the decay in coherence occurs at a rate that is linear in the number of qubits. This is consistent with a model in which the dominant noise affecting the system is uncorrelated across qubits.
The concept of quantum nondemolition (QND) measurement is extended to coherent oscillations in an individual two-state system. Such a measurement enables direct observation of intrinsic spectrum of these oscillations avoiding the detector-induced dephasing that affects the standard (non-QND) measurements. The suggested scheme can be realized in Josephson-junction qubits which combine flux and charge dynamics.
We propose that whatever quantity controls the Heisenberg uncertainty relations (for a given complementary pair of observables) it should be identified with an effective Planck parameter. With this definition it is not difficult to find examples where the Planck parameter depends on the region under study, varies in time, and even depends on which pair of observables one focuses on. In quantum cosmology the effective Planck parameter depends on the size of the comoving region under study, and so depends on that chosen region and on time. With this criterion, the classical limit is expected, no…
Quantum computers based on rare-earth-ion-doped crystals show promising properties in terms of scalability and connectivity if single ions can be used as qubits. Through simulations, we investigate gate operations on such qubits and discuss how gate and system parameters affect gate errors, the required frequency bandwidth per qubit, and the risk of instantaneous spectral diffusion (ISD) occurring. Furthermore, we examine how uncertainties in the system parameters affect the gate errors, and how precisely the system needs to be known. We find gate errors for arbitrary single-qubit gates of $2.…
We theoretically investigate the robustness of cluster states in charge qubit system based on quantum dot (QD) and double quantum point contact (DQPC). Trap state is modeled by an island structure in DQPC and represents a dynamical fluctuation. We found that the dynamical fluctuations affect the cluster states more than static fluctuation caused by QD size fluctuation.
We investigate how robust is the modified XX spin-1/2 chain of [R. Vieira and G. Rigolin, Phys. Lett. A 382, 2586 (2018)] in transmitting entanglement when several types of disorder and noise are present. First, we consider how deviations about the optimal settings that lead to almost perfect transmission of a maximally entangled two-qubit state affect the entanglement reaching the other side of the chain. Those deviations are modeled by static, dynamic, and fluctuating disorder. We then study how spurious or undesired interactions and external magnetic fields diminish the entanglement transmi…
We investigate decoherence-free evolution (DFE) of quantum discord (QD) for two initially-correlated qubits in two finite-temperature reservoirs using an exactly solvable model. We study QD dynamics of the two qubits coupled to two independent Ohmic reservoirs when the two qubits are initially prepared in X-type quantum states. It is found that reservoir temperature significantly affects the DFE dynamics. We show that it is possible to control the DFE and to prolong the DFE time by choosing suitable parameters of the two-qubit system and reservoirs.
Superqubits are the minimal supersymmetric extension of qubits. In this paper we investigate in detail their unusual properties with emphasis on their potential role in (super)quantum information theory and foundations of quantum mechanics. We propose a partial solution to the problem of negative transition probabilities that appear in the theory and has been previously reported elsewhere. The modification does not affect the performance of supersymmetric entangled states in the CHSH game - superqubits provide resources more nonlocal than it is allowed by ordinary quantum mechanics.
A scheme is presented for protecting one-qubit quantum information against decoherence due to a general environment and local exchange interactions. The scheme operates essentially by distributing information over two pairs of qubits and through error prevention procedures. In the scheme, quantum information is encoded through a decoherence-free subspace for collective phase errors and exchange errors affecting the qubits in pairs; leakage out of the encoding space due to amplitude damping is reduced by quantum Zeno effect. In addition, how to construct decoherence-free states for n-qubit info…
We discuss quantum evolution of a decaying state in relation to a recent experiment of Katz et al. Based on exact analytical and numerical solutions of a simple model, we identify a regime where qubit retains coherence over a finite time interval independently of the rates of three competing decoherence processes. In this regime, the quantum decay process can be continuously monitored via a ``weak'' measurement without affecting the qubit coherence.
Account of a system may depend on available methods of gaining information. We discuss a simple discrete system whose description is affected by a specific model of measurement and transformations. It is shown that the limited means of investigating the system make the epistemic account of the model indistinguishable from a constrained version of a qubit corresponding to the convex hull of eigenstates of Pauli operators, Clifford transformations and Pauli observables.
