The Quantum Journal

arXiv:2604.21210v1 Announce Type: new Abstract: In continuously monitored quantum systems, the feedback protocol of Garc\'ia-Pintos, Liu, and Gorshkov reshapes the arrow of time: a Hamiltonian $H_{\mathrm{meas}} = r A / \tau$ applied with gain $X$ tilts the distribution of measurement trajectories,

arXiv:2604.21230v1 Announce Type: new Abstract: Fast qubit reset is essential for qubit reuse in the noisy intermediate-scale quantum computing era, yet it conflicts with the weak decoherence required for high-fidelity computation. We solve the time-optimal reset problem for a frequency-tunable qub

arXiv:2604.21266v1 Announce Type: new Abstract: There has been intensive research on increasing the utility and performance of Parameterized Quantum Circuits (PQCs) in the past couple of years. Owing to this research, there are now several inductive biases available to a quantum algorithms research

arXiv:2604.21272v1 Announce Type: new Abstract: Quantum state tomography (QST) scales exponentially in both measurement and computational cost, making full reconstruction impractical for multi-qubit systems. Existing approaches attempt to reduce this complexity, but do not explicitly restrict the o

arXiv:2604.21274v1 Announce Type: new Abstract: A random access code (RAC) encodes an $L$-bit string into a $k$-bit $(L>k)$ message from which any designated source bit can be recovered with high probability. Its quantum counterpart, a quantum random access code (QRAC), replaces the $k$-bit message

arXiv:2604.21287v1 Announce Type: new Abstract: As quantum hardware scales toward fault tolerant operation, the demand for correct quantum error correction (QEC) circuits far outpaces manual design capacity. AI agents offer a promising path to automating this synthesis, yet no benchmark exists to m

arXiv:2604.21288v1 Announce Type: new Abstract: We revisit the quantization of the order parameter, which we refer to as third quantization, from the perspective of the commutation relation between the phase operator of the order parameter and the particle-number operator. We show that this macrosc

arXiv:2604.21320v1 Announce Type: new Abstract: The quantum Mpemba effect (ME) in Markovian systems is conventionally explained by a smaller overlap between the initial state and the slowest decay mode (SDM). Such state, initially farther away from equilibrium or steady state, relaxes faster than c

arXiv:2604.21323v1 Announce Type: new Abstract: In quantum estimation for a $d$-parameter family of density operators on a finite-dimensional Hilbert space $\mathcal{H}$, an estimator is specified by a pair $\left(M,\hat{\theta}\right)$, where $M$ is a POVM with a finite outcome set $\Omega$ and $\

arXiv:2604.21333v1 Announce Type: new Abstract: We present pygridsynth, an open-source Python library for ancilla-free approximate Clifford+$T$ synthesis that runs in $O(\log(1/\epsilon))$ for precision $\epsilon$. For $n=1, 2$ qubits, the library builds upon established efficient and high-precisio

arXiv:2604.21342v1 Announce Type: new Abstract: Magnetic quantum sensors based on trapped ions utilize properties of quantum mechanics which have optimized precision and beat current limits in sensor technology. Trapped ions are highly sensitive in a large span of signal ranging from DC or static B

arXiv:2604.21348v1 Announce Type: new Abstract: We prove an exact quantum conservation law for a harmonic oscillator coupled to a ghost degree of freedom: a second classical conserved quantity lifts to a quantum operator that commutes with the Hamiltonian with no hbar corrections, yielding a rigoro

arXiv:2604.21350v1 Announce Type: new Abstract: We investigate optimized vertical ion-shuttling protocols for trapped-ion applications across a range of ion-trap experiments, including three-dimensional gradient-measurement sensors, on-chip ion fluorescence collection and imaging, improved laser ac

arXiv:2604.21388v1 Announce Type: new Abstract: High-precision optical phase stabilization in quantum networks is fundamentally constrained by the strict photon-flux and duty-cycle limits required to avoid disturbing fragile quantum states. This challenge becomes especially critical when coordinati

arXiv:2604.21458v1 Announce Type: new Abstract: Closed-loop superconducting-qubit calibration has matured into DAG-orchestrated protocol chains, yet published frameworks treat the bath via a Markovian master equation or a phenomenological likelihood, absorbing bath structure into fit residuals inst

