arXiv subjects

Joshua Combes

Publications and source records attributed to Joshua Combes.

At least 19 recordsLinked to original sources

arXiv2026

Enumeration of all superconducting circuits up to 5 nodes

Nonlinear superconducting circuits can be used as amplifiers, transducers, and qubits. Only a handful have been analyzed or built, so useful configurations likely remain undiscovered. In this paper, we enumerate all unique nonlinear superconducting circuits, up to five nodes in size, built of capacitors, inductors, and Josephson junctions. We catalog the resulting design space by sorting circuits into "Hamiltonian classes" using a set of reference coordinates. Finally, we search for novel superconducting qubits by explicitly considering all three-node circuits, showing how the results of our enumeration can be used as a starting point for circuit design tasks.

quant-ph↗

arXiv2026

Two-qubit gates for the soft 0-π qubit

The 0-π qubit promises longer lifetimes than the transmon, making it a strong candidate for a next-generation, lower-error qubit. Gyenis et al. experimentally demonstrated an unprotected single-qubit gate in the soft 0-π regime [1], but no corresponding two-qubit gate has yet been proposed. We propose an unprotected CZ gate for capacitively coupled soft 0-π qubits. The gate uses a direct transition between a computational state and a higher non-computational state. Assuming negligible device disorder and a phenomenological noise model, the simulated CZ gate achieves a fidelity of approximately 99.9% at a gate time of approximately 160 ns.

quant-ph↗

arXiv2026

Revisiting the multi-mode rhombus circuit as a biased-noise qubit

In this work, we revisit the idea of using an interferometer of pairs of Josephson junctions as a protected rhombus qubit. Unlike in the original proposal, where the qubit states are encoded into odd and even parity charge states, here, we intentionally alter the energy of one of the junctions to investigate the soft version of the rhombus qubit. This approach allows us to directly probe the qubit transitions over several GHz and reduce the potential drawbacks of the interferometer-based protection. Away from a half flux quantum external field, the large shunting capacitors of the circuit ensure localized qubit states in different phase valleys, leading to a biased-noise qubit. In the realized circuit, we measure an average $T_1\approx500\,μ$s relaxation time in the biased-noise regime (with a Ramsey dephasing time of $T^{R}_φ\approx90\,$ns), while an average $T_1\approx27\,μ$s relaxation time at frustration (with $T^{R}_φ\approx670\,$ns). Our loss analysis on this multi-mode circuit indicates that at low frequencies, flux noise and quasiparticle tunneling limit the relaxation times, pointing toward the presence of an optimal operating regime of around a few GHz.

quant-ph↗

arXiv2026

Representation theory of inhomogeneous Gaussian unitaries

Gaussian unitaries, generated by quadratic Hamiltonians, are fundamental in quantum optics and continuous-variable computing. Their structures correspond to symplectic (bosons) and orthogonal (fermions) groups, but physical realizations give rise to their respective double covers, introducing phase and sign ambiguities. The homogeneous (quadratic-only) case has been resolved through a parameterization constructed in a recent work [arXiv:2409.11628]. We extend the previous framework to inhomogeneous Gaussian unitaries parameterized by $(M,z,Ψ)$. The Baker-Campbel-Hausdorff formula allows us then to factor any Gaussian unitary into a squeezing and a displacement transformation, from which we derive the group multiplication law.

