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Quantum Refrigerator

Michael Ben-Or, Daniel Gottesman, Avinatan Hassidim

TL;DR

This paper addresses fault-tolerant quantum computation when fresh ancilla qubits are not available and noise is modeled by general single-qubit channels. It classifies channels via Bloch-sphere fixed points into three regimes, deriving distinct time- and resource-efficiency outcomes: depolarizing-type channels permit only $O(\tilde{O}(\log n))$ steps, dephasing-type channels allow polynomial-time computation with recycled ancillas, and amplitude-damping-type channels enable exponential-time computation by exploiting cooling from non-unital noise. The authors prove formal theorems for each regime, employing entropy-based arguments and a three-component architecture (computation, storage, refrigerator) to recycle qubits and sustain fault-tolerant operation without fresh ancillas. The results illuminate when environmental cooling can substitute for external ancillas and suggest robust strategies for early quantum devices where fresh qubits are scarce. The work also highlights remaining gaps, notably upper bounds for non-unital channels and extensions to qudits and various lattice geometries.

Abstract

We consider fault-tolerant quantum computation in the context where there are no fresh ancilla qubits available during the computation, and where the noise is due to a general quantum channel. We show that there are three classes of noisy channels: In the first, typified by the depolarizing channel, computation is only possible for a logarithmic time. In the second class, of which the dephasing channel is an example, computation is possible for polynomial time. The amplitude damping channel is an example of the third class, and for this class of channels, it is possible to compute for an exponential time in the number of qubits available.

Quantum Refrigerator

TL;DR

This paper addresses fault-tolerant quantum computation when fresh ancilla qubits are not available and noise is modeled by general single-qubit channels. It classifies channels via Bloch-sphere fixed points into three regimes, deriving distinct time- and resource-efficiency outcomes: depolarizing-type channels permit only steps, dephasing-type channels allow polynomial-time computation with recycled ancillas, and amplitude-damping-type channels enable exponential-time computation by exploiting cooling from non-unital noise. The authors prove formal theorems for each regime, employing entropy-based arguments and a three-component architecture (computation, storage, refrigerator) to recycle qubits and sustain fault-tolerant operation without fresh ancillas. The results illuminate when environmental cooling can substitute for external ancillas and suggest robust strategies for early quantum devices where fresh qubits are scarce. The work also highlights remaining gaps, notably upper bounds for non-unital channels and extensions to qudits and various lattice geometries.

Abstract

We consider fault-tolerant quantum computation in the context where there are no fresh ancilla qubits available during the computation, and where the noise is due to a general quantum channel. We show that there are three classes of noisy channels: In the first, typified by the depolarizing channel, computation is only possible for a logarithmic time. In the second class, of which the dephasing channel is an example, computation is possible for polynomial time. The amplitude damping channel is an example of the third class, and for this class of channels, it is possible to compute for an exponential time in the number of qubits available.

Paper Structure

This paper contains 9 sections, 5 theorems, 18 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Previous results
  3. The Model
  4. Classification of Qubit Channels
  5. Depolarizing Class
  6. Dephasing channel
  7. Non unital channels
  8. Conclusion
  9. Acknowledgments

Key Result

Theorem 1.1

Let $C$ be any non-unitary channel close to the identity, and consider quantum computations which suffer from noise $C$ on each qubit at each time step. Up to unitary equivalence, the limit of repeatedly applying $C$ can be either a point or a diameter in the Bloch sphere.If $C$ is a dephasing chann

Figures (2)

  • Figure 1: The computer consists of three components: A computation component, a storage house, and a refrigerator.
  • Figure 2: Each block of the code has a separate storage house and refrigerator for a two-dimensional layout.

Theorems & Definitions (8)

  • Theorem 1.1: Main Theorem
  • Theorem 1.2: Threshold Theorem
  • Theorem 5.1
  • proof
  • Theorem 5.2
  • proof
  • Theorem 6.1
  • proof