arXiv:2604.21463v1 Announce Type: new Abstract: We investigate the reduced dynamics of two identical superconducting qubits capacitively coupled through a finite-length transmission line. Starting from circuit quantization, we derive a circuit Hamiltonian that naturally separates the line modes int

arXiv:2604.21472v1 Announce Type: new Abstract: Fault-tolerant quantum computing increasingly demands rigorous, circuit-level evaluation of diverse quantum error correction (QEC) protocols and efficient prototyping of new ones. Such evaluation requires both the physical circuit and its Detector Err

arXiv:2604.21475v1 Announce Type: new Abstract: Photonic quantum computing provides a promising route toward quantum computation by naturally supporting the measurement-based quantum computation (MBQC) model. In MBQC, programs are executed through measurements on a pre-generated graph state, whose

arXiv:2604.21509v1 Announce Type: new Abstract: The generalized second laws of quantum thermodynamics are usually formulated in terms of R\'enyi divergences and the associated family of generalized free energies. In catalytic thermal transformations, this framework typically certifies the existence

arXiv:2604.21513v1 Announce Type: new Abstract: We characterize nonequilibrium phases in long-range dissipative spin systems through the statistical properties of quantum jump trajectories. While the average dynamics governed by the Lindblad master equation provides access to steady-state expectati

arXiv:2604.21560v1 Announce Type: new Abstract: We construct mode-selective effective models describing the interaction of the quantum plasmon-polariton field supported by a finite dielectric medium and one or several quantum emitters. The construction of the effective model is based on the decompo

arXiv:2604.21565v1 Announce Type: new Abstract: High-fidelity control of superconducting qubits requires carefully shaped microwave pulses that account for multiple error channels. In this work, we present a pedagogical introduction to pulse-shaping techniques for transmon qubits, aiming to provide

arXiv:2604.21574v1 Announce Type: new Abstract: We propose a semiclassical framework for solving open quantum dynamics in driven-dissipative spin systems. Our method consists of generalized spin-wave approximations tailored to describing quantum trajectories unravelled from the master equation, and

arXiv:2604.21594v1 Announce Type: new Abstract: Systematic control errors remain a primary obstacle to realizing high-fidelity single-qubit gates. We introduce composite pulse sequences that implement X and Hadamard gates while simultaneously compensating amplitude (Rabi-frequency), detuning (frequ

arXiv:2604.21656v1 Announce Type: new Abstract: We present a new software package for efficient quantum circuit generation, designed to achieve optimal runtime performance. Despite being in an early stage of development, our implementation demonstrates significant advantages over existing tools. Us

arXiv:2604.21659v1 Announce Type: new Abstract: The optical spectrum of a quantum system is jointly determined by the properties of the emitter and the driving field. All-optical spectral control can hence be a promising method to engineer the properties of single photon emitters for quantum techno

arXiv:2604.21692v1 Announce Type: new Abstract: The creation of high-quality cluster states in superconducting microwave circuits is a relevant ingredient in continuous-variable quantum computing. Although large-scale cluster states have been established in optical systems, dissipation prevents the

arXiv:2604.21695v1 Announce Type: new Abstract: We describe the design, implementation, and nine-month operational experience of the software management stack for Lagrange, an IQM Spark five-qubit superconducting quantum computer jointly acquired by LINKS Foundation, Politecnico di Torino and the I

arXiv:2604.21705v1 Announce Type: new Abstract: We show that detecting steady-state Coulomb-mediated reduction in the thermal variance of the differential motional mode of two nanospheres can bound the Continuous Spontaneous Localization (CSL) parameter ($\lambda_{{\text{CSL}}}$). For realistic exp

arXiv:2604.21722v1 Announce Type: new Abstract: Modular quantum computing architectures require error correction schemes that remain effective in the presence of noisy inter-processor operations. As such, minimizing the number of such operations on logical circuits partitioned across quantum proces

arXiv:2604.21723v1 Announce Type: new Abstract: Quantum technologies in the terahertz (THz) require a coherent interface between addressable qubits and THz quantum channels -- a capacity that so far, remains largely underdeveloped. Here, we propose and demonstrate the generation of steady-state ent

arXiv:2604.21758v1 Announce Type: new Abstract: High-quality photonic Bell state measurements (BSMs) enable scalable universal quantum computing and long distance quantum communication. However, when implemented with linear optics, BSMs are fundamentally probabilistic, introducing substantial hardw

