Quantum Logic Research Articles

Optimal Qubit Assignment and Routing via Integer Programming

We consider the problem of mapping a logical quantum circuit onto a given hardware with limited 2-qubit connectivity. We model this problem as an integer linear program, using a network flow formulation with binary variables that includes the initial allocation of qubits and their routing. We consider several cost functions: an approximation of the fidelity of the circuit, its total depth, and a measure of cross-talk, all of which can be incorporated in the model. Numerical experiments on synthetic data and different hardware topologies indicate that the error rate and depth can be optimized simultaneously without significant loss. We test our algorithm on a large number of quantum volume circuits, optimizing for error rate and depth; our algorithm significantly reduces the number of CNOTs compared to Qiskit’s default transpiler SABRE [ 19 ] and produces circuits that, when executed on hardware, exhibit higher fidelity.

All-Optical Generation and Time-Resolved Polarimetry of Magnetoacoustic Resonances via Transient Grating Spectroscopy

The generation and control of surface acoustic waves (SAWs) in a magnetic material are objects of an intense research effort focused on magnetoelastic properties, with fruitful ramifications in spin-wave-based quantum logic and magnonics. We implement a transient grating setup to optically generate SAWs also seeding coherent spin waves via magnetoelastic coupling in ferromagnetic media. In this work we report on SAW-driven ferromagnetic resonance (FMR) experiments performed on polycrystalline Ni thin films in combination with time-resolved Faraday polarimetry, which allows extraction of the value of the effective magnetization and of the Gilbert damping. The results are in full agreement with measurements on the very same samples from standard FMR. Higher-order effects due to parametric modulation of the magnetization dynamics, such as down-conversion, up-conversion, and frequency mixing, are observed, testifying the high sensitivity of this technique.

On the Role of Inconsistency in Quantum Foundational Debate and Hilbert Space Formulation

This article is intended mainly to develop an expository outline of an inherently inconsistent reasoning in the development of quantum mechanics during 1920s, which set up the background of proposing different variants of quantum logic a bit later. We will discuss here two of the quantum logical variants with reference to Hilbert space formulation, based on the proposals of Bohr and Schrödinger as a result of addressing the same kernel of difficulties and will give a relative comparison. Our presentation is fairly informal, as our goal here is to simply sketch the central ideas leaving further details for other occasions.Quanta 2022; 11: 28–41.

A Modal Interpretation of Quantum Spins and Its Application to Freudian Theory

In the present paper, we aim to develop a formal quantum logic theory of the interplay between conscious and unconscious processes of the human mind, a goal that has already been envisaged in quantum cognition; in doing so, we will show how the interplay between formal language and metalanguage allows for characterizing pure quantum states as infinite singletons: in the case of the spin observable, we obtain an equation defining a modality that is then re-interpreted as an abstract projection operator. By including a temporal parameter in the equations and by defining a modal negative operator, we derive an intuitionistic-like negation, for which the non-contradiction law is seen as an equivalent of the quantum uncertainty. Building on the psychoanalytic theory of Bi-Logic by Matte Blanco, we use modalities in interpreting the emergence of conscious representations from an unconscious one, and we demonstrate that this description fits well with Freud’s view of the role of negation in mental processes. Psychoanalysis, where affect plays a prominent role in shaping not only conscious, but also unconscious representations, is therefore seen as a suitable model to expand the domain of quantum cognition to the broader field of affective quantum cognition.

Strong rojections in Hilbert Space and Quantum Logic

Strong rojections in Hilbert Space and Quantum Logic

On the noise-sensitivity of entangling quantum logic operations implemented with a semiconductor quantum dot platform

A full-stack modeling study is conducted against three types of 2-qubit (quantum bit) entangling logic operations that are implemented with a realistically sized electrode-driven Silicon (Si) quantum dot system. Using device simulations based on the bulk physics augmented with electronic structure calculations based on the effective mass theory, we computationally explore the design of a fast SWAP1/2 (S1/2), Controlled-Z (CZ), and Controlled-X (CNOT) gate, and particularly study their operational sensitivity to the charge noise that is fundamentally not easy to be removed from semiconductors. Our results indicate that a recently reported one-step CNOT logic that is implemented with a single microwave pulse, is much more sensitive to the noise than S1/2 & CZ gate are, recommending basic entangling blocks that would be desirable for designs of quantum circuits based on a Si quantum dot platform.

