Devices: Full Clifford group gates support #3639

balopat · 2021-01-06T01:30:07Z

Feature: Full Clifford group support

Problem: Currently Clifford group gates are supported via the addition of the act_on to gates in Cirq (this is a work in progress). This means only certain gates can be simulated. One could instead support the entire Clifford group via it’s specification of a symplectic matrices plus a vector describing the phases of the Pauli group. In addition this would include better support for the Pauli group and stabilizer groups to the level of supporting NISQ quantum error correction work (error mitigation)

Rough requirements:

Define general clifford group gates
Use in clifford simulators but also in normal simulations
Make clean support for Pauli group and stabilizer codes.

smitsanghavi · 2021-01-06T01:43:08Z

Prior discussion on similar lines (I think): #2423 (comment)

For the record, we already support detecting arbitrary 2x2 unitaries as Clifford or not (as the fallback strategy if the _act_on_ method isn't implemented). Generalizing this to larger unitary matrices was considered too expensive at the time.

The preparation step for making general Clifford Gates #3639. The basic logic of implementation is tracking the transformation of all generators of Pauli group. Namely, list the transform of first tableau:`U_1X_iU_1' = r_i \Prod_j X_j^{t_(i,j)} Z_i^{s_(i,j)}` and list the same thing for second tableau `U_2`, then combining them. With this method, it will allow us to build other unnamed Clifford Gates by composition.

Another preparation step for making general Clifford Gates #3639. The implementation relies on the `then` method (composing two Clifford tableaux) check the code in #4096. This branch is based on the branch used in #4096. Hence, there are a few `then` related codes, which should be orthogonal of this PR.

The preparation step for making general Clifford Gates quantumlib#3639. The basic logic of implementation is tracking the transformation of all generators of Pauli group. Namely, list the transform of first tableau:`U_1X_iU_1' = r_i \Prod_j X_j^{t_(i,j)} Z_i^{s_(i,j)}` and list the same thing for second tableau `U_2`, then combining them. With this method, it will allow us to build other unnamed Clifford Gates by composition.

Another preparation step for making general Clifford Gates quantumlib#3639. The implementation relies on the `then` method (composing two Clifford tableaux) check the code in quantumlib#4096. This branch is based on the branch used in quantumlib#4096. Hence, there are a few `then` related codes, which should be orthogonal of this PR.

…rdTableau (#4165) The current implementation of SingleQubitCliffordGate is based on `rotation_map` and `inverse_rotation_map`. It is concise for SingleQubitCliffordGate but hard to extend into any number of qubits clifford gates. For generalization, this PR replaces them by the `CliffordTableau`. All functionalities and interfaces of SingleCliffordGate should be the same after the replacement. [WIP for #3639]. I didn't deprecate PauliTransform (#4088) in this PR for minimize the PR's responsibility. But after this PR, it will be easy to do it.

Decompose clifford tableau into one/two qubits operations (X, Z, S, H, CNOT, and SWAP). The method is based on [Aaronson & Gottesman's paper](https://arxiv.org/abs/quant-ph/0406196) [WIP for #3639]. Issue #4182 is discovered in this PR's test.

@daxfohl

Add initial Clifford Gate with multiple qubits. Compared with SingleQubitCliffordGate, it has fewer functionalities since we cannot enumerate all of them with PauliGates and several special single qubit properties like Bloch rotation no longer exist. Anyway, it provides several basic interactions: 1. It uses Clifford tableau as underlying data representation (different from the state representation). 2. It can be constructed from a tableau or list of operations (`_has_stabilizer_effect_` only). All Clifford gates can be built through \{S, H, CNOT\}, so we can construct any Clifford Gate from the list of operations. We just cannot pre-define it. 3. Decomposing into several basic operations. 4. Get unitary matrix through decomposing (we cannot do this in a reverse way from unitary to Clifford gate :( ). 5. Know how to interact with ActOnCliffordTableauArgs, i.e. it should be able to use with CliffordTableau simulator (Looks like we don't have that in cirq yet? @daxfohl will add that? see #4639 and #4748.). This PR is part of efforts for #3639. Context: this PR doesn't introduce any new algorithms but the key methods are already implemented in #4183 and #4096.

