Stabilizer tableau circuit simulation using backtracking method from Stim #551
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| """ | ||
| A quantum state representation for efficient simulation using the stabilizer tableau backtracking | ||
| method [gidney-2021](@cite). | ||
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| This struct stores the inverse of all Clifford operations applied so far, enabling efficient | ||
| simulation by working backwards from measurements to the initial |0⟩^⊗n state. By conjugating the | ||
| current-time observable Pₓ by the inverse Clifford operation we get some observable from the | ||
| start of time that is equivalent to measuring Pₓ at the current time. | ||
| """ | ||
| struct BacktrackRegister <: AbstractQCState | ||
| inv_circuit::CliffordOperator | ||
| bits::Vector{Bool} | ||
| end | ||
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| BacktrackRegister(r::BacktrackRegister) = r | ||
| BacktrackRegister(qbits::Int, mbits::Int=0) = BacktrackRegister(one(CliffordOperator, qbits), falses(mbits)) | ||
| BacktrackRegister(s::AbstractStabilizer, mbits::Int=0) = BacktrackRegister(inv(CliffordOperator(Destabilizer(s))), falses(mbits)) | ||
| BacktrackRegister(r::Register) = BacktrackRegister(quantumstate(r), r.bits) | ||
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| Base.copy(r::BacktrackRegister) = BacktrackRegister(copy(r.inv_circuit), copy(r.bits)) | ||
| Base.:(==)(l::BacktrackRegister,r::BacktrackRegister) = l.inv_circuit==r.inv_circuit && l.bits==r.bits | ||
| Base.hash(r::BacktrackRegister, h::UInt) = hash(r.inv_circuit, hash(r.bits, h)) | ||
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| nqubits(r::BacktrackRegister) = nqubits(r.inv_circuit) | ||
| bitview(r::BacktrackRegister) = r.bits | ||
| quantumstate(r::BacktrackRegister) = apply_inv!(one(Stabilizer, nqubits(r)), r.inv_circuit) | ||
| tab(r::BacktrackRegister) = tab(r.inv_circuit) | ||
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| tensor(regs::BacktrackRegister...) = BacktrackRegister(tensor([r.inv_circuit for r in regs]), [bit for r in regs for bit in r.bits]) | ||
| # tensor(args::AbstractQCState...) = tensor(BacktrackRegister.(args)...) | ||
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| function apply!(r::BacktrackRegister, op, args...; kwargs...) | ||
| apply_right!(r.inv_circuit, op, args...; kwargs...) | ||
| r | ||
| end | ||
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| function apply!(r::BacktrackRegister, m::sMX) | ||
| _, res = projectXrand!(r,m.qubit) | ||
| m.bit!=0 && (bitview(r)[m.bit] = !iszero(res)) | ||
| r | ||
| end | ||
| function apply!(r::BacktrackRegister, m::sMY) | ||
| _, res = projectYrand!(r,m.qubit) | ||
| m.bit!=0 && (bitview(r)[m.bit] = !iszero(res)) | ||
| r | ||
| end | ||
| function apply!(r::BacktrackRegister, m::sMZ) | ||
| _, res = projectZrand!(r,m.qubit) | ||
| m.bit!=0 && (bitview(r)[m.bit] = !iszero(res)) | ||
| r | ||
| end | ||
| function apply!(r::BacktrackRegister, m::sMRX) | ||
| _, res = projectXrand!(r,m.qubit) | ||
| m.bit!=0 && (bitview(r)[m.bit] = !iszero(res)) | ||
| phases(tab(r))[m.qubit] = 0x00 | ||
| phases(tab(r))[nqubits(r)+m.qubit] = 0x00 | ||
| r | ||
| end | ||
| function apply!(r::BacktrackRegister, m::sMRY) | ||
| _, res = projectYrand!(r,m.qubit) | ||
| m.bit!=0 && (bitview(r)[m.bit] = !iszero(res)) | ||
| if iszero(res) | ||
| phases(tab(r))[nqubits(r)+m.qubit] ⊻= 0x02 | ||
| end | ||
| r | ||
| end | ||
| function apply!(r::BacktrackRegister, m::sMRZ) | ||
| _, res = projectZrand!(r,m.qubit) | ||
| m.bit!=0 && (bitview(r)[m.bit] = !iszero(res)) | ||
| phases(tab(r))[m.qubit] = 0x00 | ||
| phases(tab(r))[nqubits(r)+m.qubit] ⊻= 0x02 | ||
| r | ||
| end | ||
| function apply!(r::BacktrackRegister, m::PauliMeasurement) | ||
| _, res = projectrand!(r,m.pauli) | ||
| m.bit!=0 && (bitview(r)[m.bit] = !iszero(res)) | ||
| r | ||
| end | ||
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| function projectXrand!(r::BacktrackRegister, m) | ||
| if all(getxrow(tab(r), m) .== 0) | ||
| return r, phases(tab(r))[m] | ||
| end | ||
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| apply!(r, sHadamard(m)) | ||
| collapse_z!(r.inv_circuit, m) | ||
| apply!(r, sHadamard(m)) | ||
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| r, phases(tab(r))[m] | ||
| end | ||
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| function projectYrand!(r::BacktrackRegister, m) | ||
| if all(getxrow(tab(r), m) .== getxrow(tab(r), nqubits(r)+m)) | ||
| return r, eval_y_obs(r.inv_circuit, m).phase[] | ||
| end | ||
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| apply!(r, sHadamardYZ(m)) | ||