Realization of Quantum Swap Gate and Generation of Entangled Coherent States

The cross fusion of quantum mechanics and information science forms quantum information science. Quantum logic gates and quantum entanglement are very important building blocks in quantum information processing. In this paper, we propose one-step schemes for realizing quantum swap gates and generating two-mode entangled coherent states via circuit QED. In our scheme, due to the adiabatic elimination of the excited state of the qutrit under the condition of large detuning, the decoherence of the spontaneous emission of the qutrit can be ignored. The fidelity of the quantum swap gate remains at a very high level. In addition, we also explore the nonclassical properties of two-mode entangled coherent states prepared in our scheme by addressing the second-order correlation function and intermodal squeezing. In particular, two classes of entangled coherent states demonstrate distinct entanglement and nonclassical behavior.

Enhancing coherent energy transfer between quantum devices via a mediator

We investigate the coherent energy transfer between two quantum systems mediated by a quantum bus. In particular, we consider the energy transfer process between two qubits, and how it can be influenced by using a third qubit or photons in a resonant cavity as mediators. Inspecting different figures of merit and considering both on and off-resonance configurations, we characterize the energy transfer performances. We show that, while the qubit-mediated transfer shows no advantages with respect to a direct coupling case, the cavity-mediated one is progressively more and more efficient as function of the number of photons stored in the cavity that acts as a quantum bus. The speeding-up of the energy transfer time, due to a quantum mediator paves the way for new architecture designs in quantum technologies and energy based quantum logics.

Quantum Fredkin and Toffoli gates on a versatile programmable silicon photonic chip

Quantum logic gates are backbones of quantum information processing (QIP), wherein the typical three-qubit Fredkin and Toffoli gates are essential in quantum computation and communication. So far, the quantum Fredkin gate has only been demonstrated with pre-entangled input states in free-space optics, which limits its usage for independent input photons. Here, we put forward an exquisite scheme and experimentally perform a proof-of-principle demonstration of three-qubit Fredkin and Toffoli gates on a programmable quantum photonic chip. Our scheme can also be used to realize a series of other two-qubit quantum gates. Our work sheds light on the merits of quantum photonic chip in implementing quantum logic gates, and paves the way for advanced quantum chip processors.

Synchronous chip-to-chip communication with a multi-chip resonator clock distribution network *

Superconducting digital circuits are a promising approach to build integrated systems with high energy-efficiency and computational density of the packaged chips. In such systems, performance of the data link between chips mounted on a multi-chip-module (MCM) is a critical driver of performance. In this work we report a synchronous data link using reciprocal quantum logic enabled by resonant clock distribution on-chip and on the MCM carrier. The simple physical link has only four Josephson junctions and 3 fJ/bit dissipation, including a 300 W/W cooling overhead. The driver produces a signal with 35 GHz analog bandwidth and connects to a single-ended receiver via 20 Ω Nb passive transmission line. To validate this link, we have designed, fabricated, and tested two 32 × 32 mm2 MCMs with eight 5 × 5 mm2 chips connected serially and powered by a traveling-wave clock, and with four 10 × 10 mm2 chips powered with a 2 GHz resonant clock. The traveling-wave clock MCM validates performance of the data link components and achieves a 5.4 dB AC bias margin with no degradation relative to individual chip tests. The resonator MCM validates synchronization between chips, with a measured AC bias margin up to 4.8 dB between two chips. The resonator MCM is capable of powering circuits of 4 million Josephson junctions across the four chips with a projected 10 Gbps serial data rate.

