Fundamental charges for dual-unitary circuits
Dual-unitary quantum circuits have recently attracted attention as an analytically tractable model of many-body quantum dynamics. Consisting of a 1+1D lattice of 2-qudit gates arranged in a 'brickwork' pattern, these models are defined by the constraint that each gate must remain unitary u...
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2025-01-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2025-01-30-1615/pdf/ |
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| author | Tom Holden-Dye Lluis Masanes Arijeet Pal |
| author_facet | Tom Holden-Dye Lluis Masanes Arijeet Pal |
| author_sort | Tom Holden-Dye |
| collection | DOAJ |
| description | Dual-unitary quantum circuits have recently attracted attention as an analytically tractable model of many-body quantum dynamics. Consisting of a 1+1D lattice of 2-qudit gates arranged in a 'brickwork' pattern, these models are defined by the constraint that each gate must remain unitary under swapping the roles of space and time. This dual-unitarity restricts the dynamics of local operators in these circuits: the support of any such operator must grow at the effective speed of light of the system, along one or both of the edges of a causal light cone set by the geometry of the circuit. Using this property, it is shown here that for 1+1D dual-unitary circuits the set of width-$w$ conserved densities (constructed from operators supported over $w$ consecutive sites) is in one-to-one correspondence with the set of width-$w$ solitons – operators which, up to a multiplicative phase, are simply spatially translated at the effective speed of light by the dual-unitary dynamics. A number of ways to construct these many-body solitons (explicitly in the case where the local Hilbert space dimension $d=2$) are then demonstrated: firstly, via a simple construction involving products of smaller, constituent solitons; and secondly, via a construction which cannot be understood as simply in terms of products of smaller solitons, but which does have a neat interpretation in terms of products of fermions under a Jordan-Wigner transformation. This provides partial progress towards a characterisation of the microscopic structure of complex many-body solitons (in dual-unitary circuits on qubits), whilst also establishing a link between fermionic models and dual-unitary circuits, advancing our understanding of what kinds of physics can be explored in this framework. |
| format | Article |
| id | doaj-art-dc4fd1f2029540f2959dce7be40bdddd |
| institution | Kabale University |
| issn | 2521-327X |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-dc4fd1f2029540f2959dce7be40bdddd2025-01-30T15:40:36ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2025-01-019161510.22331/q-2025-01-30-161510.22331/q-2025-01-30-1615Fundamental charges for dual-unitary circuitsTom Holden-DyeLluis MasanesArijeet PalDual-unitary quantum circuits have recently attracted attention as an analytically tractable model of many-body quantum dynamics. Consisting of a 1+1D lattice of 2-qudit gates arranged in a 'brickwork' pattern, these models are defined by the constraint that each gate must remain unitary under swapping the roles of space and time. This dual-unitarity restricts the dynamics of local operators in these circuits: the support of any such operator must grow at the effective speed of light of the system, along one or both of the edges of a causal light cone set by the geometry of the circuit. Using this property, it is shown here that for 1+1D dual-unitary circuits the set of width-$w$ conserved densities (constructed from operators supported over $w$ consecutive sites) is in one-to-one correspondence with the set of width-$w$ solitons – operators which, up to a multiplicative phase, are simply spatially translated at the effective speed of light by the dual-unitary dynamics. A number of ways to construct these many-body solitons (explicitly in the case where the local Hilbert space dimension $d=2$) are then demonstrated: firstly, via a simple construction involving products of smaller, constituent solitons; and secondly, via a construction which cannot be understood as simply in terms of products of smaller solitons, but which does have a neat interpretation in terms of products of fermions under a Jordan-Wigner transformation. This provides partial progress towards a characterisation of the microscopic structure of complex many-body solitons (in dual-unitary circuits on qubits), whilst also establishing a link between fermionic models and dual-unitary circuits, advancing our understanding of what kinds of physics can be explored in this framework.https://quantum-journal.org/papers/q-2025-01-30-1615/pdf/ |
| spellingShingle | Tom Holden-Dye Lluis Masanes Arijeet Pal Fundamental charges for dual-unitary circuits Quantum |
| title | Fundamental charges for dual-unitary circuits |
| title_full | Fundamental charges for dual-unitary circuits |
| title_fullStr | Fundamental charges for dual-unitary circuits |
| title_full_unstemmed | Fundamental charges for dual-unitary circuits |
| title_short | Fundamental charges for dual-unitary circuits |
| title_sort | fundamental charges for dual unitary circuits |
| url | https://quantum-journal.org/papers/q-2025-01-30-1615/pdf/ |
| work_keys_str_mv | AT tomholdendye fundamentalchargesfordualunitarycircuits AT lluismasanes fundamentalchargesfordualunitarycircuits AT arijeetpal fundamentalchargesfordualunitarycircuits |