quant-ph↗

arXiv2025

Quantum-Enhanced Multi-Parameter Sensing in a Single Mode

Precision metrology underpins scientific and technological advancements. Quantum metrology offers a pathway to surpass classical sensing limits by leveraging quantum states and measurement strategies. However, measuring multiple incompatible observables suffers from quantum backaction, where measurement of one observable pollutes a subsequent measurement of the other. This is a manifestation of Heisenberg's uncertainty principle for two non-commuting observables, such as position and momentum. Here, we demonstrate measurements of small changes in position and momentum where the uncertainties are simultaneously reduced below the standard quantum limit (SQL). We measure $\textit{modular observables}$ using tailored, highly non-classical states that ideally evade measurement backactions. The states are deterministically prepared in the single mode of the mechanical motion of a trapped ion using an optimal quantum control protocol. Our experiment uses grid states to measure small changes in position and momentum and shows a metrological gain of up to 5.1(5)~dB over the simultaneous SQL. Using an adaptive-phase estimation algorithm with Bayesian inference, we estimate these displacements with a combined variance of 2.6(1.1)~dB below the SQL. Furthermore, we examine simultaneously estimating $\textit{number}$ and $\textit{phase}$, which are the polar counterparts of position and momentum. This is performed by preparing a novel quantum resource -- number-phase states -- and we demonstrate a metrological gain over their SQL. The combination of quantum control and multi-parameter quantum metrology marks a significant step towards unprecedented precision with applications ranging from fundamental physics to advanced quantum technologies.

quant-ph↗

arXiv2025

Sub-universal variational circuits for combinatorial optimization problems

Quantum variational circuits have gained significant attention due to their applications in the quantum approximate optimization algorithm and quantum machine learning research. This work introduces a novel class of classical probabilistic circuits designed for generating approximate solutions to combinatorial optimization problems constructed using two-bit stochastic matrices. Through a numerical study, we investigate the performance of our proposed variational circuits in solving the Max-Cut problem on various graphs of increasing sizes. Our classical algorithm demonstrates improved performance for several graph types to the quantum approximate optimization algorithm. Our findings suggest that evaluating the performance of quantum variational circuits against variational circuits with sub-universal gate sets is a valuable benchmark for identifying areas where quantum variational circuits can excel.

quant-ph↗

arXiv2025

Phase-Dependent Squeezing in Dual-Comb Interferometry

We measure phase-dependent Kerr soliton squeezing and anti-squeezing in the time-domain dualcomb interferograms generated using two independent frequency comb lasers. The signal appears as non-stationary quantum noise that varies with the fringe phase of the interferogram and dips below the shot-noise level by as much as 3.8 dB for alternating zero-crossings. The behavior arises from the periodic displacement of the Kerr squeezed comb by the coherent field of the second frequency comb, and is confirmed by a quantum noise model. These experiments support a route towards quantum-enhanced dual-comb timing applications and raise the prospect of high-speed quantum state tomography with dual-comb interferometry.

quant-ph↗

arXiv2025

Noise constraints on sensitivity scaling in super-Heisenberg quantum metrology

Quantum-enhanced metrology surpasses classical metrology by improving estimation precision scaling with a resource $N$ (e.g., particle number or energy) from $1/\sqrt{N}$ to $1/N$. Through the use of nonlinear effects, Roy and Braunstein~\cite{Roy2008} derived a $1/2^N$ scaling. However, later works argued this exponential improvement is unphysical and that even modest gains, like $1/N^2$, may vanish under noise. We show that, in the presence of small errors, the nonlinear interactions enabling metrological enhancement induce emergent errors. The errors propagate through the sensing protocol and are magnified proportional to any intended non-linear enhancement. We identify a critical value of the parameter to be estimated, for a fixed error, below which the emergent errors can be avoided.

quant-ph↗

arXiv2025

Quantum permutation puzzles with indistinguishable particles

Permutation puzzles, such as the Rubik's Cube and the 15 puzzle, are enjoyed by the general public and mathematicians alike. Here we introduce quantum versions of permutation puzzles where the pieces of the puzzles are replaced with indistinguishable quantum particles. The moves in the puzzle are achieved by swapping or permuting the particles. We show that simply permuting the particles can be mapped to a classical permutation puzzle, even though the identical particles are entangled. However, we obtain a genuine quantum puzzle by adding a quantum move: the square root of SWAP. The resulting puzzle cannot be mapped to a classical permutation puzzle. We focus predominately on the quantization of the $2\times 2$ slide puzzle and briefly treat the $2\times 2 \times 1$ Rubik's Cube.