Devitalizing noise-driven instability of entangling logic in silicon devices with bias controls

The quality of quantum bits (qubits) in silicon is highly vulnerable to charge noise that is omnipresent in semiconductor devices and is in principle hard to be suppressed. For a realistically sized quantum dot system based on a silicon-germanium heterostructure whose confinement is manipulated with electrical biases imposed on top electrodes, we computationally explore the noise-robustness of 2-qubit entangling operations with a focus on the controlled-X (CNOT) logic that is essential for designs of gate-based universal quantum logic circuits. With device simulations based on the physics of bulk semiconductors augmented with electronic structure calculations, we not only quantify the degradation in fidelity of single-step CNOT operations with respect to the strength of charge noise, but also discuss a strategy of device engineering that can significantly enhance noise-robustness of CNOT operations with almost no sacrifice of speed compared to the single-step case. Details of device designs and controls that this work presents can establish practical guideline for potential efforts to secure silicon-based quantum processors using an electrode-driven quantum dot platform.

Controlled-phase gate by dynamic coupling of photons to a two-level emitter

We propose an architecture for achieving high-fidelity deterministic quantum logic gates on dual-rail encoded photonic qubits by letting photons interact with a two-level emitter (TLE) inside an optical cavity. The photon wave packets that define the qubit are preserved after the interaction due to a quantum control process that actively loads and unloads the photons from the cavity and dynamically alters their effective coupling to the TLE. The controls rely on nonlinear wave mixing between cavity modes enhanced by strong externally modulated electromagnetic fields or on AC Stark shifts of the TLE transition energy. We numerically investigate the effect of imperfections in terms of loss and dephasing of the TLE as well as control field miscalibration. Our results suggest that III-V quantum dots in GaAs membranes is a promising platform for photonic quantum information processing.

Connecting the free energy principle with quantum cognition.

It appears that the free energy minimization principle conflicts with quantum cognition since the former adheres to a restricted view based on experience while the latter allows deviations from such a restricted view. While free energy minimization, which incorporates Bayesian inference, leads to a Boolean lattice of propositions (classical logic), quantum cognition, which seems to be very dissimilar to Bayesian inference, leads to an orthomodular lattice of propositions (quantum logic). Thus, we address this challenging issue to bridge and connect the free energy minimization principle with the theory of quantum cognition. In this work, we introduce “excess Bayesian inference” and show that this excess Bayesian inference entails an underlying orthomodular lattice, while classic Bayesian inference entails a Boolean lattice. Excess Bayesian inference is implemented by extending the key idea of Bayesian inference beyond classic Bayesian inference and its variations. It is constructed by enhancing the idea of active inference and/or embodied intelligence. The appropriate lattice structure of its logic is obtained from a binary relation transformed from a distribution of the joint probabilities of data and hypotheses by employing a rough-set lattice technique in accordance with quantum cognition logic.

Optical effects of quantum systems coupled with one- and two-dimensional structured baths

We study the probe absorption and dispersion properties of a Λ-type quantum system which is coupled to one- and two-dimensional bosonic structured reservoirs. Using as structured reservoirs the one-dimensional model with nearest-neighbor coupling, as well as, a two-dimensional bath with square-lattice symmetry, we show the modification to the optical properties of the Λ-type system and present the conditions for which the system may become transparent to a probe field. Due to the unique band structures emerge from the bath periodicity, transparency presents interesting behavior in the strong coupling regime. The potential for all-optical photon switching is also presented. The effects presented here could be useful in quantum technologies for the creation of all-optical quantum logic gates and switches.

Quantum Logic under Semiclassical Limit: Information Loss

We consider the quantum computation efficiency from a new perspective. The efficiency is reduced to its classical counterpart by imposing the semiclassical limit. We show that this reduction is caused by the fact that any elementary quantum logic operation (gate) suffers the information loss during the transition to its classical analog. Amount of the information lost is estimated for any gate from the complete set. We demonstrate that the largest loss is obtained for non-commuting gates. This allows us to consider the non-commutativity as the quantum computational speed-up resource. Our method allows us to quantify advantages of a quantum computation as compared to the classical one by the direct analysis of the involved basic logic. The obtained results are illustrated by the application to a quantum discrete Fourier transform and Grover search algorithms.