@daxfohl

Add initial Clifford Gate with multiple qubits. Compared with SingleQubitCliffordGate, it has fewer functionalities since we cannot enumerate all of them with PauliGates and several special single qubit properties like Bloch rotation no longer exist. Anyway, it provides several basic interactions: 1. It uses Clifford tableau as underlying data representation (different from the state representation). 2. It can be constructed from a tableau or list of operations (`_has_stabilizer_effect_` only). All Clifford gates can be built through \{S, H, CNOT\}, so we can construct any Clifford Gate from the list of operations. We just cannot pre-define it. 3. Decomposing into several basic operations. 4. Get unitary matrix through decomposing (we cannot do this in a reverse way from unitary to Clifford gate :( ). 5. Know how to interact with ActOnCliffordTableauArgs, i.e. it should be able to use with CliffordTableau simulator (Looks like we don't have that in cirq yet? @daxfohl will add that? see quantumlib#4639 and quantumlib#4748.). This PR is part of efforts for quantumlib#3639. Context: this PR doesn't introduce any new algorithms but the key methods are already implemented in quantumlib#4183 and quantumlib#4096.

95-martin-orion · 2022-03-28T20:28:49Z

@MichaelBroughton is this resolved as of #4791?

95-martin-orion · 2022-05-18T18:51:44Z

Confirmed with Mike, this is complete.

The preparation step for making general Clifford Gates quantumlib#3639. The basic logic of implementation is tracking the transformation of all generators of Pauli group. Namely, list the transform of first tableau:`U_1X_iU_1' = r_i \Prod_j X_j^{t_(i,j)} Z_i^{s_(i,j)}` and list the same thing for second tableau `U_2`, then combining them. With this method, it will allow us to build other unnamed Clifford Gates by composition.

Another preparation step for making general Clifford Gates quantumlib#3639. The implementation relies on the `then` method (composing two Clifford tableaux) check the code in quantumlib#4096. This branch is based on the branch used in quantumlib#4096. Hence, there are a few `then` related codes, which should be orthogonal of this PR.

…rdTableau (quantumlib#4165) The current implementation of SingleQubitCliffordGate is based on `rotation_map` and `inverse_rotation_map`. It is concise for SingleQubitCliffordGate but hard to extend into any number of qubits clifford gates. For generalization, this PR replaces them by the `CliffordTableau`. All functionalities and interfaces of SingleCliffordGate should be the same after the replacement. [WIP for quantumlib#3639]. I didn't deprecate PauliTransform (quantumlib#4088) in this PR for minimize the PR's responsibility. But after this PR, it will be easy to do it.

Decompose clifford tableau into one/two qubits operations (X, Z, S, H, CNOT, and SWAP). The method is based on [Aaronson & Gottesman's paper](https://arxiv.org/abs/quant-ph/0406196) [WIP for quantumlib#3639]. Issue quantumlib#4182 is discovered in this PR's test.

@daxfohl

Add initial Clifford Gate with multiple qubits. Compared with SingleQubitCliffordGate, it has fewer functionalities since we cannot enumerate all of them with PauliGates and several special single qubit properties like Bloch rotation no longer exist. Anyway, it provides several basic interactions: 1. It uses Clifford tableau as underlying data representation (different from the state representation). 2. It can be constructed from a tableau or list of operations (`_has_stabilizer_effect_` only). All Clifford gates can be built through \{S, H, CNOT\}, so we can construct any Clifford Gate from the list of operations. We just cannot pre-define it. 3. Decomposing into several basic operations. 4. Get unitary matrix through decomposing (we cannot do this in a reverse way from unitary to Clifford gate :( ). 5. Know how to interact with ActOnCliffordTableauArgs, i.e. it should be able to use with CliffordTableau simulator (Looks like we don't have that in cirq yet? @daxfohl will add that? see quantumlib#4639 and quantumlib#4748.). This PR is part of efforts for quantumlib#3639. Context: this PR doesn't introduce any new algorithms but the key methods are already implemented in quantumlib#4183 and quantumlib#4096.