quant-ph↗

arXiv2024

Squeezed dual-comb spectroscopy

Laser spectroscopy and interferometry have provided an unparalleled view into the fundamental nature of matter and the universe through ultra-precise measurements of atomic transition frequencies and gravitational waves. Optical frequency combs have expanded metrology capabilities by phase-coherently bridging radio frequency and optical domains to enable traceable high-resolution spectroscopy across bandwidths greater than hundreds of terahertz. However, quantum mechanics limits the measurement precision achievable with laser frequency combs and traditional laser sources, ultimately impacting fundamental interferometry and spectroscopy. Squeezing the distribution of quantum noise to enhance measurement precision of either the amplitude or phase quadrature of an optical field leads to significant measurement improvements with continuous wave lasers. In this work, we generate bright amplitude-squeezed frequency comb light and apply it to molecular spectroscopy using interferometry that leverages the high-speed and broad spectral coverage of the dual-comb technique. Using the Kerr effect in nonlinear optical fiber, the amplitude quadrature of a frequency comb centered at 1560 nm is squeezed by >3 dB over a 2.5 THz of bandwidth that includes 2500 comb teeth spaced by 1 GHz. Interferometry with a second coherent state frequency comb yields mode-resolved spectroscopy of hydrogen sulfide gas with a signal-to-noise ratio (SNR) nearly 3 dB beyond the shot noise limit, taking full metrological advantage of the amplitude squeezing when the electrical noise floor is considered. The quantum noise reduction leads to a two-fold quantum speedup in the determination of gas concentration, with impact for fast, broadband, and high SNR ratio measurements of multiple species in dynamic chemical environments.

physics.optics↗

arXiv2024

Precisely determining photon-number in real-time

Superconducting transition-edge sensors (TES) are extremely sensitive microcalorimeters used as photon detectors with unparalleled energy resolution. They have found application from measuring astronomical spectra through to determining the quantum property of photon-number, $\hat{n} {=} \hat{a}^† \hat{a}$, for energies from 0.6-2.33eV. However, achieving optimal energy resolution requires considerable data acquisition -- on the order of 1GB/min -- followed by post-processing, which does not allow access to energy information in real time. Here we use a custom hardware processor to process TES pulses while new detections are still being registered, allowing photon-number to be measured in real time as well as reducing data requirements by orders-of-magnitude. We resolve photon number up to n=16 -- achieving up to parts-per-billion discrimination for low photon numbers on the fly -- providing transformational capacity for applications of TES detectors from astronomy through to quantum technology.

physics.ins-det↗

arXiv2024

A Quantum Theory of Temporally Mismatched Homodyne Measurements with Applications to Optical Frequency Comb Metrology

The fields of precision timekeeping and spectroscopy increasingly rely on optical frequency comb interferometry. However, comb-based measurements are not described by existing quantum theory because they exhibit both large mode mismatch and finite strength local oscillators. To establish this quantum theory, we derive measurement operators for homodyne detection with arbitrary mode overlap. These operators are a combination of quadrature and intensity-like measurements, which inform a filter that maximizes the quadrature measurement signal-to-noise ratio. Furthermore, these operators establish a foundation to extend frequency-comb interferometry to a wide range of scenarios, including metrology with nonclassical states of light.

quant-ph↗

arXiv2024

Explicit error-correction scheme and code distance for bosonic codes with rotational symmetry

Bosonic codes with rotational symmetry are currently one of the best performing quantum error correcting codes. Little is known about error propagation and code distance for these rotation codes in contrast with qubit codes and Bosonic codes with translation symmetry. We use a general purpose error basis that is naturally suited to codes with rotation symmetry to compute how errors propagate through gates. This error basis allows us to give an explicit error detection, decoding, and correction scheme for any code with rotation symmetry. We also prove that codes with an $N$-fold rotation symmetry have a distance of $(d_n, d_θ)=(N, π/N)$ with respect to number and rotation errors.