High-fidelity universal quantum gates for hybrid systems via the practical photon scattering

High-fidelity quantum logic gates are essential in quantum computation, and both photons and electron spins in quantum dots (QDs) have their own unique advantages in implementing quantum computation. It is of critical significance to achieve high-fidelity quantum gates for photon-QD hybrid systems. Here, we propose two schemes for implementing high-fidelity universal quantum gates including Toffoli gate and Fredkin gate for photon-QD hybrid systems, utilizing the practical scattering of a single photon off a QD-cavity system. The computation errors from the imperfections involved in the practical scattering are detected and prevented from arising in the final results of the two gates. Accordingly, the unity fidelity of each quantum gate is obtained in the nearly realistic condition, and the requirement for experimental realization is relaxed. Furthermore, the quantum circuits for the two gates are compact and no auxiliary qubits are required, which would also be the advantages regarding their experimental feasibility. These features indicate that our schemes may be useful in the practical quantum computation tasks.

Natural Deduction for Quantum Logic

Natural Deduction for Quantum Logic

Evaluation of the systematic shifts of a $${}^{40}\text {Ca}^{+}$$–$${}^{27}\text {Al}^{+}$$ optical clock

Quantum-logic-based ${}^{27}\textrm{Al}^+$ optical clock has been demonstrated in several schemes as there are different choices of the auxiliary ion species. In this paper, we present the first detailed evaluation of the systematic shift and the total uncertainty of an ${}^{27}\textrm{Al}^+$ optical clock sympathetically cooled by a ${}^{40}\textrm{Ca}^+$ ion. The total systematic uncertainty of the ${}^{40}\textrm{Ca}^+ - {}^{27}\textrm{Al}^+$ quantum logic clock has been estimated to be $7.9 \times 10^{-18}$, which was mainly limited by the uncertainty of the quadratic Zeeman shift. By comparing the frequency of two counter-propagating clock beams on the same ion, we measured the frequency stability to be $3.7 \times 10^{-14} /\sqrt{\tau}$.

A Novel Clock Tree Aware Placement Methodology for Single Flux Quantum Logic Circuits With Maximum Path Length Consideration

In a single-flux-quantum (SFQ) circuit, almost all cells need to receive the clock signal that incurs a high clock routing overhead. Besides, the clock tree of an SFQ circuit requires the insertion of a clock splitter cell at every tree branching point that renders the conventional design flow of placement followed by clock tree synthesis (CTS) ineffective to obtain a high quality clock tree with low clock skew. Moreover, very few works in the literature attempted to minimize the maximum path length during SFQ circuit placement. The maximum path length, which is the length of the longest source-to-sink path of any data signal, should be minimized to achieve a higher final performance and to reduce the overhead for length matching in subsequent routing. To address these issues, we propose a two-stage global placement methodology and a placement refinement algorithm after placement legalization. Our two-stage global placement methodology first applies a conventional global placement algorithm to place the cells in the given SFQ circuit evenly, which is followed by CTS and clock splitter insertion, and then, performs a second stage of global placement to replace both the original cells and clock splitters at the same time. In the second global placement stage, the look-ahead legalization technique is used to spread out the original cells and the clock splitters, and the clock tree is resynthesized several times to obtain an optimized clock tree topology such that there are little overlaps of the clock splitters with the original circuit cells. We propose a novel net model in global placement that facilitates the concurrent optimization of the total wirelength and the maximum path length. After legalizing the placement of all cells, a specialized placement refinement method is run to further reduce the clock skew and the maximum path length. Compared with the previous state-of-the-art work, on average, we reduced the total half-perimeter wirelength by 9%, reduced the maximum path length by 58%, and reduced the clock skew by 32%.

High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source

Compared to other types of qubits, photon is one of a kind due to its unparalleled advantages in long-distance quantum information exchange. Therefore, photon is a natural candidate for building a large-scale, modular optical quantum computer operating at room temperature. However, low-fidelity two-photon quantum logic gates and their probabilistic nature result in a large resource overhead for fault tolerant quantum computation. While the probabilistic problem can, in principle, be solved by employing multiplexing and error correction, the fidelity of linear-optical quantum logic gate is limited by the imperfections of single photons. Here, we report the demonstration of a linear-optical quantum logic gate with truth table fidelity of 99.84(3)% and entangling gate fidelity of 99.69(4)% post-selected upon the detection of photons. The achieved high gate fidelities are made possible by our near-optimal Rydberg single-photon source. Our work paves the way for scalable photonic quantum applications based on near-optimal single-photon qubits and photon-photon gates.