Minimal Quantum Research Articles

Performance and scaling analysis of variational quantum simulation

Abstract We present an empirical analysis of the scaling of the minimal quantum circuit depth required for a variational quantum simulation (VQS) method to obtain a solution to the time evolution of a quantum system within a predefined error tolerance. In a comparison against a non-variational method based on Trotterized time evolution, we observe a better scaling of the depth requirements using the VQS approach with respect to both the size of the system and the simulated time. Results are also put into perspective by discussing the corresponding classical complexity required for VQS. Our results allow us to identify a possible advantage region for VQS over Trotterization.

Exponential Learning Advantages with Conjugate States and Minimal Quantum Memory

The ability of quantum computers to directly manipulate and analyze quantum states stored in quantum memory allows them to learn about aspects of our physical world that would otherwise be invisible given a modest number of measurements. Here we investigate a new learning resource, which could be available to quantum computers in the future—measurements on the unknown state accompanied by its complex conjugate ρ⊗ρ∗. For a certain shadow tomography task, we surprisingly find that measurements on only copies of ρ⊗ρ∗ can be exponentially more powerful than measurements on ρ⊗K, even for large K. This expands the class of provable exponential advantages using only a constant overhead quantum memory, or minimal quantum memory, and we provide a number of examples where the state ρ∗ is naturally available in both computational and physical applications. In addition, we precisely quantify the power of classical shadows on single copies under a generalized Clifford ensemble and give a class of quantities that can be efficiently learned. The learning task we study in both the single copy and quantum memory settings is physically natural and corresponds to real-space observables with a limit of bosonic modes, where it achieves an exponential improvement in detecting certain signals under a noisy background. We quantify a new and powerful resource in quantum learning, and we believe the advantage may find applications in improving quantum simulation, learning from quantum sensors, and uncovering new physical phenomena. Published by the American Physical Society 2024

From the quantum breakdown model to the lattice gauge theory

The one-dimensional quantum breakdown model, which features spatially asymmetric fermionic interactions simulating the electrical breakdown phenomenon, exhibits an exponential U(1) symmetry and a variety of dynamical phases including many-body localization and quantum chaos with quantum scar states. We investigate the minimal quantum breakdown model with the minimal number of on-site fermion orbitals required for the interaction and identify a large number of local conserved charges in the model. We then reveal a mapping between the minimal quantum breakdown model in certain charge sectors and a quantum link model which simulates the U(1) lattice gauge theory and show that the local conserved charges map to the gauge symmetry generators. A special charge sector of the model further maps to the PXP model, which shows quantum many-body scars. This mapping unveils the rich dynamics in different Krylov subspaces characterized by different gauge configurations in the quantum breakdown model.

Compressing continuous variable quantum measurements

We generalize the notion of joint measurability to continuous variable systems by extending a recently introduced compression algorithm of quantum measurements to this realm. The extension results in a property that asks for the minimal dimensional quantum system required for representing a given set of quantum measurements. To illustrate the concept, we show that the canonical pair of position and momentum is completely incompressible. We translate the concept of measurement compression to the realm of quantum correlations, where it results in a generalization of continuous variable quantum steering. In contrast to the steering scenario, which detects entanglement, the generalization detects the dimensionality of entanglement. We illustrate the bridge between the concepts by showing that an analogue of the original EPR argument is genuinely infinite-dimensional with respect to our figure of merit, and that a fundamental discrete variable result on preparability of unsteerable state assemblages with separable states does not directly carry over to the continuous variable setting. We further prove a representation result for partially entanglement breaking channels that can be of independent interest.

Quantum extreme learning of molecular potential energy surfaces and force fields

Quantum machine learning algorithms are expected to play a pivotal role in quantum chemistry simulations in the immediate future. One such key application is the training of a quantum neural network to learn the potential energy surface and force field of molecular systems. We address this task by using the quantum extreme learning machine paradigm. This particular supervised learning routine allows for resource-efficient training, consisting of a simple linear regression performed on a classical computer. We have tested a setup that can be used to study molecules of any dimension and is optimized for immediate use on NISQ devices with a limited number of native gates. We have applied this setup to three case studies: lithium hydride, water, and formamide, carrying out both noiseless simulations and actual implementation on IBM quantum hardware. Compared to other supervised learning routines, the proposed setup requires minimal quantum resources, making it feasible for direct implementation on quantum platforms, while still achieving a high level of predictive accuracy compared to simulations. Our encouraging results pave the way towards the future application to more complex molecules, being the proposed setup scalable.