arXiv:2604.21778v1 Announce Type: new Abstract: We present a fast, memory-efficient, unitarity-preserving numerical method beyond the rotating-wave approximation for the closed Tavis-Cummings model in which a multilevel spin system interacts with a cavity mode. This model can describe the interacti

arXiv:2604.21788v1 Announce Type: new Abstract: The partial oracles framework is a quantum search algorithm that has the potential to exceed the quadratic speedup of Grover's algorithm, up to a theoretical maximum of an exponential speedup. Until now, however, the framework has lacked an explicit m

arXiv:2604.21791v1 Announce Type: new Abstract: This thesis is concerned with rigorous security analyses of practical Quantum Key Distribution (QKD) protocols, using a variety of modern proof techniques. The main results are as follows. First, we establish a security proof for variable-length QKD p

arXiv:2604.21800v1 Announce Type: new Abstract: Exact quantum codes detecting a prescribed set of Pauli errors are approached through algebraic constructions--stabilizer, codeword-stabilized, permutation-invariant, topological, and related families. Geometrically, exact Pauli detection is governed

arXiv:2604.21805v1 Announce Type: new Abstract: Page and Wootters (1983) showed how time and dynamics can emerge in a stationary system containing a clock. Albrecht (1995) later showed, for discrete time, that within this framework any dynamical evolution can be obtained simply by choosing a differ

arXiv:2604.21820v1 Announce Type: new Abstract: The Dicke model (DM) serves as a paradigm for understanding collective light-matter interactions. We introduce the chiral Dicke model, a generalization where an atomic ensemble couples to a two-mode cavity via chiral interactions. Unlike the standard

arXiv:2604.21824v1 Announce Type: new Abstract: Bosonic quantum error correction enables hardware-efficient protection of quantum information by encoding logical qubits in harmonic oscillators. Bosonic grid states, such as Gottesman-Kitaev-Preskill (GKP) states, are particularly promising due to th

arXiv:2604.21863v1 Announce Type: new Abstract: Deep reinforcement learning (RL) for quantum circuit optimization faces three fundamental bottlenecks: replay buffers that ignore the reliability of temporal-difference (TD) targets, curriculum-based architecture search that triggers a full quantum-cl

arXiv:2604.21866v1 Announce Type: new Abstract: Execution of quantum algorithms on large-scale quantum computers will require extremely low logical error rates, which necessitates the development of scalable decoding architectures. Local decoders are promising candidates for this task, as they avoi

arXiv:2604.21874v1 Announce Type: new Abstract: Solid-state spin defects hold great promise as building blocks for various quantum technologies. Embedding spin centers in $p$-$n$ diodes under reverse bias has proved to be a powerful strategy to narrow the optical linewidth and increase spin coheren

arXiv:2604.21876v1 Announce Type: new Abstract: We investigate the limits of quantum error correction (QEC) in neutral-atom processors approaching high-fidelity gates and fast cycle times. We show that shorter QEC cycles amplify platform-specific errors, notably Rydberg excitation hopping, and hind

arXiv:2604.21902v1 Announce Type: new Abstract: Quantum networks are a keystone of the quantum internet. However, existing implementations remain largely confined to static point-to-point links due to the absence of a switching paradigm capable of dynamically routing fragile quantum entanglement wi

arXiv:2604.21908v1 Announce Type: new Abstract: Peaked quantum circuits, whose output distribution is sharply concentrated on a single bitstring, have emerged as a promising candidate for verifiable quantum advantage, as the correctness of the quantum output can be checked by simply comparing again

arXiv:2604.21913v1 Announce Type: new Abstract: Quantum resources such as entanglement form the backbone of quantum technologies and their efficient generation is a central objective of modern quantum platforms. Independently, quantum batteries have emerged as nanoscale devices that utilize collect

arXiv:2604.21919v1 Announce Type: new Abstract: Belief propagation has recently emerged as a powerful framework for evaluating tensor networks in higher dimensions, combining computational efficiency with provable analytical guarantees. In this work, we develop the first end-to-end theory of tensor

