Examples

1// Bell pair: the two measurements always agree.2program bell3qubits a, b4bits m0, m15​6h a7cx a, b8measure a -> m09measure b -> m1

1// GHZ state on four qubits: all bits read 0000 or 1111.2program ghz3qubits q[4]4bits m[4]5​6h q[0]7cx q[0], q[1]8cx q[1], q[2]9cx q[2], q[3]10repeat i in 0..4 {11  measure q[i] -> m[i]12}

1// Teleportation: the state ry(pi / 3)|0> moves from msg to bob,2// using two measurements and real-time corrections.3program teleport4qubits msg, alice, bob5bits m0, m1, out6​7ry(pi / 3) msg8​9// Shared Bell pair between alice and bob.10h alice11cx alice, bob12​13// Bell measurement on msg and alice.14cx msg, alice15h msg16measure msg -> m017measure alice -> m118​19// Corrections decided at run time.20if m1 {21  x bob22}23if m0 {24  z bob25}26measure bob -> out

1// Superdense coding: two classical bits travel on one qubit.2// Alice applies z to set b0 and x to set b1; here she sends b0 = 0, b1 = 1.3program superdense4qubits alice, bob5bits b0, b16​7h alice8cx alice, bob9​10// Encode b1 = 1 with x. A z here would also set b0.11x alice12​13cx alice, bob14h alice15measure alice -> b016measure bob -> b1

1// Deutsch-Jozsa with a balanced oracle f(x) = x0 xor x1 xor x2.2// A constant oracle reads 000; this one never does.3program deutsch_jozsa4qubits x[3], y5bits m[3]6​7x y8h y9repeat i in 0..3 {10  h x[i]11}12​13// Oracle: y ^= f(x).14repeat i in 0..3 {15  cx x[i], y16}17​18repeat i in 0..3 {19  h x[i]20  measure x[i] -> m[i]21}

1// Bernstein-Vazirani: recover the hidden string s = 101 in one query.2program bernstein_vazirani3qubits x[3], y4bits m[3]5​6x y7h y8repeat i in 0..3 {9  h x[i]10}11​12// Oracle for s = 101: y ^= x0 xor x2.13cx x[0], y14cx x[2], y15​16repeat i in 0..3 {17  h x[i]18  measure x[i] -> m[i]19}

1// Grover search on two qubits for the marked state 11.2// One iteration finds it with certainty.3program grover4qubits a, b5bits ma, mb6​7routine diffusion(p, q) {8  within {9    h p10    h q11    x p12    x q13  } do {14    cz p, q15  }16}17​18h a19h b20​21// Oracle: phase flip on 11.22cz a, b23​24call diffusion(a, b)25measure a -> ma26measure b -> mb

1// Phase estimation of the T gate (phase 1/8) with three counting qubits.2// The counting register reads 001 (read backwards: 0.001 in binary = 1/8).3program phase_estimation4qubits c[3], target5bits m[3]6​7x target8repeat i in 0..3 {9  h c[i]10}11​12// Controlled T^(2^k): c[0] applies T once, c[1] twice, c[2] four times.13cp(pi / 4) c[0], target14cp(pi / 2) c[1], target15cp(pi) c[2], target16​17// Inverse QFT on the counting register.18swap c[0], c[2]19h c[0]20cp(-pi / 2) c[1], c[0]21h c[1]22cp(-pi / 4) c[2], c[0]23cp(-pi / 2) c[2], c[1]24h c[2]25​26repeat i in 0..3 {27  measure c[i] -> m[i]28}

1// Repeat until success: try again until the ancilla reads 1, at most 16 times,2// counting the attempts, then act on the count.3program repeat_until_success4qubits a, anc5bits m6uint8 attempts7​8while !m budget 16 {9  h anc10  measure anc -> m11  reset anc12  attempts = attempts + 113}14​15match attempts {16  1 => { x a }17  2, 3 => { z a }18  _ => { h a }19}

1// Quantum Fourier transform on three qubits, applied to the basis state 101.2program qft3qubits q[3]4bits m[3]5​6routine qft3(a, b, c) {7  h a8  cp(pi / 2) b, a9  cp(pi / 4) c, a10  h b11  cp(pi / 2) c, b12  h c13  swap a, c14}15​16x q[0]17x q[2]18call qft3(q[0], q[1], q[2])19repeat i in 0..3 {20  measure q[i] -> m[i]21}

