About

Assistant Professor Josh Combes is based in the Department of Electrical, Computer and Energy Engineering at the University of Colorado Boulder. His research focuses on transforming the quantum technology landscape, particularly in the development of more reliable quantum computing components. Combes has earned a National Science Foundation CAREER Award to advance his work on designing second-generation qubits, which are significantly more error-resistant than current first-generation qubits. These low-error qubits aim to accelerate the timeline for large-scale superconducting quantum computers, which have applications in e-commerce, communications, GPS navigation, and national security. In addition to his research, Combes is dedicated to building a robust national quantum workforce. He designed a quantum engineering minor to help STEM students outside of physics become proficient in quantum technology, emphasizing the multidisciplinary nature of the field. Combes advocates for drawing expertise from various disciplines such as electrical, mechanical, and chemical engineering to foster a diverse quantum community. His efforts include mentoring students and contributing to the broader impact of quantum research through education and workforce development.

Research topics

• Computer Science
• Mathematics
• Algorithm
• Quantum mechanics
• Software engineering
• Systems engineering
• Computational science
• Engineering
• Applied mathematics
• Mathematical optimization
• Biology
• Engineering physics
• Physics
• Mathematical analysis

Selected publications

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

  arXiv (Cornell University) · 2026-05-07

  preprintOpen access

  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.

  PublisherDOI

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

  ArXiv.org · 2026-05-07

  articleOpen access

  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.

  PublisherOA PDF

• Representation theory of inhomogeneous Gaussian unitaries

  Open MIND · 2026-02-09

  preprint

  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.

  DOI

• Representation theory of inhomogeneous Gaussian unitaries

  ArXiv.org · 2026-02-09

  articleOpen access

  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.

  PublisherOA PDF

• Quantum permutation puzzles with indistinguishable particles

  Physical review. A/Physical review, A · 2025-04-14 · 2 citations

  articleSenior author

  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 $2\ifmmode\times\else\texttimes\fi{}2$ slide puzzle and briefly treat the $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}1$ Rubik's Cube.

  PublisherDOI

• Squeezed dual-comb spectroscopy

  Science · 2025-01-16 · 42 citations

  article

  Optical frequency combs have enabled distinct advantages in broadband, high-resolution spectroscopy and precision interferometry. However, quantum mechanics ultimately limits the metrological precision achievable with laser frequency combs. Quantum squeezing has led to substantial measurement improvements with continuous wave lasers, but experiments demonstrating metrological advantage with squeezed combs are less developed. Using the Kerr effect in nonlinear optical fiber, a 1-gigahertz frequency comb centered at 1560 nanometers is amplitude-squeezed by >3 decibels (dB) over a 2.5-terahertz bandwidth. Dual-comb interferometry yields mode-resolved spectroscopy of hydrogen sulfide gas with a signal-to-noise ratio nearly 3 dB beyond the shot-noise limit. The quantum noise reduction leads to a twofold quantum speedup in the determination of gas concentration, with implications for high-speed measurements of multiple species in dynamic chemical environments.

  PublisherDOI

• Noise Constraints on Sensitivity Scaling in Quantum Nonlinear Metrology

  Physical Review Letters · 2025-11-06 · 1 citations

  articleSenior author

  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 [Exponentially enhanced quantum metrology, Phys. Rev. Lett. 100, 220501 (2008)PRLTAO0031-900710.1103/PhysRevLett.100.220501] 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 nonlinear enhancement. We identify a critical value of the parameter to be estimated, for a fixed error, below which the emergent errors can be avoided.

  PublisherDOI

• Subuniversal variational circuits for combinatorial optimization problems

  Physical review. A/Physical review, A · 2025-09-09 · 1 citations

  articleSenior author

  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 subuniversal gate sets is a valuable benchmark for identifying areas where quantum variational circuits can excel.

  PublisherDOI

• Quantum-enhanced multiparameter sensing in a single mode

  Science Advances · 2025-09-24 · 9 citations

  articleOpen access

  Precise measurements underpin scientific and technological advancements. Quantum mechanics provides an avenue to enhance precision, but it comes with a restriction: Incompatible observables, such as position and momentum, cannot be simultaneously measured to arbitrary accuracy as decreed by Heisenberg's uncertainty principle. This restriction can be bypassed by instead measuring commuting modular observables, which are counterparts to the naturally incompatible observables. Here, we measure modular observables to estimate small changes in position and momentum with a single-mode multiparameter sensor. We deterministically prepare grid states in the mechanical motion of a trapped ion and demonstrate uncertainties in position and momentum below the standard quantum limit (SQL). Further, we examine another pair of incompatible observables-number and phase. We prepare a different resource-number-phase states-and demonstrate a metrological gain over the SQL. These results introduce previously unidentified measurement capabilities unavailable to classical systems and mark a substantial step in quantum metrology.

  PublisherDOI

• Power-Dependent Squeezing in Dual-Comb Interferometry

  2025-01-01

  article

  We measure up to 3 dB of phase-dependent squeezing in a dual comb interferometry experiment between a coherent and Kerr squeezed comb. We analyze the power-dependence of the squeezing and compare to a theoretical model.

  PublisherDOI

Recent grants

• CAREER: Second Generation Qubits -- the future of superconducting quantum computing

  NSF · $117k · 2023–2024

Frequent coauthors

• Howard M. Wiseman

  Centre for Quantum Computation and Communication Technology

  116 shared

• Carlton M. Caves

  University of New Mexico

  43 shared

• Christopher Ferrie

  Quantum (Australia)

  37 shared

• Ben Q. Baragiola

  34 shared

• G. J. Milburn

  29 shared

• Anushya Chandran

  Harvard University

  27 shared

• Thomas M. Stace

  University of Queensland

  25 shared

• Nathan Walk

  Freie Universität Berlin

  20 shared

Awards & honors

• National Science Foundation CAREER Award