arXiv:2604.21929v1 Announce Type: new Abstract: We study spectral properties of quantum many-body Hamiltonians through a subsystem-based framework. Given a Hamiltonian of the form $H = \sum_{X \subseteq \Lambda} \Phi(X)$ acting on a tensor product Hilbert space, we associate to each subset $S \subs

arXiv:2604.20901v1 Announce Type: cross Abstract: Nitrogen-vacancy (NV) centers in diamond are of great interest for nano- and macro-scale magnetic field sensing. Most sensing protocols rely on conventional optical readout, which is limited by photon shot noise. The recently developed photoelectric

arXiv:2604.20969v1 Announce Type: cross Abstract: We investigate the effects of coupling a quantum-magnetic cavity field to molecules. Our high-precision auxiliary-field quantum Monte Carlo calculations capture the effect of the cavity field in the presence of electron correlations, and their inter

arXiv:2604.21005v1 Announce Type: cross Abstract: Accurate modeling of ion-molecule reaction networks is essential for understanding the chemical evolution of planetary ionospheres, particularly for giant planets where proton-transfer chains drive atmospheric composition. However, predicting reacti

arXiv:2604.21206v1 Announce Type: cross Abstract: We study the magnetic-field dependence of the interactions between two alkaline-earth(-like) Rydberg atoms, ${}^{88}$Sr and ${}^{174}$Yb. Considering the pair of Rydberg states $|ns,{}^3S_1,m_J\rangle$ and $|(n+1)s,{}^3S_1,m_J\rangle$, we show that

arXiv:2604.21366v1 Announce Type: cross Abstract: Several approximation procedures, such as the full or partial rotating-wave, time-averaging, and geometric-arithmetic approximations, have been proposed to derive Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) generators from the Born-Markov quantum m

arXiv:2604.21373v1 Announce Type: cross Abstract: We consider two-dimensional harmonic oscillator in the complex Bargmann-Fock-Segal representation with $T^*{\mathbb R}^{2}={\mathbb C}^2$ as classical phase space. We show that the eigenfunctions $\psi_n$ of the quantum Hamiltonian correspond to com

arXiv:2604.21374v1 Announce Type: cross Abstract: We show in this article the improvements which can be obtained in the description of the luminescence properties of Pr3+ doped materials by using an extension of the Judd-Ofelt theory in order to relax some strong selection rules and approximations

arXiv:2604.21630v1 Announce Type: cross Abstract: We establish a relation between the exponential decay rates of quantum Markov semigroups with respect to different inner products. More precisely, it was conjectured by Fagnola, Poletti, Sasso and Umanit\`a that for a Gaussian quantum Markov semigro

arXiv:2604.21755v1 Announce Type: cross Abstract: In this work, we systematically investigate the quantum-information diagnostics of cosmological perturbations with a nontrivial sound speed, utilizing a normalized open two-mode squeezed-state framework. Rather than introducing new observables, our

arXiv:2604.21823v1 Announce Type: cross Abstract: We quantize a classically stable system of a harmonic oscillator polynomially coupled to a ghost with negative kinetic energy. We prove that due to an integral of motion with a positive discrete spectrum: i) the Hamiltonian has a pure point spectrum

arXiv:2604.21857v1 Announce Type: cross Abstract: New sources of charge-parity (CP) violation beyond those described in the Standard Model (SM) are required to explain the observed matter--antimatter asymmetry of the Universe. The Standard Model Effective Field Theory (SMEFT) provides a framework t

arXiv:1307.4144v2 Announce Type: replace Abstract: Non-locality is one of the hallmarks of quantum mechanics and is responsible for paradigmatic features such as entanglement and the Aharonov-Bohm effect. Non-locality comes in two flavours: a \emph{kinematic} non-locality -- arising from the struct

arXiv:2211.00333v2 Announce Type: replace Abstract: We present a microscopic derivation from a nonequilibrium spin-boson model to a $\PT$-symmetric non-Hermitian sine-Gordon (SG) effective theory, via the Keldysh functional-integral formalism, a Lang-Firsov polaron transformation, bosonization, and

arXiv:2409.13113v3 Announce Type: replace Abstract: Dissipative tunneling remains a cornerstone effect in quantum mechanics. In chemistry, it plays a crucial role in governing the rates of chemical reactions, often modeled as the motion along the reaction coordinate from one potential well to anoth