The preparation step for making general Clifford Gates quantumlib#3639. The basic logic of implementation is tracking the transformation of all generators of Pauli group. Namely, list the transform of first tableau:`U_1X_iU_1' = r_i \Prod_j X_j^{t_(i,j)} Z_i^{s_(i,j)}` and list the same thing for second tableau `U_2`, then combining them. With this method, it will allow us to build other unnamed Clifford Gates by composition.

Another preparation step for making general Clifford Gates quantumlib#3639. The implementation relies on the `then` method (composing two Clifford tableaux) check the code in quantumlib#4096. This branch is based on the branch used in quantumlib#4096. Hence, there are a few `then` related codes, which should be orthogonal of this PR.

…rdTableau (quantumlib#4165) The current implementation of SingleQubitCliffordGate is based on `rotation_map` and `inverse_rotation_map`. It is concise for SingleQubitCliffordGate but hard to extend into any number of qubits clifford gates. For generalization, this PR replaces them by the `CliffordTableau`. All functionalities and interfaces of SingleCliffordGate should be the same after the replacement. [WIP for quantumlib#3639]. I didn't deprecate PauliTransform (quantumlib#4088) in this PR for minimize the PR's responsibility. But after this PR, it will be easy to do it.

Decompose clifford tableau into one/two qubits operations (X, Z, S, H, CNOT, and SWAP). The method is based on [Aaronson & Gottesman's paper](https://arxiv.org/abs/quant-ph/0406196) [WIP for quantumlib#3639]. Issue quantumlib#4182 is discovered in this PR's test.

@daxfohl

Add initial Clifford Gate with multiple qubits. Compared with SingleQubitCliffordGate, it has fewer functionalities since we cannot enumerate all of them with PauliGates and several special single qubit properties like Bloch rotation no longer exist. Anyway, it provides several basic interactions: 1. It uses Clifford tableau as underlying data representation (different from the state representation). 2. It can be constructed from a tableau or list of operations (`_has_stabilizer_effect_` only). All Clifford gates can be built through \{S, H, CNOT\}, so we can construct any Clifford Gate from the list of operations. We just cannot pre-define it. 3. Decomposing into several basic operations. 4. Get unitary matrix through decomposing (we cannot do this in a reverse way from unitary to Clifford gate :( ). 5. Know how to interact with ActOnCliffordTableauArgs, i.e. it should be able to use with CliffordTableau simulator (Looks like we don't have that in cirq yet? @daxfohl will add that? see quantumlib#4639 and quantumlib#4748.). This PR is part of efforts for quantumlib#3639. Context: this PR doesn't introduce any new algorithms but the key methods are already implemented in quantumlib#4183 and quantumlib#4096.

balopat added kind/roadmap-item for higher level roadmap items to capture conversations and feedback (not for project tracking) roadmap-candidate labels Jan 6, 2021

balopat added area/clifford-group and removed roadmap-candidate labels Feb 19, 2021

This was referenced May 9, 2021

Add then method for composing two Clifford tableaux #4096

Merged

Add inverse method for Clifford tableau #4111

Merged

This was referenced Jun 5, 2021

Replace the underlying representation of SingleCliffordGate by CliffordTableau #4165

Merged

Add Clifford Tableau decomposition function #4183

Merged

vcatherine changed the title ~~Full Clifford group support~~ Devices: Full Clifford group gates support Sep 3, 2021

BichengYing mentioned this issue Jan 2, 2022

Multiple Qubits Clifford Gate #4791

Merged

95-martin-orion added the time/before-1.0 label Mar 28, 2022

vtomole added the triage/discuss Needs decision / discussion, bring these up during Cirq Cynque label May 4, 2022

95-martin-orion closed this as completed May 18, 2022

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Devices: Full Clifford group gates support #3639

Devices: Full Clifford group gates support #3639

balopat commented Jan 6, 2021

smitsanghavi commented Jan 6, 2021

95-martin-orion commented Mar 28, 2022

95-martin-orion commented May 18, 2022

Devices: Full Clifford group gates support #3639

Devices: Full Clifford group gates support #3639

Comments

balopat commented Jan 6, 2021

smitsanghavi commented Jan 6, 2021

95-martin-orion commented Mar 28, 2022

95-martin-orion commented May 18, 2022