quant-ph↗

arXiv2023

The performance of random bosonic rotation codes

Bosonic error correcting codes utilize the infinite dimensional Hilbert space of a harmonic oscillator to encode a qubit. Bosonic rotation codes are characterized by a discrete rotation symmetry in their Wigner functions and include codes such as the cat and binomial codes.We define two different notions of random bosonic rotation codes and numerically explore their performance against loss and dephasing. We find that the best random rotation codes can outperform cat and binomial codes in a certain parameter regime where loss is large and dephasing errors are small.

quant-ph↗

arXiv2023

Nonlinear Sideband Cooling to a Cat State of Motion

The ability to prepare a macroscopic mechanical resonator into a quantum superposition state is an outstanding goal of cavity optomechanics. Here, we propose a technique to generate cat states of motion using the intrinsic nonlinearity of a dispersive optomechanical interaction. By applying a bichromatic drive to an optomechanical cavity, our protocol enhances the inherent second-order processes of the system, inducing the requisite two-phonon dissipation. We show that this nonlinear sideband cooling technique can dissipatively engineer a mechanical resonator into a cat state, which we verify using the full Hamiltonian and an adiabatically reduced model. While the fidelity of the cat state is maximized in the single-photon, strong-coupling regime, we demonstrate that Wigner negativity persists even for weak coupling. Finally, we show that our cat state generation protocol is robust to significant thermal decoherence of the mechanical mode, indicating that such a procedure may be feasible for near-term experimental systems.

quant-ph↗

arXiv2022

Homodyne measurement with a Schrödinger cat state as a local oscillator

Homodyne measurements are a widely used quantum measurement. Using a coherent state of large amplitude as the local oscillator, it can be shown that the quantum homodyne measurement limits to a field quadrature measurement. In this work, we give an example of a general idea: injecting non-classical states as a local oscillator can led to non-classical measurements. Specifically we consider injecting a superposition of coherent states, a Schrödinger cat state, as a local oscillator. We derive the Kraus operators and the positive operator-valued measure (POVM) in this situation.

quant-ph↗

arXiv2022

A Projection Operator-based Newton Method for the Trajectory Optimization of Closed Quantum Systems

Quantum optimal control is an important technology that enables fast state preparation and gate design. In the absence of an analytic solution, most quantum optimal control methods rely on an iterative scheme to update the solution estimate. At present, the convergence rate of existing solvers is at most superlinear. This paper develops a new general purpose solver for quantum optimal control based on the PRojection Operator Newton method for Trajectory Optimization, or PRONTO. Specifically, the proposed approach uses a projection operator to incorporate the Schrödinger equation directly into the cost function, which is then minimized using a quasi-Newton method. At each iteration, the descent direction is obtained by computing the analytic solution to a Linear-Quadratic trajectory optimization problem. The resulting method guarantees monotonic convergence at every iteration and quadratic convergence in proximity of the solution. To highlight the potential of PRONTO, we present an numerical example that employs it to solve the optimal state-to-state mapping problem for a qubit and compares its performance to a state-of-the-art quadratic optimal control method.

quant-ph↗

arXiv2022

Qubit models of weak continuous measurements

In this paper we approach the theory of continuous measurements and the associated unconditional and conditional (stochastic) master equations from the perspective of quantum information and quantum computing. We do so by showing how the continuous-time evolution of these master equations arises from discretizing in time the interaction between a system and a probe field and by formulating quantum-circuit diagrams for the discretized evolution. We then reformulate this interaction by replacing the probe field with a bath of qubits, one for each discretized time segment, reproducing all of the standard quantum-optical master equations. This provides an economical formulation of the theory, highlighting its fundamental underlying assumptions.

quant-ph↗