arXiv:2501.08036v3 Announce Type: replace Abstract: Fault tolerance in quantum protocols requires contributions from error-correcting codes and their suitable decoders. Quantum Low-Density Parity Check (QLDPC) codes are one of the most explored quantum codes that have good coding rate and efficient

arXiv:2505.15521v3 Announce Type: replace Abstract: One of the premier utilities of present day noisy quantum computers is simulation of many-body quantum systems. We study how long in time is such a discrete-time simulation representative of a continuous time Hamiltonian evolution, namely, a finit

arXiv:2507.07520v3 Announce Type: replace Abstract: We offer the first operational interpretation of the $\alpha$-z relative entropies, a measure of distinguishability between two quantum states introduced by Jak\v{s}i\'c et al. and Audenaert and Datta. We show that these relative entropies appear

arXiv:2507.18351v3 Announce Type: replace Abstract: Exploring potential empirical manifestations of quantum gravity is a challenging pursuit. In this study, we utilise a lattice representation of a (2+1)D massive gravity toy model interacting with Dirac fermions that can support specific spacetime

arXiv:2508.17395v3 Announce Type: replace Abstract: In an earlier letter [Ducharme \textit{et al.} Phys. Rev. Lett. \textbf{126}, 134803 (2021)], a solution to the Dirac equation for a relativistic Gaussian electron beam showed that for a diverging beam the spin of each electron is the sum of fract

arXiv:2508.19160v2 Announce Type: replace Abstract: In the emerging field of Fault Tolerant Quantum Computation (FTQC), resource estimation is an important tool for quantitatively comparing prospective architectures, identifying hardware bottlenecks and informing which research paths are most valua

arXiv:2509.02309v2 Announce Type: replace Abstract: We describe a simple and flexible method for implementing semi-definite programming relaxations for bounding the set of quantum correlations. The method relies on obtaining equality constraints from randomly sampled moment matrices and hence allow

arXiv:2509.06086v3 Announce Type: replace Abstract: Quantum machine learning (QML) has the potential to achieve quantum advantage for specific tasks by combining quantum computation with classical machine learning (ML). In classical ML, a significant challenge is membership-privacy leakage, whereby

arXiv:2510.08210v4 Announce Type: replace Abstract: Calculating the quantum weight enumerator polynomial (WEP) is a valuable tool for characterizing quantum error-correcting (QEC) codes, but it is computationally hard for large or complex codes. The Quantum LEGO (QL) framework provides a tensor net

arXiv:2510.13671v3 Announce Type: replace Abstract: We study the collective emission of a disordered array of $N$ excited two-level atoms into a one-dimensional photonic waveguide. In the perfectly ordered case, where atoms are spaced by exact integer multiples of the wavelength, the system exhibit

arXiv:2511.23470v5 Announce Type: replace Abstract: Accurate identification of Hamiltonian parameters is essential for modeling and controlling open quantum systems. In this work, we demonstrate that the multichannel Hankel alternative view of Koopman (mHAVOK) algorithm is a robust and reliable spe

arXiv:2512.04649v2 Announce Type: replace Abstract: The hallmark of two-dimensional chiral topological phases is the existence of anomalous gapless modes at the spatial boundary. Yet, the manifestation of this edge anomaly within the bulk ground-state wavefunction itself remains only partially unde

arXiv:2512.12342v2 Announce Type: replace Abstract: We investigate how quantum coherence can be distributed among the several off-diagonal elements of an arbitrary density matrix. An easily computable quantity that captures this variability notion is proposed and it is argued that it presents marke

arXiv:2512.16400v2 Announce Type: replace Abstract: We propose a quantum circuit design for implementing coined quantum walks on complex networks. In complex networks, the coin and shift operators depend on the varying degrees of the nodes, which makes circuit construction more challenging than for

arXiv:2601.05627v2 Announce Type: replace Abstract: We investigate thermalization and the quantum-classical correspondence in the collective Bose-Hubbard model, focusing on the four-site case. Our analysis of the classical phase-space structure and its excited-state quantum phase transitions leads

arXiv:2601.07890v2 Announce Type: replace Abstract: This work provides a quantum-computing-first derivation of the Unitary Coupled Cluster ansatz, showing that its structure emerges naturally from fermionic algebra under unitary constraints. By explicitly connecting second quantization, Jordan-Wign