Coherent spin qubit shuttling through germanium quantum dots

Quantum links can interconnect qubit registers and are therefore essential in networked quantum computing. Semiconductor quantum dot qubits have seen significant progress in the high-fidelity operation of small qubit registers but establishing a compelling quantum link remains a challenge. Here, we show that a spin qubit can be shuttled through multiple quantum dots while preserving its quantum information. Remarkably, we achieve these results using hole spin qubits in germanium, despite the presence of strong spin-orbit interaction. In a minimal quantum dot chain, we accomplish the shuttling of spin basis states over effective lengths beyond 300 microns and demonstrate the coherent shuttling of superposition states over effective lengths corresponding to 9 microns, which we can extend to 49 microns by incorporating dynamical decoupling. These findings indicate qubit shuttling as an effective approach to route qubits within registers and to establish quantum links between registers.

Abstract ladder operators for non self-adjoint Hamiltonians, with applications

Ladder operators are useful, if not essential, in the analysis of some given physical system since they can be used to find easily eigenvalues and eigenvectors of its Hamiltonian. In this paper we extend our previous results on abstract ladder operators considering in many details what happens if the Hamiltonian of the system is not self-adjoint. Among other results, we give an existence criterion for coherent states constructed as eigenstates of our lowering operators. In the second part of the paper we discuss two different examples of our framework: pseudo-quons and a deformed generalized Heisenberg algebra. Incidentally, and interestingly enough, we show that pseudo-quons can be used to diagonalize an oscillator-like Hamiltonian written in terms of (non self-adjoint) position and momentum operators which obey a deformed commutation rule of the kind often considered in minimal length quantum mechanics.

Minimal quantum heat pump based on high-frequency driving and non-Markovianity.

We propose a minimal setup for a quantum heat pump consisting of two tunnel-coupled quantum dots, each hosting a single level and each being coupled to a different fermionic reservoir. The working principle relies on both non-Markovian system-bath coupling and driving-induced resonant coupling. We describe the system using a reaction-coordinate mapping in combination with Floquet-Born-Markov theory and characterize its performance.

Semiquantum Key Distribution Using Initial States in Only One Basis Without the Classical User Measuring

AbstractFrom the perspective of resource theory, it is interesting to achieve the same quantum task using as few quantum resources as possible. Semiquantum key distribution (SQKD), which allows a quantum user to share a confidential key with a classical user who prepares and operates qubits on only one basis, is an important example for studying this issue. To further limit the quantum resources used by users, in this paper, the first SQKD protocol is constructed, which restricts the quantum user to prepare quantum states on only one basis and removes the classical user's measurement capability. Furthermore, it is proven that the constructed protocol is secure against the restricted attack by deriving a key rate expression of the error rate in the asymptotic scenario. The work in this paper provides inspiration for achieving quantum superiority with minimal quantum resources.

Advancing nanoscale computing: Efficient reversible ALU in quantum-dot cellular automata

This paper presents a significant contribution to the field of nanoscale computing by proposing an innovative reversible Arithmetic and Logic Unit (ALU) implemented in Quantum-Dot Cellular Automata (QCA). Reversible logic and QCA technology offer promising alternatives to conventional CMOS technology, addressing the challenges of operating at nanoscale dimensions. The primary objective is to develop a highly efficient ALU capable of performing 26 distinct arithmetic and logical operations. The ALU design is based on a novel reversible full adder-subtractor optimized for minimal quantum cost, which is crucial for energy-efficient quantum computation. The evaluation encompasses various criteria related to reversibility, such as gate count, number of constant inputs, number of garbage outputs, and quantum cost. QCA-specific criteria, including cell count, occupied area, and clock cycles, are also considered. The outcomes of this research contribute to the advancement of cell-efficient nanoscale computing, with implications for quantum computation, emerging technologies, and future integrated circuit design.