1// Parity checks with one reused ancilla: each check allocates a fresh2// qubit, measures it and releases it with a reset, so the peak is the data3// qubits plus one, not plus two.4program parity_ancilla5qubits d[3]6bits syndrome[2]7​8x d[1]9​10alloc anc11cx d[0], anc12cx d[1], anc13measure anc -> syndrome[0]14release anc reset15​16alloc anc17cx d[1], anc18cx d[2], anc19measure anc -> syndrome[1]20release anc reset

1# Quantum Fourier transform on N qubits, for any N of 2 or more.2# The controlled phase between qubits i and j is pi / 2^(j - i).3program qft4const N = 45const HALF = N >> 16qubit q[N]7bit m[N]8​9x q[0]10for i = 0 to N - 211  h q[i]12  for j = i + 1 to N - 113    cp(pi / (1 << (j - i))) q[j], q[i]14  next15next16h q[N - 1]17for i = 0 to HALF - 118  swap q[i], q[N - 1 - i]19next20for i = 0 to N - 121  measure q[i] into m[i]22next

1# Three-qubit bit-flip code: encode, inject one error, measure the two2# parities with a reused ancilla, and correct from the syndrome.3program repetition_code4qubit d[3]5bit s[2], out[3]6uint8 syndrome = 07​8# Encode |1> as |111>.9x d[0]10cx d[0], d[1]11cx d[0], d[2]12​13# The error: a flip on the middle qubit.14x d[1]15​16for i = 0 to 117  alloc anc18  cx d[i], anc19  cx d[i + 1], anc20  measure anc into s[i]21  free anc reset22next23​24if s[0] then25  let syndrome = syndrome + 126end27if s[1] then28  let syndrome = syndrome + 229end30​31select syndrome32  case 1:33    x d[0]34  case 3:35    x d[1]36  case 2:37    x d[2]38end39​40for i = 0 to 241  measure d[i] into out[i]42next

1# Two independent preparations written as tasks. The checker proves they2# share no qubit and no variable, so the reported depth overlaps them.3program parallel_preparation4qubit a[2], b[2]5bit ma[2], mb[2]6​7parallel8  task bell_a9    h a[0]10    cx a[0], a[1]11  end12  task bell_b13    h b[0]14    cx b[0], b[1]15  end16end17​18for i = 0 to 119  measure a[i] into ma[i]20  measure b[i] into mb[i]21next

1# GHZ state on N qubits. Change N and nothing else.2program ghz3const N = 54qubit q[N]5bit m[N]6​7h q[0]8for i = 0 to N - 29  cx q[i], q[i + 1]10next11for i = 0 to N - 112  measure q[i] into m[i]13next

1# Bernstein-Vazirani on N bits: the oracle adds every bit of x where the2# hidden string s has a 1. Here s = 1011, read as q[0] q[1] q[2] q[3].3program bernstein_vazirani4const N = 45qubit x[N], y6bit m[N]7​8x y9h y10for i = 0 to N - 111  h x[i]12next13​14cx x[0], y15cx x[2], y16cx x[3], y17​18for i = 0 to N - 119  h x[i]20  measure x[i] into m[i]21next

1# Grover search on three qubits for the marked state 111.2# Two iterations find it with probability about 0.95.3program grover4const N = 35const ROUNDS = 26qubit q[N]7bit m[N]8​9sub diffusion(a, b, c)10  compute11    h a12    h b13    h c14    x a15    x b16    x c17  do18    ccz a, b, c19  end20end21​22for i = 0 to N - 123  h q[i]24next25for r = 1 to ROUNDS26  ccz q[0], q[1], q[2]27  call diffusion(q[0], q[1], q[2])28next29for i = 0 to N - 130  measure q[i] into m[i]31next

1# Repeat until success in L2: run the body, then try again until the2# measurement reads 1, at most eight times in total.3program repeat_until_success4qubit a, anc5bit m6uint8 tries = 07​8repeat9  h anc10  measure anc into m11  reset anc12  let tries = tries + 113until m limit 814​15if m and tries <= 2 then16  x a17end

