[Paper Review] Mediated interactions beyond the nearest neighbor in an array of superconducting qubits

Yariv Yanay, Jochen Braumüller+4 more|arXiv (Cornell University)|Oct 4, 2021

Quantum many-body systems37 references17 citations

TL;DR

This paper proposes a design strategy for superconducting qubit arrays using floating transmon qubits to enable tunable, long-range mediated interactions beyond nearest-neighbor coupling. By exploiting extraneous capacitive modes (Φ+), the method induces effective qubit-qubit coupling that can be independently tuned in strength and range via circuit capacitance ratios, enabling a continuum from nearest-neighbor to long-range interactions without direct physical connections.

ABSTRACT

We consider mediated interactions in an array of floating transmons, where each qubit capacitor consists of two superconducting pads galvanically isolated from ground. Each such pair contributes two quantum degrees of freedom, one of which is used as a qubit, while the other remains fixed. However, these extraneous modes can generate coupling between the qubit modes that extends beyond the nearest neighbor. We present a general formalism describing the formation of this coupling and calculate it for a one-dimensional chain of transmons. We show that the strength of coupling and its range (that is, the exponential falloff) can be tuned independently via circuit design to realize a continuum from nearest-neighbor-only interactions to interactions that extend across the length of the chain. We present designs with capacitance and microwave simulations showing that various interaction configurations can be achieved in realistic circuits. Such coupling could be used in analog simulation of different quantum regimes or to increase connectivity in digital quantum systems. Thus mechanism must also be taken into account in other types of qubits with extraneous modes.

Motivation & Objective

• To develop a design strategy for controlling long-range qubit interactions in superconducting qubit lattices.
• To understand and harness mediated interactions arising from extraneous quantum modes in floating transmon qubits.
• To demonstrate that coupling strength and range can be independently tuned via circuit parameters.
• To show experimental feasibility of achieving diverse interaction profiles in realistic circuit designs.

Proposed method

• Formalizing the circuit Hamiltonian using ± mode transformations to separate qubit (Φ−) and auxiliary (Φ+) degrees of freedom.
• Deriving the effective coupling matrix Ceff = C−− − C−+ (C++)−1 C+− to describe mediated interactions.
• Performing momentum-space analysis on infinite 1D chains to derive analytical expressions for coupling decay (J|i−j| ∝ ξ−|i−j|).
• Using capacitance and microwave simulations to validate design feasibility and tune interaction profiles.
• Comparing 'A-B' and 'A-A' coupling schemes to optimize interaction range and strength.
• Applying boundary corrections to finite chains to assess edge effects on long-range coupling.

Experimental results

Research questions

• RQ1 Can mediated interactions in floating transmon arrays extend beyond nearest-neighbor coupling, and if so, how can they be controlled?
• RQ2 Can the strength and range of long-range coupling be tuned independently via circuit design?
• RQ3 How do capacitance ratios (Cq, CG, Cc) affect the effective coupling strength and decay length?
• RQ4 What is the impact of finite system size and boundary effects on long-range coupling?
• RQ5 Can realistic circuit simulations demonstrate the feasibility of achieving diverse interaction profiles?

Key findings

• The effective coupling strength follows a power-law decay with distance, J|i−j| ≈ J1 ξ−|i−j|−1, where ξ is the decay length.
• The coupling strength J1 and decay length ξ can be independently tuned via capacitance ratios, enabling a continuum from nearest-neighbor to long-range interactions.
• In the infinite chain limit, the inverse effective capacitance matrix is analytically derived, yielding C−1_eff(k) ∝ 1 / [Cq + (CG/2) (1 − η1η2) / (η2 − η1) ] with η1, η2 defined by capacitance ratios.
• For finite chains, boundary effects introduce corrections that decay as ξ−|i−j| and ξ−(N−|i+j−N−1|), with the latter becoming significant at large distances.
• Capacitance simulations confirm that various interaction profiles—including long-range and next-nearest-neighbor coupling—can be realized in realistic circuit designs.
• The mechanism is robust and applicable to other qubit types with extraneous modes, necessitating consideration in future quantum processor designs.