We consider whether quantum coherence in the form of mutual entanglement between a pair of qubits is susceptible to decay that may be more rapid than the decay of the coherence of either qubit individually. An instance of potential importance for solid state quantum computing arises if embedded qubits (spins, quantum dots, Cooper pair boxes, etc.) are exposed to global and local noise at the same time. Here we allow separate phase-noisy channels to affect local and non-local measures of system coherence. We find that the time for decay of the qubit entanglement can be significantly shorter tha…
We report the creation of Greenberger-Horne-Zeilinger states with up to 14 qubits. By investigating the coherence of up to 8 ions over time, we observe a decay proportional to the square of the number of qubits. The observed decay agrees with a theoretical model which assumes a system affected by correlated, Gaussian phase noise. This model holds for the majority of current experimental systems developed towards quantum computation and quantum metrology.
High-Frequency Gravitational Wave Detection with Superconducting Qubits
Yonsei University（延世大学）；Korea Institute for Advanced Study（韩国高等研究院）；University of Kansas（堪萨斯大学）；Seoultech（首尔科学技术院）；Institute of Convergent Fundamental Studies, Seoultech（首尔科学技术院融合基础研究所）；Institute for Basic Science（基础科学研究院）
In this paper, we investigate how quantum architectures affect the efficiency of the execution of the quantum Fourier transform (QFT) and linear transformations, which are essential parts of the stabilizer/Clifford group circuits. In particular, we show that in most common and realistic physical architectures including the linear nearest neighbor, two-dimensional lattice, and bounded degree graph (containing a chain of length n), n-qubit QFT and n-qubit stabilizer circuits can be parallelized to linear depth using no auxiliary qubits. We construct lower bounds that show the efficiency of our a…
We study exact solutions of the steady state behaviour of several non-linear open quantum systems which can be applied to the field of circuit quantum electrodynamics. Using Fokker-Planck equations in the generalised P-representation we investigate the analytical solutions of two fundamental models. First, we solve for the steady-state response of a linear cavity that is coupled to an approximate transmon qubit and use this solution to study both the weak and strong driving regimes, using analytical expressions for the moments of both cavity and transmon fields, along with the Husimi Q-functio…
Quantum properties of the probes used to estimate a classical parameter can be used to attain accuracies that beat the standard quantum limit. When qubits are used to construct a quantum probe, it is known that initializing $n$ qubits in an entangled "cat state," rather than in a separable state, can improve the measurement uncertainty by a factor of $1/\sqrt{n}$. We investigate how the measurement uncertainty is affected when the individual qubits in a probe are subjected to decoherence. In the face of such decoherence, we regard the rate $R$ at which qubits can be generated and the total dur…
Detailed schemes are investigated for experimental verification of Quantum Zeno effect with a superconducting qubit. A superconducting qubit is affected by a dephasing noise whose spectrum is 1/f, and so the decay process of a superconducting qubit shows a naturally non-exponential behavior due to an infinite correlation time of 1/f noise. Since projective measurements can easily influence the decay dynamics having such non-exponential feature, a superconducting qubit is a promising system to observe Quantum Zeno effect. We have studied how a sequence of projective measurements can change the …
Both the electron transport-based qubits, implemented through double quantum dots, and the sources of indistinguishable single-photons like self-assembled quantum dots are strong candidates for the implementation of quantum technologies, such as quantum computers and quantum repeaters. Here, we demonstrate a reliable way of coupling these two types of qubits, uncovering the possibility of controlling and reading out the population of the double quantum dot via optical excitation. It is also showed that, in spite of the decoherence mechanisms affecting the qubits, the entanglement between them …
A new class of error-correcting quantum codes is introduced capable of stabilizing qubits against spontaneous decay arising from couplings to statistically independent reservoirs. These quantum codes are based on the idea of using an embedded quantum code and exploiting the classical information available about which qubit has been affected by the environment. They are immediately relevant for quantum computation and information processing using arrays of trapped ions or nuclear spins. Interesting relations between these quantum codes and basic notions of design theory are established.