arXiv:2601.10479v2 Announce Type: replace Abstract: Variational Quantum Algorithms (VQAs) are critically threatened by the Barren Plateau (BP) phenomenon. In this work, we introduce the H-EFT Variational Ansatz (H-EFT-VA), an architecture inspired by Effective Field Theory (EFT). By enforcing a hie

arXiv:2601.20700v4 Announce Type: replace Abstract: In molecular aggregates, multiple delocalized exciton states interact with phonons, making the state-resolved spectroscopic monitoring of dynamics challenging. We propose a protocol that combines photon-entanglement-enhanced narrowband excitation

arXiv:2602.01943v2 Announce Type: replace Abstract: Establishing quantitative adiabaticity criteria at finite temperature remains substantially less developed than in the pure-state setting, even though realistic quantum systems are never at absolute zero. Here, by combining a mixed-state quantum s

arXiv:2603.05320v2 Announce Type: replace Abstract: Quantum error correction will likely be essential for building a large-scale quantum computer, but it comes with significant requirements at the level of classical control software. In particular, a quantum error-correcting code must be supplement

arXiv:2603.23656v2 Announce Type: replace Abstract: We establish an exact information-geometric inequality that remains valid regardless of the underlying dynamics, encompassing both Markovian and non-Markovian evolutions within the mixed-state domain. This inequality can be viewed as an extension

arXiv:2603.26826v4 Announce Type: replace Abstract: A generalized formulation of non-relativistic quantum mechanics is developed within multidimensional geometric (NG) frameworks characterized by a power-law dispersion relation \(E \propto |p|^{j}\), where \(j = N - 1\). Starting from the generaliz

arXiv:2603.27397v2 Announce Type: replace Abstract: Both Superconducting and Ion-Trap are leading quantum architectures common in the current landscape of the quantum computing field, each with distinct characteristics and operational constraints. Understanding and measuring the underlying quantumn

arXiv:2603.29439v3 Announce Type: replace Abstract: Superconducting quantum processor units (QPUs) are incapable of producing massive datasets for quantum error correction (QEC) because of hardware limitations. Thus, QEC decoders heavily depend on synthetic data from qubit error models. Classic dep

arXiv:2604.04685v2 Announce Type: replace Abstract: We propose a data-adaptive probabilistic intensity remapping framework for structure-preserving transformation of grayscale images. The suggested method formulates intensity transformation as a continuous, data-driven remapping process, in contras

arXiv:2604.12577v2 Announce Type: replace Abstract: Quantum key distribution protocols based on the quantum eraser phenomenon offer an operational advantage: automatic identification of matching and mismatching encoding choices through interference, eliminating basis reconciliation. However, binary

arXiv:2604.19855v2 Announce Type: replace Abstract: Practical quantum advantage is expected to depend on fault-tolerant quantum computing, although the architectural overhead needed to support fault tolerance is still extremely high. Prior FTQC designs generally emphasize either fast logical-qubit

arXiv:2506.21534v2 Announce Type: replace-cross Abstract: One of the most important physical effects in condensed matter physics is the Rashba spin-orbit coupling (RSOC), introduced in seminal works by Emmanuel Rashba. In this article, we discuss, describe, and review (providing critical perspectiv

npj Quantum Information, Published online: 22 April 2026; doi:10.1038/s41534-026-01241-ySurface-code hardware Hamiltonian

npj Quantum Information, Published online: 21 April 2026; doi:10.1038/s41534-026-01247-6Distributed quantum inner product estimation with structured random circuits

npj Quantum Information, Published online: 21 April 2026; doi:10.1038/s41534-026-01221-2Two-qubit gates using on-demand single-photons from ordered shape and size controlled large-volume superradiant quantum dots

npj Quantum Information, Published online: 17 April 2026; doi:10.1038/s41534-026-01228-9Collective purification of interacting quantum networks beyond symmetry constraints

npj Quantum Information, Published online: 17 April 2026; doi:10.1038/s41534-026-01229-8Quantum reservoir computing induced by controllable damping

npj Quantum Information, Published online: 17 April 2026; doi:10.1038/s41534-026-01236-9Time-series forecasting with multiphoton quantum states and integrated photonics

npj Quantum Information, Published online: 17 April 2026; doi:10.1038/s41534-026-01246-7Beyond boson sampling: higher spin sampling as a practical path to quantum supremacy