| collapse_z!(r.inv_circuit, m) | ||
| apply!(r, sHadamardYZ(m)) | ||
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| r, eval_y_obs(r.inv_circuit, m).phase[] | ||
| end | ||
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| function projectZrand!(r::BacktrackRegister, m) | ||
| if all(getxrow(tab(r), nqubits(r)+m) .== 0) | ||
| return r, phases(tab(r))[nqubits(r)+m] | ||
| end | ||
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| collapse_z!(r.inv_circuit, m) | ||
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| r, phases(tab(r))[nqubits(r)+m] | ||
| end | ||
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| function projectrand!(r::BacktrackRegister, pauli) | ||
| if all(iszero.(pauli.xz)) | ||
| return pauli.phase[] & 0x02 | ||
| end | ||
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| h_xz = [] | ||
| h_yz = [] | ||
| cnot = [] | ||
| meas = 0 | ||
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| for q in nqubits(pauli) | ||
| x, z = pauli[q] | ||
| if x | ||
| if z | ||
| push!(h_yz, q) | ||
| else | ||
| push!(h_xz, q) | ||
| end | ||
| end | ||
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| if iszero(meas) | ||
| meas = q | ||
| else | ||
| push!(cnot, q) | ||
| end | ||
| end | ||
| @assert meas > 0 | ||
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| for q in h_xz | ||
| apply!(r, sHadamard(q)) | ||
| end | ||
| for q in h_yz | ||
| apply!(r, sHadamardYZ(q)) | ||
| end | ||
| for q1 in cnot | ||
| apply!(r, sCNOT(q1, meas)) | ||
| end | ||
| _, res = projectZrand!(r, meas) | ||
| for q1 in reverse(cnot) | ||
| apply!(r, sCNOT(q1, meas)) | ||
| end | ||
| for q in reverse(h_yz) | ||
| apply!(r, sHadamardYZ(q)) | ||
| end | ||
| for q in reverse(h_xz) | ||
| apply!(r, sHadamard(q)) | ||
| end | ||
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| r, res | ||
| end | ||
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| # function traceout!(r::BacktrackRegister, arg) | ||
| # TODO | ||
| # end | ||
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| # function applybranches(r::BacktrackRegister, op) | ||
| # TODO | ||
| # end | ||
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| function eval_y_obs(c::CliffordOperator, q::Int) | ||
| result = c[q] | ||
| @assert result.phase[] & 0x01 == 0 | ||
| og_result_sign = result.phase[] | ||
| mul_right!(result, c[nqubits(c)+q]; phases=Val(true)) | ||
| log_i = result.phase[] + 1 | ||
| @assert log_i & 0x01 == 0 | ||
| if log_i & 2 != 0 | ||
| og_result_sign ⊻= 0x02 | ||
| end | ||
| result.phase[] = og_result_sign | ||
| return result | ||
| end | ||
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| function collapse_z!(c::CliffordOperator, q::Int) | ||
| n = nqubits(c) | ||
| t = tab(c) | ||
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| # Search for any stabilizer generator that anti-commutes with the measurement observable. | ||
| pivot = 1 | ||
| while pivot <= n && getxbit(t, n+q, pivot) == 0 | ||
| pivot += 1 | ||
| end | ||
| if pivot >= n+1 | ||
| # No anti-commuting stabilizer generator. Measurement is deterministic. | ||
| return -1 | ||
| end | ||
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| # Perform partial Gaussian elimination over the stabilizer generators that anti-commute with the measurement. | ||
| # Do this by introducing no-effect-because-control-is-zero CNOTs at the beginning of time. | ||
| for k in pivot+1:n | ||
| if getxbit(t, n+q, k) > 0 | ||
| apply!(c, sCNOT(pivot, k); phases=true) | ||
| end | ||
| end | ||
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| # Swap the now-isolated anti-commuting stabilizer generator for one that commutes with the measurement. | ||
| if getzbit(t, n+q, pivot) == 0 | ||
| apply!(c, sHadamard(pivot); phases=true) | ||
| else | ||
| apply!(c, sHadamardYZ(pivot); phases=true) | ||
| end | ||
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| # Assign a measurement result. | ||
| if rand(Bool) | ||
| apply!(c, sX(pivot); phases=true) | ||
| end | ||
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| return pivot | ||
| end | ||
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| @inline getxrow(s::Tableau, r::Int) = s.xzs[1:2:end, r] | ||
| @inline getzrow(s::Tableau, r::Int) = s.xzs[2:2:end, r] | ||
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There was a problem hiding this comment. is there elsewhere in the codebase that functions like this are defined, maybe in the linalg file or somewhere near where Tableau is defined -- just double check that there is no better place to put them |
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double check that the recent 0.19 does not break this