Geometric heat pumping on a quantum processor

AI summary

Overview

Research area: Quantum thermodynamics on near-term quantum hardware — specifically geometric (adiabatic) heat pumping in a driven open quantum system, implemented on a superconducting processor.

Technical level: Intermediate. The paper assumes familiarity with open quantum systems (Lindblad master equations, collision models) and with superconducting-qubit circuit execution, but its central idea — using a driven qubit to shuttle heat between two equally cold reservoirs — is stated in accessible terms.

Scope (one sentence): The authors realize a single-qubit geometric heat pump on IBM's ibm_kingston (Heron r2) processor using a collision model with two thermal ancillas, and show that the orientation-odd component of the measured heat reproduces parameter-free simulations of the pump and approaches the geometric (Lindblad) limit in the slow-driving regime.

What This Paper Is About

Two reservoirs held at exactly the same temperature should exchange no net heat. But if a quantum system is coupled asymmetrically to both and is driven around a closed loop in parameter space, it can still move energy from one reservoir to the other — a thermal analogue of geometric particle pumping, where the pumped quantity is governed by the shape of the loop rather than by the speed at which it is traversed. The goal of this paper is to demonstrate that effect experimentally on a programmable quantum processor, and to separate the genuinely geometric (pumping) heat from ordinary irreversible heating caused by the drive and by device noise.

Key Contributions

1. An experimental implementation of geometric heat pumping on a superconducting quantum processor. A working qubit is driven around closed contours in a two-parameter space (level splitting and field orientation) while interacting repeatedly with two ancilla qubits prepared in thermal states, which act simultaneously as the two reservoirs and as calorimeters.

2. A calorimetric measurement protocol for heat at the single-collision level. Ancilla energy is projectively measured before and after each partial-swap interaction, giving the stochastic heat delivered to each reservoir; the ensemble average over a cycle is compared against theory.

3. An orientation-odd estimator that isolates the pumped heat from a much larger noise background. By running each contour in both traversal directions with the same timing and taking the half-difference, the authors cancel the orientation-even heating background and extract the pumping contribution, which changes sign under contour reversal.

4. A quantitative, parameter-free comparison across driving speeds. Measurements at periods 𝒯 = 5, 𝒯 = 60 and 𝒯 = 80, and across loop widths δ_B, are compared with the exact discrete collision model (N = 48 cells per cycle) and with the continuous-time Lindblad dynamics, with no adjustable parameters.

Main Findings

• The pump works as predicted: Measured cumulative pumped heat along a cycle at 𝒯 = 5 and 𝒯 = 80 shows "remarkable agreement" with the ideal collision-model calculation using the same initial state; the net pumped components obey Q_L,odd ≃ −Q_R,odd, i.e. heat leaves one reservoir and enters the other.

• Pumping grows with the enclosed area and vanishes without it: At 𝒯 = 60, deep in the adiabatic regime, the measured odd heat grows with the loop width δ_B, and vanishes within error bars at δ_B = 0, where the contour encloses zero area.

• Adiabatic limit and finite-speed corrections are resolved in theory: For the parameters of Fig. 2 (δ_B = 0.45, B_0 = 0.61, ϑ_0 = 45°, δ_ϑ = 40°, T = g_L = g_R = 1, ω_c = 120, κ = 2.5), the geometric adiabatic values are Q_L^geo = −Q_R^geo ≃ 0.334 with quadratic (dissipative) coefficients 𝒞_L = 𝒞_R ≃ 5.887. The expansion Q_α^geo + 𝒞_α/𝒯 matches the full Lindblad solution for long periods.

• Collision model converges quickly: Agreement between the discrete collision model and the full time-dependent Lindblad equation is excellent already at N = 48 cells per cycle.

• Fast driving reverses the sign of the total heat flow: For fast cycles (𝒯 < 14 for the parameters of Fig. 2), Q_α > 0 for both reservoirs, meaning dissipated heat exceeds the pumped component. At short periods the heat depends nonmonotonically on 𝒯 near the precession timescale π/B_0.

• Energy balance and bound: For a periodic state, Σ_α Q_α = W_q ≥ 0; the pumped heat approaches the bound T ln 2 (the Landauer limit) as the contour area covers the first quadrant.

• Device noise prevents net cooling in this implementation: Noise produces a predominantly orientation-even heat background substantially larger than the odd pumped heat, so no net cooling is achieved. The adiabatic pumped heat converges to a value smaller in absolute magnitude than the expected geometric value; circuit-level noise simulations trace this to gate errors and relaxation/dephasing, dominated by relaxation of the working qubit during waiting intervals for ancilla measurement and reset.

• Robustness to thermal bias: Although the experiment uses equal reservoir temperatures, the authors state that in numerical simulations the pumping remains robust against a small thermal bias in the intermediate-𝒯 regime (results not shown).

Methodology in Plain English

The team encoded a well-known theoretical model of an open quantum system — a "collision model" — directly into a quantum circuit.