1// Grover search with the oracle passed as an object. Any class that2// implements Oracle can be searched for; dispatch is resolved at compile time.3​4interface Oracle { def mark(a: qubit, b: qubit) }5​6// Marks 11.7class MarkEleven implements Oracle {8  public def mark(a: qubit, b: qubit) { cz a, b }9}10​11// Marks 01 (a = 0, b = 1).12class MarkZeroOne implements Oracle {13  public def mark(a: qubit, b: qubit) {14    within {15      x a16    } do {17      cz a, b18    }19  }20}21​22class Search(oracle: Oracle) {23  public qubit a24  public qubit b25  public bit ma26  public bit mb27​28  def diffuse() {29    within {30      h a31      h b32      x a33      x b34    } do {35      cz a, b36    }37  }38​39  public def run() {40    h a41    h b42    oracle.mark(a, b)43    diffuse()44    measure a -> ma45    measure b -> mb46  }47}48​49main {50  MarkZeroOne target51  Search search(target)52  search.run()53}

1// A quantum register class with a Fourier transform and its inverse,2// sized at compile time. Applying qft then iqft returns the input.3​4class Register(n: int) {5  public qubit q[n]6  public bit m[n]7​8  public def load_one(k: int) { x q[k] }9​10  public def qft() {11    for i in 0..n {12      h q[i]13      for j in i + 1..n {14        cp(pi / (1 << (j - i))) q[j], q[i]15      }16    }17  }18​19  public def iqft() {20    inverse {21      self.qft()22    }23  }24​25  public def read() {26    for i in 0..n {27      measure q[i] -> m[i]28    }29  }30}31​32main {33  Register r(3)34  r.load_one(1)35  r.qft()36  r.iqft()37  r.read()38}

1// A three-qubit bit-flip code as a class hierarchy: a base code that2// encodes and decodes, and a subclass that adds a deliberate error.3​4class BitFlipCode {5  public qubit d[3]6  public bit s07  public bit s18  public bit out[3]9​10  public def encode() {11    cx d[0], d[1]12    cx d[0], d[2]13  }14​15  def error() { }16​17  public def correct() {18    qubit anc19    cx d[0], anc20    cx d[1], anc21    measure anc -> s022    reset anc23    cx d[1], anc24    cx d[2], anc25    measure anc -> s126    reset anc27    if s0 {28      if s1 { x d[1] } else { x d[0] }29    } else {30      if s1 { x d[2] }31    }32  }33​34  public def run() {35    x d[0]36    encode()37    error()38    correct()39    for i in 0..3 {40      measure d[i] -> out[i]41    }42  }43}44​45class NoisyChannel extends BitFlipCode {46  override def error() { x d[2] }47}48​49main {50  NoisyChannel channel51  channel.run()52}

1# A Rabi point: one Gaussian drive pulse on qubit 0, then a readout.2# Sweep amp across programs to trace the Rabi oscillation.3pulse rabi4dt 0.5 ns5bits 16port d0 drive qubits 07port m0 measure qubits 08frame drive on d0 freq 5.1 GHz9frame read on m0 freq 7.2 GHz10waveform pi_half gaussian duration 40 ns amp 0.25 sigma 10 ns11waveform tone constant duration 1 us amp 0.112play pi_half on drive13barrier14play tone on read15capture read 1 us -> 0

1# Ramsey: two half-pi pulses separated by a free evolution delay,2# with a virtual phase advance on the second pulse.3pulse ramsey4dt 1 ns5bits 16port d0 drive qubits 07port m0 measure qubits 08frame drive on d0 freq 5.1 GHz9frame read on m0 freq 7.2 GHz10waveform half gaussian duration 32 ns amp 0.25 sigma 8 ns11play half on drive12delay 200 ns on drive13shift_phase drive pi/214play half on drive15barrier16capture read 2 us -> 0

1# Hahn echo: half-pi, wait, pi, wait, half-pi. The pi pulse is a2# Blackman window at twice the amplitude.3pulse echo4dt 1 ns5bits 16port d0 drive qubits 07port m0 measure qubits 08frame drive on d0 freq 5.1 GHz9frame read on m0 freq 7.2 GHz10waveform half blackman duration 40 ns amp 0.211waveform full blackman duration 40 ns amp 0.412play half on drive13delay 500 ns on drive14play full on drive15delay 500 ns on drive16play half on drive17barrier18capture read 2 us -> 0