Geometry-independent superfluid weight in multiorbital lattices from the generalized random phase approximation

The superfluid weight of a generic lattice model with attractive Hubbard interaction is computed analytically in the isolated band limit within the generalized random phase approximation. Time-reversal symmetry, spin rotational symmetry, and the uniform pairing condition are assumed. It is found that the relation obtained in Huhtinen [] between the superfluid weight in the flat band limit and the so-called minimal quantum metric is valid even at the level of the generalized random phase approximation. For an isolated, but not necessarily flat, band it is found that the correction to the superfluid weight obtained from the generalized random phase approximation Ds(1)=Ds,c(1)+Ds,g(1) is also the sum of a conventional contribution Ds,c(1) and a geometric contribution Ds,g(1), as in the case of the known mean-field result Ds(0)=Ds,c(0)+Ds,g(0), in which the geometric term Ds,g(0) is a weighted average of the quantum metric. The conventional contribution is geometry independent, that is, independent of the orbital positions, while it is possible to find a preferred, or natural, set of orbital positions such that Ds,g(1)=0. Useful analytic expressions are derived for both the natural orbital positions and the minimal quantum metric, including its extension to bands that are not necessarily flat. Finally, using some simple examples, it is argued that the natural orbital positions may lead to a more refined classification of the topological properties of the band structure. Published by the American Physical Society 2024

Defining Relations for Minimal Unitary Quantum Affine W-Algebras

We prove that any unitary highest weight module over a universal minimal quantum affine W-algebra at non-critical level descends to its simple quotient. We find the defining relations of the unitary simple minimal quantum affine W-algebras and the list of all their irreducible positive energy modules. We also classify all irreducible highest weight modules for the simple affine vertex algebras in the cases when the associated simple minimal W-algebra is unitary.

Optimized design and investigation of novel reversible toffoli and peres gates using QCA techniques

The QCA is a revolutionary dominating transistor-less computational nanotechnology based on quantum dots. As such, it might be used in the next generation of quantum computational nano-electronics devices. New molecular materials like QCA are being developed for use in nanoscale devices and cables. The major objective of this research is to optimize the design and investigate numerous properties of a QCA reversible logic circuit design. These locations include, limited Toffoli Gate (TG) and Peres Gate (PG). To address the key problems associated with the physical integration of digital circuits is power consumption and power dissipation which leads to synchronization issues, this research proposes a novel reversible logic gates (RLG-TG) a single layer coplanar approach. RLG designs with minimal design area, latency, and quantum cell count (QCA) are given and implemented using a Bijection functional method. Using the QD-E (Energy) tool, the first-order energy dissipation of the proposed shape and the impact of output bias cell temperature are also investigated. The proposed circuit designs were tested using the CVSE parameters, which had high clock signal saturation energies of 9.8e-22 d (Jules), recovery times for damping factors of 1e-15 s, and relative dielectric constants of 12.90 for GaAs and AlGaAs. The number of quantum cells used by the described new RLG-TG and RLG-PG designs is decreased by 38.23 % and 21.14 %, respectively, when compared to the optimal RLG designs employed in the state-of-the-art RLG designs. In this investigation of the proposed four-bit EPG and OPG circuits occupies 18.91 % and 38.27 % less design area, requires 46.15 % and 46.25 % less number of cells, and both designs has been 66.66 % improvement in delay.

Time–Energy Uncertainty Relation in Nonrelativistic Quantum Mechanics

The time–energy uncertainty relation in nonrelativistic quantum mechanics has been intensely debated with regard to its formal derivation, validity, and physical meaning. Here, we analyze two formal relations proposed by Mandelstam and Tamm and by Margolus and Levitin and evaluate their validity using a minimal quantum toy model composed of a single qubit inside an external magnetic field. We show that the ℓ1 norm of energy coherence C is invariant with respect to the unitary evolution of the quantum state. Thus, the ℓ1 norm of energy coherence C of an initial quantum state is useful for the classification of the ability of quantum observables to change in time or the ability of the quantum state to evolve into an orthogonal state. In the single-qubit toy model, for quantum states with the submaximal ℓ1 norm of energy coherence, C<1, the Mandelstam–Tamm and Margolus–Levitin relations generate instances of infinite “time uncertainty” that is devoid of physical meaning. Only for quantum states with the maximal ℓ1 norm of energy coherence, C=1, the Mandelstam–Tamm and Margolus–Levitin relations avoid infinite “time uncertainty”, but they both reduce to a strict equality that expresses the Einstein–Planck relation between energy and frequency. The presented results elucidate the fact that the time in the Schrödinger equation is a scalar variable that commutes with the quantum Hamiltonian and is not subject to statistical variance.