• The system: One working qubit plays the part of the heat-pump working medium. Two ancilla qubits stand in for the left and right thermal reservoirs. The working qubit's energy splitting and the orientation of its effective field are swept around a closed loop (specifically a rectangle with rounded corners in the splitting–angle plane).

• The reservoirs: Each ancilla is repeatedly reset, rotated by a small angle, and then measured. Averaged over measurement outcomes, this prepares an exact thermal state at the chosen temperature; the same measurement records the ancilla's incoming energy.

• The interaction: A partial-swap gate exchanges one excitation between the working qubit and the ancilla with a prescribed probability tied to the bath transition rate. The rate is engineered to depend on the angle between the field and the reservoir coupling direction, so left and right baths are switched on and off differently as the field rotates — this asymmetry is what produces directed pumping.

• Avoiding bias: Four collisions per time cell, ordered L–R–R–L, implement a symmetric (Strang-type) splitting so that neither reservoir is favored and discretization error is reduced.

• Reading out heat: A second ancilla measurement after the swap gives the outgoing energy. The difference is the stochastic heat to that reservoir. Summing over all cells and shots gives the heat per cycle.

• Separating pumping from heating: Each contour is run clockwise and counterclockwise with identical timing. The half-difference cancels the even (dissipative and noise) part and isolates the odd (geometric) part.

• Hardware details: The circuit was compiled with Qiskit and run on IBM's Heron r2 processor ibm_kingston, on qubits (q, a_L, a_R) = (47, 48, 46), with no error mitigation or readout correction. Each circuit contains 384 CZ gates and runs in ≈690 μs; measurements used 3000 shots per circuit and N = 48 collision cells per period.

Why This Matters

Impact on research: This is a proof of concept that geometric heat pumping — previously a theoretical construct in driven open quantum systems — can be programmed and measured on existing quantum hardware. It also shows that quantum processors can serve as controllable platforms for quantum thermodynamics with microscopic, per-collision bookkeeping of heat, complementing earlier experimental work on discrete-stroke quantum thermal machines. The direct comparison between the discrete collision model and its continuous Lindblad limit provides a benchmark for how coarse a circuit-level discretization can be while still reproducing the intended open-system physics.

Real-world applications (as motivated in the paper):

• Cooling and heat management for qubits, where the paper notes that efficient qubit cooling is essential for accurate operation and that many proposals use auxiliary qubits as a thermal machine to cool a target.
• Designing and characterizing fast periodic driving protocols, where geometric concepts are already used as tools.
• Continuously operated heat engines and refrigerators built from qubits coupled to reservoirs at different temperatures, which require operation against a continuous heat leak.
• Thermoelectric-style machines and adiabatically driven motors, which the paper cites as the classical/electronic analogues of this mechanism.

Industry relevance: The work uses commercially available IBM Quantum superconducting hardware and standard Qiskit compilation, and identifies concrete hardware-level bottlenecks — readout/reset latency, gate fidelity and coherence time — that limit thermodynamic experiments on today's processors. These are the same metrics that gate progress in quantum computing generally.

Future Directions

• Reduce measurement/reset latency: The dominant noise contribution comes from working-qubit relaxation during the waiting intervals needed for ancilla measurement and reset; shortening these intervals is identified as a promising route toward net heat extraction.
• Improve gate fidelities and coherence times so that the measured adiabatic pumped heat reaches the predicted geometric value rather than being attenuated below it.
• Achieve net cooling: At present noise-induced heating exceeds the pumped heat; demonstrating actual heat extraction (refrigeration) is the stated next milestone.
• Extend the working medium: The authors highlight using more than one working qubit to generate the pumping as an interesting direction, and note that the robustness of pumping to a small thermal bias has so far been checked only in numerical simulations.

Target Audience

Researchers and graduate students in quantum thermodynamics, open quantum systems and quantum information, particularly those interested in implementing thermodynamic protocols on near-term superconducting hardware. It is also useful for experimentalists working on qubit control and calibration who want to understand how readout/reset latency and gate errors limit calorimetric measurements, and for theorists seeking an experimental benchmark for collision models and adiabatic (geometric) expansions of Lindblad dynamics.

Authors’ abstract

Geometric heat pumping is the transfer of energy between reservoirs at equal temperature where the heat exchanged in an adiabatic cycle depends only on the driving contour in parameter space. We implement this mechanism on a superconducting quantum processor using a collision model, where a driven qubit interacts repeatedly with two ancilla qubits that are prepared in thermal states and emulate the reservoirs. Energy measurements before and after each interaction provide a calorimetric record of the heat exchanged with each reservoir. By reversing the driving contour, we extract a heat contribution associated with pumping. Its dependence on the period and on the contour follows exact simulations of the collision model, without adjustable parameters, and approaches in the slow-driving regime the geometric limit of the corresponding Lindblad dynamics.