Superconducting qubits are a promising candidate for building a quantum computer. A continued challenge for fast yet accurate gates to minimize the effects of decoherence. Here we apply numerical methods to design fast entangling gates, specifically the controlled Z, in an architecture where two qubits are coupled via a resonator. We find that the gates can be sped up by a factor of two and reach any target fidelity. We also discuss how systematic errors arising from experimental conditions affect the pulses and how to remedy them, providing a strategy for the experimental implementation of ou…
We consider two qubits interacting by means of an optical cavity, where each qubit is represented by a single electron spin confined to a quantum dot. It is known that electron spins in III-V semiconductor quantum dots are affected by the decoherence due to the hyperfine interaction with nuclear spins. Here we show that the interaction between two qubits is influenced by the Overhauser field as well. Starting from an unpolarizied nuclear ensemble, we investigate the dependance of the fidelities for two-qubit gates on the Overhauser field. We include the hyperfine interaction perturbatively to …
It is widely known that spin-locking noise-spectroscopy is a powerful technique for the characterization of low-frequency noise mechanisms in superconducting qubits. Here we show that the relaxation rate of the driven spin-locking state of a qubit can be significantly affected by the presence of an off-resonant high-frequency two-level-system defect. Thus, both low- and high-frequency defects should be taken into account in the interpretation of spin-locking measurements and other types of driven-state noise-spectroscopy.
We investigate the experimental setup proposed in [New J. Phys., 15, 115006 (2013)] for calorimetric measurements of thermodynamic indicators in an open quantum system. As theoretical model we consider a periodically driven qubit coupled with a large yet finite electron reservoir, the calorimeter. The calorimeter is initially at equilibrium with an infinite phonon bath. As time elapses, the temperature of the calorimeter varies in consequence of energy exchanges with the qubit and the phonon bath. We show how under weak coupling assumptions, the evolution of the qubit-calorimeter system can be…
We consider the temporal correlations of the quantum state of a qubit subject to simultaneous continuous measurement of two non-commuting qubit observables. Such qubit state correlators are defined for an ensemble of qubit trajectories, which has the same fixed initial state and can also be optionally constrained by a fixed final state. We develop a stochastic path integral description for the continuous quantum measurement and use it to calculate the considered correlators. Exact analytic results are possible in the case of ideal measurements of equal strength and are also shown to agree with…
A better understanding of the noise causing qubit decoherence is crucial for improving qubit performance. The noise spectrum affecting the qubit may be extracted by measuring dephasing under the application of pulse sequences but requires accurate qubit control and sufficiently long relaxation times, which are not always available. Here, we describe an alternative method to extract the spectrum from correlations of single-shot measurement outcomes of successive free induction decays. This method only requires qubit initialization and readout with a moderate fidelity and also allows independent…
We consider charge qubits based on shallow donor electron states in silicon and coupled quantum dots in GaAs. Specifically, we study the feasibility of P$_2^+$ charge qubits in Si, focusing on single qubit properties in terms of tunnel coupling between the two phosphorus donors and qubit decoherence caused by electron-phonon interaction. By taking into consideration the multi-valley structure of the Si conduction band, we show that inter-valley quantum interference has important consequences for single-qubit operations of P$_2^+$ charge qubits. In particular, the valley interference leads to a…
Standard thermometry employs the thermalisation of a probe with the system of interest. This approach can be extended by incorporating the possibility of using the non-equilibrium states of the probe, and the presence of coherence. Here, we illustrate how these concepts apply to the single-qubit thermometer introduced by Jevtic et al. by performing a simulation of the qubit-environment interaction in a linear-optical device. We discuss the role of the coherence, and how this affects the usefulness of non-equilibrium conditions. The origin of the observed behaviour is traced back to the propens…
We study quantum information transmission in a Heisenberg-XY chain where qubits are affected by quasi-local environment action and compare it with the case of local action of the environment. We find that for open boundary conditions the former situation always improves quantum state transfer process, especially for short chains. In contrast, for closed boundary conditions quasi-local environment results advantageous in the strong noise regime. When the noise strength is comparable with the XY interaction strength, the state transfer fidelity through chain of odd/even number of qubits in prese…
The unit of quantum information is the qubit, a vector in a two-dimensional Hilbert space. On the other hand, quantum hardware often operates in two-dimensional subspaces of vector spaces of higher dimensionality. The presence of higher quantum states may affect the accuracy of quantum information processing. In this Letter we show how to cope with {\em quantum leakage} in devices based on small Josephson junctions. While the presence of higher charge states of the junction reduces the fidelity during gate operations we demonstrate that errors can be minimized by appropriately designing and op…
We study the performance of common quantum stabilizer codes in the presence of asymmetric and correlated errors. Specifically, we consider the depolarizing noisy quantum memory channel and perform quantum error correction via the five and seven-qubit stabilizer codes. We characterize these codes by means of the entanglement fidelity as function of the error probability and the degree of memory. We show that their performances are lowered by the presence of correlations and we compute the error probability threshold values for codes effectiveness. Furthermore, we uncover that the asymmetry in t…