Minimal quantum dot based Kitaev chain with only local superconducting proximity effect

The possibility to engineer a Kitaev chain in quantum dots coupled via superconductors has recently emerged as a promising path toward topological superconductivity and possibly non-Abelian physics. Here we show that it is possible to avoid some of the main experimental hurdles on this path by using only local proximity effect on each quantum dot in a geometry that resembles a two-dot version of the proposal in Fulga []. There is no need for narrow superconducting couplers, additional Andreev bound states, or spatially varying magnetic fields; it suffices with spin-orbit interaction and a constant magnetic field in combination with control of the superconducting phase to tune the relative strengths of elastic cotunneling and an effective crossed-Andreev-reflection-like process generated by higher-order tunneling. We use a realistic spinful, interacting model and show that high-quality Majorana bound states can be generated already in a double quantum dot. Published by the American Physical Society 2024

Transition to chaos in extended systems and their quantum impurity models

Chaos sets a fundamental limit to quantum-information processing schemes. We study the onset of chaos in spatially extended quantum many-body systems that are relevant to quantum optical devices. We consider an extended version of the Tavis–Cummings model on a finite chain. By studying level-spacing statistics, adjacent gap ratios, and spectral form factors, we observe the transition from integrability to chaos as the hopping between the Tavis–Cummings sites is increased above a finite value. The results are obtained by means of exact numerical diagonalization which becomes notoriously hard for extended lattice geometries. In an attempt to circumvent these difficulties, we identify a minimal single-site quantum impurity model that successfully captures the spectral properties of the lattice model. This approach is intended to be adaptable to other lattice models with large local Hilbert spaces.

The quartic Blochnium: an anharmonic quasicharge superconducting qubit

The quasicharge superconducting qubit realizes the dual of the transmon and shows strong robustness to flux and charge fluctuations thanks to a very large inductance closed on a Josephson junction. At the same time, a weak anharmonicity of the spectrum is inherited from the parent transmon, that introduces leakage errors and is prone to frequency crowding in multi-qubit setups. We propose a novel design that employs a quartic superinductor and confers a good degree of anharmonicity to the spectrum. The quartic regime is achieved through a properly designed chain of Josephson junction loops that shows minimal quantum fluctuations without introducing a severe dependence on the external fluxes.

A practical approach to determine minimal quantum gate durations using amplitude-bounded quantum controls

A practical approach to determine minimal quantum gate durations using amplitude-bounded quantum controls

Multi-client distributed blind quantum computation with the Qline architecture

Universal blind quantum computing allows users with minimal quantum resources to delegate a quantum computation to a remote quantum server, while keeping intrinsically hidden input, algorithm, and outcome. State-of-art experimental demonstrations of such a protocol have only involved one client. However, an increasing number of multi-party algorithms, e.g. federated machine learning, require the collaboration of multiple clients to carry out a given joint computation. In this work, we propose and experimentally demonstrate a lightweight multi-client blind quantum computation protocol based on a recently proposed linear quantum network configuration (Qline). Our protocol originality resides in three main strengths: scalability, since we eliminate the need for each client to have its own trusted source or measurement device, low-loss, by optimizing the orchestration of classical communication between each client and server through fast classical electronic control, and compatibility with distributed architectures while remaining intact even against correlated attacks of server nodes and malicious clients.

Realization of a quantum neural network using repeat-until-success circuits in a superconducting quantum processor

Artificial neural networks are becoming an integral part of digital solutions to complex problems. However, employing neural networks on quantum processors faces challenges related to the implementation of non-linear functions using quantum circuits. In this paper, we use repeat-until-success circuits enabled by real-time control-flow feedback to realize quantum neurons with non-linear activation functions. These neurons constitute elementary building blocks that can be arranged in a variety of layouts to carry out deep learning tasks quantum coherently. As an example, we construct a minimal feedforward quantum neural network capable of learning all 2-to-1-bit Boolean functions by optimization of network activation parameters within the supervised-learning paradigm. This model is shown to perform non-linear classification and effectively learns from multiple copies of a single training state consisting of the maximal superposition of all inputs.